How does ice melt when immersed in water? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern) 2019 Moderator Election Q&A - Question CollectionDensity of ice < water?Ice cube left in water at 0 °C for a thousand yearsWhat happens when ice melts?Does an ice cube change its core temperature as it melts?How cold does this ice have to be to freeze this water bottle solid?How much energy is released by decompressing water?Is there a melting analogy for evaporative coolingIce melts slower in salt water?Ice cube in a thermally isolated system … Will any of it melt?Why does ice form when you break the seal on a very cold bottle of water?Density of ice < water?

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How does ice melt when immersed in water?



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)
2019 Moderator Election Q&A - Question CollectionDensity of ice < water?Ice cube left in water at 0 °C for a thousand yearsWhat happens when ice melts?Does an ice cube change its core temperature as it melts?How cold does this ice have to be to freeze this water bottle solid?How much energy is released by decompressing water?Is there a melting analogy for evaporative coolingIce melts slower in salt water?Ice cube in a thermally isolated system … Will any of it melt?Why does ice form when you break the seal on a very cold bottle of water?Density of ice < water?










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When an ice cube is immersed in water at a room temperature, how is the thermal energy from the water transferred to the ice cube?



Currently I have two answers:



  • Infrared radiation from the water transfers thermal energy to the ice cube, which increases the ice cube particles KE store, breaking the intermolecular bonds of the ice cube, melting it.


  • The Brownian motion of the water particles causes them to collide with the ice cube, transferring KE to the ice cubes particles, increasing temperature, breaking intermolecular bonds and melting it.






thermodynamics water phase-transition ice







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  • 1




    $begingroup$
    Natural convection.
    $endgroup$
    – Steeven
    Apr 13 at 13:14











  • $begingroup$
    Does this rule out the first answer I gave? because infra red is a wave and doesn’t transfer matter whereas natural convection does “Heat convection occurs when bulk flow of a fluid (gas or liquid) carries heat along with the flow of matter in the fluid.”~wiki
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 13:34






  • 1




    $begingroup$
    No no, it doesn't rule it out. Both are present at the same time, but radiation (following Stefan-Boltzmann's law) is very small at lower temperatures and becomes negligible in comparison to convection in a liquid.
    $endgroup$
    – Steeven
    Apr 13 at 13:35











  • $begingroup$
    When you say radiation, are you referring to infrared radiation? ~so to summarise, the heat transfer of water to ice is the combination of natural convection and thermal(including infrared) radiation? If so-does the transfer of KE by water particles colliding with the ice cube come into the picture at all?
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 13:44










  • $begingroup$
    Water and ice are opaque (black) for thermal infrared. They are also at the same temperature, so radiating equally.
    $endgroup$
    – Pieter
    Apr 13 at 21:24
















6












$begingroup$


When an ice cube is immersed in water at a room temperature, how is the thermal energy from the water transferred to the ice cube?



Currently I have two answers:



  • Infrared radiation from the water transfers thermal energy to the ice cube, which increases the ice cube particles KE store, breaking the intermolecular bonds of the ice cube, melting it.


  • The Brownian motion of the water particles causes them to collide with the ice cube, transferring KE to the ice cubes particles, increasing temperature, breaking intermolecular bonds and melting it.






thermodynamics water phase-transition ice







share|cite|improve this question









New contributor




Ubaid Hassan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$







  • 1




    $begingroup$
    Natural convection.
    $endgroup$
    – Steeven
    Apr 13 at 13:14











  • $begingroup$
    Does this rule out the first answer I gave? because infra red is a wave and doesn’t transfer matter whereas natural convection does “Heat convection occurs when bulk flow of a fluid (gas or liquid) carries heat along with the flow of matter in the fluid.”~wiki
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 13:34






  • 1




    $begingroup$
    No no, it doesn't rule it out. Both are present at the same time, but radiation (following Stefan-Boltzmann's law) is very small at lower temperatures and becomes negligible in comparison to convection in a liquid.
    $endgroup$
    – Steeven
    Apr 13 at 13:35











  • $begingroup$
    When you say radiation, are you referring to infrared radiation? ~so to summarise, the heat transfer of water to ice is the combination of natural convection and thermal(including infrared) radiation? If so-does the transfer of KE by water particles colliding with the ice cube come into the picture at all?
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 13:44










  • $begingroup$
    Water and ice are opaque (black) for thermal infrared. They are also at the same temperature, so radiating equally.
    $endgroup$
    – Pieter
    Apr 13 at 21:24














6












6








6


1



$begingroup$


When an ice cube is immersed in water at a room temperature, how is the thermal energy from the water transferred to the ice cube?



Currently I have two answers:



  • Infrared radiation from the water transfers thermal energy to the ice cube, which increases the ice cube particles KE store, breaking the intermolecular bonds of the ice cube, melting it.


  • The Brownian motion of the water particles causes them to collide with the ice cube, transferring KE to the ice cubes particles, increasing temperature, breaking intermolecular bonds and melting it.






thermodynamics water phase-transition ice







share|cite|improve this question









New contributor




Ubaid Hassan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




When an ice cube is immersed in water at a room temperature, how is the thermal energy from the water transferred to the ice cube?



Currently I have two answers:



  • Infrared radiation from the water transfers thermal energy to the ice cube, which increases the ice cube particles KE store, breaking the intermolecular bonds of the ice cube, melting it.


  • The Brownian motion of the water particles causes them to collide with the ice cube, transferring KE to the ice cubes particles, increasing temperature, breaking intermolecular bonds and melting it.






thermodynamics water phase-transition ice




thermodynamics water phase-transition ice






share|cite|improve this question









New contributor




Ubaid Hassan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




Ubaid Hassan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited Apr 14 at 1:21









Qmechanic♦

108k122001247




108k122001247






New contributor




Ubaid Hassan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked Apr 13 at 13:08









Ubaid HassanUbaid Hassan

38014




38014




New contributor




Ubaid Hassan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor





Ubaid Hassan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Ubaid Hassan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







  • 1




    $begingroup$
    Natural convection.
    $endgroup$
    – Steeven
    Apr 13 at 13:14











  • $begingroup$
    Does this rule out the first answer I gave? because infra red is a wave and doesn’t transfer matter whereas natural convection does “Heat convection occurs when bulk flow of a fluid (gas or liquid) carries heat along with the flow of matter in the fluid.”~wiki
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 13:34






  • 1




    $begingroup$
    No no, it doesn't rule it out. Both are present at the same time, but radiation (following Stefan-Boltzmann's law) is very small at lower temperatures and becomes negligible in comparison to convection in a liquid.
    $endgroup$
    – Steeven
    Apr 13 at 13:35











  • $begingroup$
    When you say radiation, are you referring to infrared radiation? ~so to summarise, the heat transfer of water to ice is the combination of natural convection and thermal(including infrared) radiation? If so-does the transfer of KE by water particles colliding with the ice cube come into the picture at all?
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 13:44










  • $begingroup$
    Water and ice are opaque (black) for thermal infrared. They are also at the same temperature, so radiating equally.
    $endgroup$
    – Pieter
    Apr 13 at 21:24













  • 1




    $begingroup$
    Natural convection.
    $endgroup$
    – Steeven
    Apr 13 at 13:14











  • $begingroup$
    Does this rule out the first answer I gave? because infra red is a wave and doesn’t transfer matter whereas natural convection does “Heat convection occurs when bulk flow of a fluid (gas or liquid) carries heat along with the flow of matter in the fluid.”~wiki
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 13:34






  • 1




    $begingroup$
    No no, it doesn't rule it out. Both are present at the same time, but radiation (following Stefan-Boltzmann's law) is very small at lower temperatures and becomes negligible in comparison to convection in a liquid.
    $endgroup$
    – Steeven
    Apr 13 at 13:35











  • $begingroup$
    When you say radiation, are you referring to infrared radiation? ~so to summarise, the heat transfer of water to ice is the combination of natural convection and thermal(including infrared) radiation? If so-does the transfer of KE by water particles colliding with the ice cube come into the picture at all?
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 13:44










  • $begingroup$
    Water and ice are opaque (black) for thermal infrared. They are also at the same temperature, so radiating equally.
    $endgroup$
    – Pieter
    Apr 13 at 21:24








1




1




$begingroup$
Natural convection.
$endgroup$
– Steeven
Apr 13 at 13:14





$begingroup$
Natural convection.
$endgroup$
– Steeven
Apr 13 at 13:14













$begingroup$
Does this rule out the first answer I gave? because infra red is a wave and doesn’t transfer matter whereas natural convection does “Heat convection occurs when bulk flow of a fluid (gas or liquid) carries heat along with the flow of matter in the fluid.”~wiki
$endgroup$
– Ubaid Hassan
Apr 13 at 13:34




$begingroup$
Does this rule out the first answer I gave? because infra red is a wave and doesn’t transfer matter whereas natural convection does “Heat convection occurs when bulk flow of a fluid (gas or liquid) carries heat along with the flow of matter in the fluid.”~wiki
$endgroup$
– Ubaid Hassan
Apr 13 at 13:34




1




1




$begingroup$
No no, it doesn't rule it out. Both are present at the same time, but radiation (following Stefan-Boltzmann's law) is very small at lower temperatures and becomes negligible in comparison to convection in a liquid.
$endgroup$
– Steeven
Apr 13 at 13:35





$begingroup$
No no, it doesn't rule it out. Both are present at the same time, but radiation (following Stefan-Boltzmann's law) is very small at lower temperatures and becomes negligible in comparison to convection in a liquid.
$endgroup$
– Steeven
Apr 13 at 13:35













$begingroup$
When you say radiation, are you referring to infrared radiation? ~so to summarise, the heat transfer of water to ice is the combination of natural convection and thermal(including infrared) radiation? If so-does the transfer of KE by water particles colliding with the ice cube come into the picture at all?
$endgroup$
– Ubaid Hassan
Apr 13 at 13:44




$begingroup$
When you say radiation, are you referring to infrared radiation? ~so to summarise, the heat transfer of water to ice is the combination of natural convection and thermal(including infrared) radiation? If so-does the transfer of KE by water particles colliding with the ice cube come into the picture at all?
$endgroup$
– Ubaid Hassan
Apr 13 at 13:44












$begingroup$
Water and ice are opaque (black) for thermal infrared. They are also at the same temperature, so radiating equally.
$endgroup$
– Pieter
Apr 13 at 21:24





$begingroup$
Water and ice are opaque (black) for thermal infrared. They are also at the same temperature, so radiating equally.
$endgroup$
– Pieter
Apr 13 at 21:24











4 Answers
4






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Energy transfer methods



In general, there exist three heat transfer mechanisms:



  • Thermal radiation transfers heat across a distance. More accurately, it is the transfer of wavelengths on the spectrum of light that when absorbed by the body is converted into heat). It follows Stefan-Boltzmann's law: $$dot q_textrad=varepsilonsigma_sA(T_1^4-T_2^4)$$ ($dot q$ is energy per second transferred from body 1 to body 2, $T$ temperature, $varepsilon$ emissivity, $sigma$ the Stefan-Boltzmann constant, $A$ the radiating surface area.)


  • Thermal conduction transfers heat through a solid. It is defined for a continuum, a solid material, but can be thought of as heat passed on between neighbour particles. It follows Fourier's law: $$dot q_textcond=AkappafracDelta TDelta x$$ ($A$ is area through which the heat flows, $kappa$ thermal conductivity, $Delta T$ temperature difference between two points, $Delta x$ distance between those two points over which the heat is tranferred.)


When you mention Brownian motion, it is relevant here with conduction: The random motion of particles, electrons etc. cause them to "bump into" and interact with neighbour particles. If one particles is more energetic, at a collision between particles they will share some of the kinetic energy. This is how thermal energy is conductively transferred.




  • Thermal convection transfers heat to/from a body by flowing close to it and deliver/absorb thermal energy to/from the surface. In some sense, it can be thought of as conduction between a fluid particle and a surface particle, where the fluid particle right after is replaced with a new, fresh one. Delivery/absorption of thermal energy from a single fluid particle is negligible as it carries a very little amount of energy, but with constant replacement of particles with newer ones, the energy transferred accumulates and becomes significant. This fluid-in-motion-induced heating/cooling effect is termed convection. It follows the relationship: $$dot q_textconv=Ah(T_textfluid-T_textbody)$$ $A$ is area exposed to the fluid. $h$ is the heat transfer coefficient and it highly depends on the scenario (the fluid, the flow, the surface interaction etc). $h$ is often experimentally determined beforehand.

There are two types of thermal convection:



  • Natural convection caused purely by natural factors such as differences in temperature or density (the cooling water near the ice surface becomes denser and sinks, and is thus replaced by other warmer fluid molecules. In general, natural convection is the mechanism behind hot air rising and cold air falling and similar phenomena.)


  • Forced convection, which is fluid flow caused by non-natural mechanisms such as by a pump.


In your case we have natural convection: The water particles near the ice surface deliver heat to the ice and in turn cool down. These now "colder" water particles are denser or "heavier" and will sink. New, warmer particles will take their place, ready to deliver more energy to the ice surface and repeat the process.



Which is more dominant?



The above three energy transfer factors are all the possibilities there are to transport energy. They are generally considered on equal terms as three distinct mechanisms with each their own energy transfer models. But, as you can see, convection is basically a "flow-version" of conduction if we consider it microscopically.



  • For thin fluids (with low viscosity), the convective effect of effective heating/cooling due to fluid motion is dominant.

  • For very thick fluids (with very high viscosity), so thick that you might mistake them for solids, heat can flow from particle to particle in a conductive manner, and conduction is dominant.

  • For some-what thick fluids, we may see a mix of these factors. The higher the heat capacity (corresponding to lower $kappa$) of the fluid, the weaker is the conductive mechanism.

In your case with water that has a rather low $kappa$, we should be able to assume only a predominantly convective mechanism and no/negligible conduction over longer distances in the water. Thermal radiation could still be a factor as well, but at fairly low temperatures, radiation is low (note the power of 4 in the model) and possibly negligible. We end up with only convection (natural in your case) having a large influence in your case - in fluids, this is often the only effect that is relevant to consider, unless when sinking a glowing-hot metal into a very volatile liquid.



This analysis can be verified by looking up numbers, as some comments ask for, of water and ice for the different models as well by comparing with the viscosity. I will not do this in this answer, but it should be fairly easy to find online; other answers are giving some of such numbers to justify the conclusion.






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  • $begingroup$
    +100 if I could, but I have one final question. If thermal conduction is the transfer of heat “particle to particle” as you put it, then I assume you meant the transfer of KE between the particles. If so, the particles(and the bodies)must be touching so there should not be any “distance” between the “two points”. But this doesn’t fit the formula you gave where X =distance
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 14:42






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    @UbaidHassan Yes, at the atomic level, heat and temperature is nothing but kinetic "vibrational" energy. Thermal conduction is not really defined for particle-to-particle. Fourier's law is found emperically under the assumption of a continuous material, and thus under the assumption that there is enough material for particle-particle interactions to be indistinguishable and only for their overall collective effect to play a role. Of this reason you will never hear conduction described for atomic particles; which is why it doesn't make much sense in your scenario either.
    $endgroup$
    – Steeven
    Apr 13 at 14:54











  • $begingroup$
    Can you give an estimate about the ratio of infrared? It's certainly minor, but how minor? Single-digit percent?
    $endgroup$
    – Peter A. Schneider
    Apr 13 at 17:24






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    @PeterA.Schneider It should be much less than single digit percents. Consider the heat we get from the sun, at 6000K. If you have an object that's around 300K, that's 20 lower temperatures. Radiation is a 4th power effect, so that means the effects will be 20^4 less. That's 160,000 times less than the effect of the sun. The areas wont line up, obviously, so you'd have to do some conversions, but we're talking 5 orders of magnitude weaker than the sun. How long does it take the sun to melt an ice cube?
    $endgroup$
    – Cort Ammon
    Apr 14 at 3:23






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    @CortAmmon Thanks, this was the kind of estimate I had in mind -- I missed the 4th power in the Boltzmann equation.
    $endgroup$
    – Peter A. Schneider
    Apr 14 at 9:35


















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Thermal energy transfer is in the form of heat from the water to the ice cube by natural convection.



If the cube and water together form an isolated system (no heat transfer between them and their surroundings) the heat transfer will continue until all the ice is melted, or until the water temperature equals 0 C at which point any ice remaining will be in two phase thermal equilibrium with the water.



Hope this helps






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  • $begingroup$
    How do you know it's natural convection?
    $endgroup$
    – pentane
    Apr 13 at 21:25










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    @pentane There are two kinds of convection: forced and natural. Forced usually involves some kind of forced movement of the fluid over a surface. Say, by way of a fan, the wind, a pump for water, etc. Natural involves movement due to buoyancy, warm fluid rising over cool.
    $endgroup$
    – Bob D
    Apr 13 at 21:53










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    no I know what it is but how do you know an ice cube in a glass of water is convection. where's the flow?
    $endgroup$
    – pentane
    Apr 13 at 21:57



















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I am in complete disagreement with previous answers which consider convection as the main mechanism for heat transfer from liquid water to the ice cube.



Convection is an important and dominant mechanism to maintain the liquid layers close to the ice surface at higher temperature. Thus, its main role is to ensure that at the surface between liquid and solid a constant difference of temperature is maintained. However, as a mechanism to carry energy from the liquid into the solid, convection simply does not exist! Unless one would think of fluid streams penetrating into the solid, which is not the case.



Therefore we are left with conduction or radiation as possible ways to tranfer thermal energy from liquid water to the ice. A simple order-of-magnitude estimate, based on the formulae of the Stefan-Boltzmann's law and Fourier's law, taking into account the SI values of about $10^-7$ for $sigma_s$, of about $2$ for $kappa$ of ice, the values of the two temperatures and a value of $Delta x$ of the order of a few interatomic distances, shows that the radiation contribution is negligible.



An additional remark could be added on the microscopic description of the melting process.
It is a well established observation that pre-melting, i.e. the melting of a solid starting from the surface layers, instead of than from the bulk, is a phenomenon present even in the case of ice. This observation would exclude the possibility that the melting process in the present case could start in the bulk of the ice.






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  • $begingroup$
    So convection according to you is only the maintenance of a constant temperature of the liquid layers around the ice cube (in this case)? Then what actually is the mechanism of heat transfer to the ice cube from water?
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 21:44






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    I wrote it above. Thermal conduction prevails by orders of magnitude on radiation. That is the only relevant mechanism to transfer thermal energy across the liquid solid border. Convection cennot play a direct role by definition. It plays an indirect role, as I tryed to explain.
    $endgroup$
    – GiorgioP
    Apr 13 at 22:17







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    I have added an explicit statement at the beginning of the third paragraph. In the original post it was implicit since, after exclusion of convection, I was considering the relative role played by conduction and radiation.
    $endgroup$
    – GiorgioP
    Apr 13 at 22:29










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    To provide a counterpoint, convection exists in the same way the sound barrier exists. While, at the microscopic level, convection is merely conduction, the macroscopic fluid flow in convection makes it so much more effective at transfering heat that we have to use entirely different equations to model it. Likewise, gas molecules simply move according to the equations of motion at any speed. However, there's a key point where the momentum of the gas particles becomes substantially more anisotropic (starts to have a direction), and when that happens we see shock waves anda "sound barrier."
    $endgroup$
    – Cort Ammon
    Apr 14 at 16:48










  • $begingroup$
    While you are right that convection and the sound barrier do not exist in the most strict of technical senses, I just wanted to make sure somebody doesn't get the wrong idea from the words.
    $endgroup$
    – Cort Ammon
    Apr 14 at 16:49


















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Heat Transfer Modes



The three forms of heat transfer between a system and the surroundings are as follows:



Conduction



This is the transport of heat by particles exchanging their internal energy. It occurs by one of three modes -- molecular collisions (gases), collisions/vibrations (local in liquids and lattice in solids), and free electron transport (in conductors and semiconductors). Conduction requires (or sets up) a temperature gradient in the material that is transporting the heat.



Convection



This is the transport of heat content by the bulk motion of a fluid over an object. It occurs in one of two modes -- free or forced. In free convection, the fluid moves because it is subject to a buoyancy force. In forced convection, we push the fluid. Convection requires a temperature difference. Convection can be modeled using principles of conduction across a film between the fluid and the object.



Radiation



This is the transport of energy from an object as electromagnetic radiation. Radiation only requires that objects have a temperature.



The Melting Process



To melt, atoms in a solid must gain enough energy to leave their bonds in the solid. Fusion is endothermic.



The energy arrives as heat from the surroundings. It arrives by the motion of the hotter liquid water molecules hitting the colder solid. The energy difference between moving liquid molecules and static (vibrating) solid molecules is a temperature difference in internal energy coordinates. That temperature difference needs only be infinitesimal to support the flow of heat from hot to cold. Liquid water does not support free electrons (of course not!) nor does it support lattice vibrations (that is what is happening in the ice). So, the one mode of transport of heat is conduction by molecular collisions from liquid water to solid ice.



The energy as heat can arrive by convection flow. When the system is in a gravitational field, and when the liquid immediately around the ice might become colder than the bulk water, the colder water will be denser. It will start to flow downward by natural convection. Thus, natural convection can be a factor in the heat flow. When the ice is floating on the water (typical), the colder water below the ice will fall down in the warmer water below it. As an inverse case, when you could put the ice cube at the bottom of a container and have hot water above it, you will shut down the natural convection mode. Think also about a cold penny that sits inserted into an insulated floor with hot air above it. The penny will have no natural convection modes because the cold air that might form around it is already denser than the hot air above it. This same thought is behind the formation of cold and hot fronts with thunderstorms in weather patterns.



You did not say whether the tank was stirred. So we can ignore forced convection.



The ice is radiating from it. The hotter water is radiating to the ice. The net radiation flux is to the ice from the water.



Estimates of Magnitudes



The temperatures of the solid ice and liquid water control the net radiation flux. When the liquid is only infinitesimally above the ice in temperature, the net radiation flux is ... small. Add to this that both ice and water have emissivities well below unity and their emissivities are comparable. At the end, you can pretty much say radiation is ... to be neglected.



Natural convection, when it occurs, swamps conduction heat transfer (well, not literally of course). Presuming the ice is at the top allows for this. Saying the ice is surrounding by water and mixed with it will lower its contribution.



At the end, we have conduction. Those "hotter" liquid water molecules are colliding constantly with those "colder" solid ice molecules (hot and cold as measures of internal energy). The transfer of heat is occurring constantly. A reference graph showing the variations in conductivity is found at this link.



Remaining Clarification



In pure materials (water), fusion occurs at a constant temperature. Never, ever can you discuss fusion as a process where the solid becomes hotter. The solid ice in this case stays pinned at one temperature as it completely melts. Inversely, you might find that when you mistakenly think the ice gets hotter during melting, you will immediately have to shut down any and all net heat transfer from the surroundings (liquid) to the system (ice). It is the second law of thermodynamics at play.






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$endgroup$












  • $begingroup$
    Liquids have a physics much closer to that of solids than gases (it is enough to compare the difference of densities to acknowledge it). Describing transport of energy in a liquid in term of collision is as good or as bad as using the same explanation for conduction in solids.
    $endgroup$
    – GiorgioP
    Apr 14 at 17:13










  • $begingroup$
    No doubt about important differences at level of the numbers. My point was about modeling the atomic dynamics of a liquid as collisions. The term collision is physically justified whenever an important change of momentum is concentrated in a short time interval. This is not the case for liquids. Atomic dynamic in liquids is much more complicate than phonon dynamics but collective modes (the equivalet of phonons in a harmonic solid) are routinely used to describe it.
    $endgroup$
    – GiorgioP
    2 days ago










  • $begingroup$
    A reasonable one-particle description of the atomic dynamics in dense liquids is a kind of superposition between diffusion and the so called cage motion which is the analogous of atomic vibration in a solid. The key point motivating my comment is that neither diffusion nor cage vibrations can be reasonably modeled as simple collisions.
    $endgroup$
    – GiorgioP
    2 days ago










  • $begingroup$
    @GiorgioP Much appreciated. I've modified my description to account for your insights in a manner that keeps it simple without I distorting the truth I hope.
    $endgroup$
    – Jeffrey J Weimer
    2 days ago











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4 Answers
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active

oldest

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active

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active

oldest

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6












$begingroup$

Energy transfer methods



In general, there exist three heat transfer mechanisms:



  • Thermal radiation transfers heat across a distance. More accurately, it is the transfer of wavelengths on the spectrum of light that when absorbed by the body is converted into heat). It follows Stefan-Boltzmann's law: $$dot q_textrad=varepsilonsigma_sA(T_1^4-T_2^4)$$ ($dot q$ is energy per second transferred from body 1 to body 2, $T$ temperature, $varepsilon$ emissivity, $sigma$ the Stefan-Boltzmann constant, $A$ the radiating surface area.)


  • Thermal conduction transfers heat through a solid. It is defined for a continuum, a solid material, but can be thought of as heat passed on between neighbour particles. It follows Fourier's law: $$dot q_textcond=AkappafracDelta TDelta x$$ ($A$ is area through which the heat flows, $kappa$ thermal conductivity, $Delta T$ temperature difference between two points, $Delta x$ distance between those two points over which the heat is tranferred.)


When you mention Brownian motion, it is relevant here with conduction: The random motion of particles, electrons etc. cause them to "bump into" and interact with neighbour particles. If one particles is more energetic, at a collision between particles they will share some of the kinetic energy. This is how thermal energy is conductively transferred.




  • Thermal convection transfers heat to/from a body by flowing close to it and deliver/absorb thermal energy to/from the surface. In some sense, it can be thought of as conduction between a fluid particle and a surface particle, where the fluid particle right after is replaced with a new, fresh one. Delivery/absorption of thermal energy from a single fluid particle is negligible as it carries a very little amount of energy, but with constant replacement of particles with newer ones, the energy transferred accumulates and becomes significant. This fluid-in-motion-induced heating/cooling effect is termed convection. It follows the relationship: $$dot q_textconv=Ah(T_textfluid-T_textbody)$$ $A$ is area exposed to the fluid. $h$ is the heat transfer coefficient and it highly depends on the scenario (the fluid, the flow, the surface interaction etc). $h$ is often experimentally determined beforehand.

There are two types of thermal convection:



  • Natural convection caused purely by natural factors such as differences in temperature or density (the cooling water near the ice surface becomes denser and sinks, and is thus replaced by other warmer fluid molecules. In general, natural convection is the mechanism behind hot air rising and cold air falling and similar phenomena.)


  • Forced convection, which is fluid flow caused by non-natural mechanisms such as by a pump.


In your case we have natural convection: The water particles near the ice surface deliver heat to the ice and in turn cool down. These now "colder" water particles are denser or "heavier" and will sink. New, warmer particles will take their place, ready to deliver more energy to the ice surface and repeat the process.



Which is more dominant?



The above three energy transfer factors are all the possibilities there are to transport energy. They are generally considered on equal terms as three distinct mechanisms with each their own energy transfer models. But, as you can see, convection is basically a "flow-version" of conduction if we consider it microscopically.



  • For thin fluids (with low viscosity), the convective effect of effective heating/cooling due to fluid motion is dominant.

  • For very thick fluids (with very high viscosity), so thick that you might mistake them for solids, heat can flow from particle to particle in a conductive manner, and conduction is dominant.

  • For some-what thick fluids, we may see a mix of these factors. The higher the heat capacity (corresponding to lower $kappa$) of the fluid, the weaker is the conductive mechanism.

In your case with water that has a rather low $kappa$, we should be able to assume only a predominantly convective mechanism and no/negligible conduction over longer distances in the water. Thermal radiation could still be a factor as well, but at fairly low temperatures, radiation is low (note the power of 4 in the model) and possibly negligible. We end up with only convection (natural in your case) having a large influence in your case - in fluids, this is often the only effect that is relevant to consider, unless when sinking a glowing-hot metal into a very volatile liquid.



This analysis can be verified by looking up numbers, as some comments ask for, of water and ice for the different models as well by comparing with the viscosity. I will not do this in this answer, but it should be fairly easy to find online; other answers are giving some of such numbers to justify the conclusion.






share|cite|improve this answer











$endgroup$












  • $begingroup$
    +100 if I could, but I have one final question. If thermal conduction is the transfer of heat “particle to particle” as you put it, then I assume you meant the transfer of KE between the particles. If so, the particles(and the bodies)must be touching so there should not be any “distance” between the “two points”. But this doesn’t fit the formula you gave where X =distance
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 14:42






  • 1




    $begingroup$
    @UbaidHassan Yes, at the atomic level, heat and temperature is nothing but kinetic "vibrational" energy. Thermal conduction is not really defined for particle-to-particle. Fourier's law is found emperically under the assumption of a continuous material, and thus under the assumption that there is enough material for particle-particle interactions to be indistinguishable and only for their overall collective effect to play a role. Of this reason you will never hear conduction described for atomic particles; which is why it doesn't make much sense in your scenario either.
    $endgroup$
    – Steeven
    Apr 13 at 14:54











  • $begingroup$
    Can you give an estimate about the ratio of infrared? It's certainly minor, but how minor? Single-digit percent?
    $endgroup$
    – Peter A. Schneider
    Apr 13 at 17:24






  • 2




    $begingroup$
    @PeterA.Schneider It should be much less than single digit percents. Consider the heat we get from the sun, at 6000K. If you have an object that's around 300K, that's 20 lower temperatures. Radiation is a 4th power effect, so that means the effects will be 20^4 less. That's 160,000 times less than the effect of the sun. The areas wont line up, obviously, so you'd have to do some conversions, but we're talking 5 orders of magnitude weaker than the sun. How long does it take the sun to melt an ice cube?
    $endgroup$
    – Cort Ammon
    Apr 14 at 3:23






  • 1




    $begingroup$
    @CortAmmon Thanks, this was the kind of estimate I had in mind -- I missed the 4th power in the Boltzmann equation.
    $endgroup$
    – Peter A. Schneider
    Apr 14 at 9:35















6












$begingroup$

Energy transfer methods



In general, there exist three heat transfer mechanisms:



  • Thermal radiation transfers heat across a distance. More accurately, it is the transfer of wavelengths on the spectrum of light that when absorbed by the body is converted into heat). It follows Stefan-Boltzmann's law: $$dot q_textrad=varepsilonsigma_sA(T_1^4-T_2^4)$$ ($dot q$ is energy per second transferred from body 1 to body 2, $T$ temperature, $varepsilon$ emissivity, $sigma$ the Stefan-Boltzmann constant, $A$ the radiating surface area.)


  • Thermal conduction transfers heat through a solid. It is defined for a continuum, a solid material, but can be thought of as heat passed on between neighbour particles. It follows Fourier's law: $$dot q_textcond=AkappafracDelta TDelta x$$ ($A$ is area through which the heat flows, $kappa$ thermal conductivity, $Delta T$ temperature difference between two points, $Delta x$ distance between those two points over which the heat is tranferred.)


When you mention Brownian motion, it is relevant here with conduction: The random motion of particles, electrons etc. cause them to "bump into" and interact with neighbour particles. If one particles is more energetic, at a collision between particles they will share some of the kinetic energy. This is how thermal energy is conductively transferred.




  • Thermal convection transfers heat to/from a body by flowing close to it and deliver/absorb thermal energy to/from the surface. In some sense, it can be thought of as conduction between a fluid particle and a surface particle, where the fluid particle right after is replaced with a new, fresh one. Delivery/absorption of thermal energy from a single fluid particle is negligible as it carries a very little amount of energy, but with constant replacement of particles with newer ones, the energy transferred accumulates and becomes significant. This fluid-in-motion-induced heating/cooling effect is termed convection. It follows the relationship: $$dot q_textconv=Ah(T_textfluid-T_textbody)$$ $A$ is area exposed to the fluid. $h$ is the heat transfer coefficient and it highly depends on the scenario (the fluid, the flow, the surface interaction etc). $h$ is often experimentally determined beforehand.

There are two types of thermal convection:



  • Natural convection caused purely by natural factors such as differences in temperature or density (the cooling water near the ice surface becomes denser and sinks, and is thus replaced by other warmer fluid molecules. In general, natural convection is the mechanism behind hot air rising and cold air falling and similar phenomena.)


  • Forced convection, which is fluid flow caused by non-natural mechanisms such as by a pump.


In your case we have natural convection: The water particles near the ice surface deliver heat to the ice and in turn cool down. These now "colder" water particles are denser or "heavier" and will sink. New, warmer particles will take their place, ready to deliver more energy to the ice surface and repeat the process.



Which is more dominant?



The above three energy transfer factors are all the possibilities there are to transport energy. They are generally considered on equal terms as three distinct mechanisms with each their own energy transfer models. But, as you can see, convection is basically a "flow-version" of conduction if we consider it microscopically.



  • For thin fluids (with low viscosity), the convective effect of effective heating/cooling due to fluid motion is dominant.

  • For very thick fluids (with very high viscosity), so thick that you might mistake them for solids, heat can flow from particle to particle in a conductive manner, and conduction is dominant.

  • For some-what thick fluids, we may see a mix of these factors. The higher the heat capacity (corresponding to lower $kappa$) of the fluid, the weaker is the conductive mechanism.

In your case with water that has a rather low $kappa$, we should be able to assume only a predominantly convective mechanism and no/negligible conduction over longer distances in the water. Thermal radiation could still be a factor as well, but at fairly low temperatures, radiation is low (note the power of 4 in the model) and possibly negligible. We end up with only convection (natural in your case) having a large influence in your case - in fluids, this is often the only effect that is relevant to consider, unless when sinking a glowing-hot metal into a very volatile liquid.



This analysis can be verified by looking up numbers, as some comments ask for, of water and ice for the different models as well by comparing with the viscosity. I will not do this in this answer, but it should be fairly easy to find online; other answers are giving some of such numbers to justify the conclusion.






share|cite|improve this answer











$endgroup$












  • $begingroup$
    +100 if I could, but I have one final question. If thermal conduction is the transfer of heat “particle to particle” as you put it, then I assume you meant the transfer of KE between the particles. If so, the particles(and the bodies)must be touching so there should not be any “distance” between the “two points”. But this doesn’t fit the formula you gave where X =distance
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 14:42






  • 1




    $begingroup$
    @UbaidHassan Yes, at the atomic level, heat and temperature is nothing but kinetic "vibrational" energy. Thermal conduction is not really defined for particle-to-particle. Fourier's law is found emperically under the assumption of a continuous material, and thus under the assumption that there is enough material for particle-particle interactions to be indistinguishable and only for their overall collective effect to play a role. Of this reason you will never hear conduction described for atomic particles; which is why it doesn't make much sense in your scenario either.
    $endgroup$
    – Steeven
    Apr 13 at 14:54











  • $begingroup$
    Can you give an estimate about the ratio of infrared? It's certainly minor, but how minor? Single-digit percent?
    $endgroup$
    – Peter A. Schneider
    Apr 13 at 17:24






  • 2




    $begingroup$
    @PeterA.Schneider It should be much less than single digit percents. Consider the heat we get from the sun, at 6000K. If you have an object that's around 300K, that's 20 lower temperatures. Radiation is a 4th power effect, so that means the effects will be 20^4 less. That's 160,000 times less than the effect of the sun. The areas wont line up, obviously, so you'd have to do some conversions, but we're talking 5 orders of magnitude weaker than the sun. How long does it take the sun to melt an ice cube?
    $endgroup$
    – Cort Ammon
    Apr 14 at 3:23






  • 1




    $begingroup$
    @CortAmmon Thanks, this was the kind of estimate I had in mind -- I missed the 4th power in the Boltzmann equation.
    $endgroup$
    – Peter A. Schneider
    Apr 14 at 9:35













6












6








6





$begingroup$

Energy transfer methods



In general, there exist three heat transfer mechanisms:



  • Thermal radiation transfers heat across a distance. More accurately, it is the transfer of wavelengths on the spectrum of light that when absorbed by the body is converted into heat). It follows Stefan-Boltzmann's law: $$dot q_textrad=varepsilonsigma_sA(T_1^4-T_2^4)$$ ($dot q$ is energy per second transferred from body 1 to body 2, $T$ temperature, $varepsilon$ emissivity, $sigma$ the Stefan-Boltzmann constant, $A$ the radiating surface area.)


  • Thermal conduction transfers heat through a solid. It is defined for a continuum, a solid material, but can be thought of as heat passed on between neighbour particles. It follows Fourier's law: $$dot q_textcond=AkappafracDelta TDelta x$$ ($A$ is area through which the heat flows, $kappa$ thermal conductivity, $Delta T$ temperature difference between two points, $Delta x$ distance between those two points over which the heat is tranferred.)


When you mention Brownian motion, it is relevant here with conduction: The random motion of particles, electrons etc. cause them to "bump into" and interact with neighbour particles. If one particles is more energetic, at a collision between particles they will share some of the kinetic energy. This is how thermal energy is conductively transferred.




  • Thermal convection transfers heat to/from a body by flowing close to it and deliver/absorb thermal energy to/from the surface. In some sense, it can be thought of as conduction between a fluid particle and a surface particle, where the fluid particle right after is replaced with a new, fresh one. Delivery/absorption of thermal energy from a single fluid particle is negligible as it carries a very little amount of energy, but with constant replacement of particles with newer ones, the energy transferred accumulates and becomes significant. This fluid-in-motion-induced heating/cooling effect is termed convection. It follows the relationship: $$dot q_textconv=Ah(T_textfluid-T_textbody)$$ $A$ is area exposed to the fluid. $h$ is the heat transfer coefficient and it highly depends on the scenario (the fluid, the flow, the surface interaction etc). $h$ is often experimentally determined beforehand.

There are two types of thermal convection:



  • Natural convection caused purely by natural factors such as differences in temperature or density (the cooling water near the ice surface becomes denser and sinks, and is thus replaced by other warmer fluid molecules. In general, natural convection is the mechanism behind hot air rising and cold air falling and similar phenomena.)


  • Forced convection, which is fluid flow caused by non-natural mechanisms such as by a pump.


In your case we have natural convection: The water particles near the ice surface deliver heat to the ice and in turn cool down. These now "colder" water particles are denser or "heavier" and will sink. New, warmer particles will take their place, ready to deliver more energy to the ice surface and repeat the process.



Which is more dominant?



The above three energy transfer factors are all the possibilities there are to transport energy. They are generally considered on equal terms as three distinct mechanisms with each their own energy transfer models. But, as you can see, convection is basically a "flow-version" of conduction if we consider it microscopically.



  • For thin fluids (with low viscosity), the convective effect of effective heating/cooling due to fluid motion is dominant.

  • For very thick fluids (with very high viscosity), so thick that you might mistake them for solids, heat can flow from particle to particle in a conductive manner, and conduction is dominant.

  • For some-what thick fluids, we may see a mix of these factors. The higher the heat capacity (corresponding to lower $kappa$) of the fluid, the weaker is the conductive mechanism.

In your case with water that has a rather low $kappa$, we should be able to assume only a predominantly convective mechanism and no/negligible conduction over longer distances in the water. Thermal radiation could still be a factor as well, but at fairly low temperatures, radiation is low (note the power of 4 in the model) and possibly negligible. We end up with only convection (natural in your case) having a large influence in your case - in fluids, this is often the only effect that is relevant to consider, unless when sinking a glowing-hot metal into a very volatile liquid.



This analysis can be verified by looking up numbers, as some comments ask for, of water and ice for the different models as well by comparing with the viscosity. I will not do this in this answer, but it should be fairly easy to find online; other answers are giving some of such numbers to justify the conclusion.






share|cite|improve this answer











$endgroup$



Energy transfer methods



In general, there exist three heat transfer mechanisms:



  • Thermal radiation transfers heat across a distance. More accurately, it is the transfer of wavelengths on the spectrum of light that when absorbed by the body is converted into heat). It follows Stefan-Boltzmann's law: $$dot q_textrad=varepsilonsigma_sA(T_1^4-T_2^4)$$ ($dot q$ is energy per second transferred from body 1 to body 2, $T$ temperature, $varepsilon$ emissivity, $sigma$ the Stefan-Boltzmann constant, $A$ the radiating surface area.)


  • Thermal conduction transfers heat through a solid. It is defined for a continuum, a solid material, but can be thought of as heat passed on between neighbour particles. It follows Fourier's law: $$dot q_textcond=AkappafracDelta TDelta x$$ ($A$ is area through which the heat flows, $kappa$ thermal conductivity, $Delta T$ temperature difference between two points, $Delta x$ distance between those two points over which the heat is tranferred.)


When you mention Brownian motion, it is relevant here with conduction: The random motion of particles, electrons etc. cause them to "bump into" and interact with neighbour particles. If one particles is more energetic, at a collision between particles they will share some of the kinetic energy. This is how thermal energy is conductively transferred.




  • Thermal convection transfers heat to/from a body by flowing close to it and deliver/absorb thermal energy to/from the surface. In some sense, it can be thought of as conduction between a fluid particle and a surface particle, where the fluid particle right after is replaced with a new, fresh one. Delivery/absorption of thermal energy from a single fluid particle is negligible as it carries a very little amount of energy, but with constant replacement of particles with newer ones, the energy transferred accumulates and becomes significant. This fluid-in-motion-induced heating/cooling effect is termed convection. It follows the relationship: $$dot q_textconv=Ah(T_textfluid-T_textbody)$$ $A$ is area exposed to the fluid. $h$ is the heat transfer coefficient and it highly depends on the scenario (the fluid, the flow, the surface interaction etc). $h$ is often experimentally determined beforehand.

There are two types of thermal convection:



  • Natural convection caused purely by natural factors such as differences in temperature or density (the cooling water near the ice surface becomes denser and sinks, and is thus replaced by other warmer fluid molecules. In general, natural convection is the mechanism behind hot air rising and cold air falling and similar phenomena.)


  • Forced convection, which is fluid flow caused by non-natural mechanisms such as by a pump.


In your case we have natural convection: The water particles near the ice surface deliver heat to the ice and in turn cool down. These now "colder" water particles are denser or "heavier" and will sink. New, warmer particles will take their place, ready to deliver more energy to the ice surface and repeat the process.



Which is more dominant?



The above three energy transfer factors are all the possibilities there are to transport energy. They are generally considered on equal terms as three distinct mechanisms with each their own energy transfer models. But, as you can see, convection is basically a "flow-version" of conduction if we consider it microscopically.



  • For thin fluids (with low viscosity), the convective effect of effective heating/cooling due to fluid motion is dominant.

  • For very thick fluids (with very high viscosity), so thick that you might mistake them for solids, heat can flow from particle to particle in a conductive manner, and conduction is dominant.

  • For some-what thick fluids, we may see a mix of these factors. The higher the heat capacity (corresponding to lower $kappa$) of the fluid, the weaker is the conductive mechanism.

In your case with water that has a rather low $kappa$, we should be able to assume only a predominantly convective mechanism and no/negligible conduction over longer distances in the water. Thermal radiation could still be a factor as well, but at fairly low temperatures, radiation is low (note the power of 4 in the model) and possibly negligible. We end up with only convection (natural in your case) having a large influence in your case - in fluids, this is often the only effect that is relevant to consider, unless when sinking a glowing-hot metal into a very volatile liquid.



This analysis can be verified by looking up numbers, as some comments ask for, of water and ice for the different models as well by comparing with the viscosity. I will not do this in this answer, but it should be fairly easy to find online; other answers are giving some of such numbers to justify the conclusion.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 2 days ago

























answered Apr 13 at 14:04









SteevenSteeven

28k866113




28k866113











  • $begingroup$
    +100 if I could, but I have one final question. If thermal conduction is the transfer of heat “particle to particle” as you put it, then I assume you meant the transfer of KE between the particles. If so, the particles(and the bodies)must be touching so there should not be any “distance” between the “two points”. But this doesn’t fit the formula you gave where X =distance
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 14:42






  • 1




    $begingroup$
    @UbaidHassan Yes, at the atomic level, heat and temperature is nothing but kinetic "vibrational" energy. Thermal conduction is not really defined for particle-to-particle. Fourier's law is found emperically under the assumption of a continuous material, and thus under the assumption that there is enough material for particle-particle interactions to be indistinguishable and only for their overall collective effect to play a role. Of this reason you will never hear conduction described for atomic particles; which is why it doesn't make much sense in your scenario either.
    $endgroup$
    – Steeven
    Apr 13 at 14:54











  • $begingroup$
    Can you give an estimate about the ratio of infrared? It's certainly minor, but how minor? Single-digit percent?
    $endgroup$
    – Peter A. Schneider
    Apr 13 at 17:24






  • 2




    $begingroup$
    @PeterA.Schneider It should be much less than single digit percents. Consider the heat we get from the sun, at 6000K. If you have an object that's around 300K, that's 20 lower temperatures. Radiation is a 4th power effect, so that means the effects will be 20^4 less. That's 160,000 times less than the effect of the sun. The areas wont line up, obviously, so you'd have to do some conversions, but we're talking 5 orders of magnitude weaker than the sun. How long does it take the sun to melt an ice cube?
    $endgroup$
    – Cort Ammon
    Apr 14 at 3:23






  • 1




    $begingroup$
    @CortAmmon Thanks, this was the kind of estimate I had in mind -- I missed the 4th power in the Boltzmann equation.
    $endgroup$
    – Peter A. Schneider
    Apr 14 at 9:35
















  • $begingroup$
    +100 if I could, but I have one final question. If thermal conduction is the transfer of heat “particle to particle” as you put it, then I assume you meant the transfer of KE between the particles. If so, the particles(and the bodies)must be touching so there should not be any “distance” between the “two points”. But this doesn’t fit the formula you gave where X =distance
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 14:42






  • 1




    $begingroup$
    @UbaidHassan Yes, at the atomic level, heat and temperature is nothing but kinetic "vibrational" energy. Thermal conduction is not really defined for particle-to-particle. Fourier's law is found emperically under the assumption of a continuous material, and thus under the assumption that there is enough material for particle-particle interactions to be indistinguishable and only for their overall collective effect to play a role. Of this reason you will never hear conduction described for atomic particles; which is why it doesn't make much sense in your scenario either.
    $endgroup$
    – Steeven
    Apr 13 at 14:54











  • $begingroup$
    Can you give an estimate about the ratio of infrared? It's certainly minor, but how minor? Single-digit percent?
    $endgroup$
    – Peter A. Schneider
    Apr 13 at 17:24






  • 2




    $begingroup$
    @PeterA.Schneider It should be much less than single digit percents. Consider the heat we get from the sun, at 6000K. If you have an object that's around 300K, that's 20 lower temperatures. Radiation is a 4th power effect, so that means the effects will be 20^4 less. That's 160,000 times less than the effect of the sun. The areas wont line up, obviously, so you'd have to do some conversions, but we're talking 5 orders of magnitude weaker than the sun. How long does it take the sun to melt an ice cube?
    $endgroup$
    – Cort Ammon
    Apr 14 at 3:23






  • 1




    $begingroup$
    @CortAmmon Thanks, this was the kind of estimate I had in mind -- I missed the 4th power in the Boltzmann equation.
    $endgroup$
    – Peter A. Schneider
    Apr 14 at 9:35















$begingroup$
+100 if I could, but I have one final question. If thermal conduction is the transfer of heat “particle to particle” as you put it, then I assume you meant the transfer of KE between the particles. If so, the particles(and the bodies)must be touching so there should not be any “distance” between the “two points”. But this doesn’t fit the formula you gave where X =distance
$endgroup$
– Ubaid Hassan
Apr 13 at 14:42




$begingroup$
+100 if I could, but I have one final question. If thermal conduction is the transfer of heat “particle to particle” as you put it, then I assume you meant the transfer of KE between the particles. If so, the particles(and the bodies)must be touching so there should not be any “distance” between the “two points”. But this doesn’t fit the formula you gave where X =distance
$endgroup$
– Ubaid Hassan
Apr 13 at 14:42




1




1




$begingroup$
@UbaidHassan Yes, at the atomic level, heat and temperature is nothing but kinetic "vibrational" energy. Thermal conduction is not really defined for particle-to-particle. Fourier's law is found emperically under the assumption of a continuous material, and thus under the assumption that there is enough material for particle-particle interactions to be indistinguishable and only for their overall collective effect to play a role. Of this reason you will never hear conduction described for atomic particles; which is why it doesn't make much sense in your scenario either.
$endgroup$
– Steeven
Apr 13 at 14:54





$begingroup$
@UbaidHassan Yes, at the atomic level, heat and temperature is nothing but kinetic "vibrational" energy. Thermal conduction is not really defined for particle-to-particle. Fourier's law is found emperically under the assumption of a continuous material, and thus under the assumption that there is enough material for particle-particle interactions to be indistinguishable and only for their overall collective effect to play a role. Of this reason you will never hear conduction described for atomic particles; which is why it doesn't make much sense in your scenario either.
$endgroup$
– Steeven
Apr 13 at 14:54













$begingroup$
Can you give an estimate about the ratio of infrared? It's certainly minor, but how minor? Single-digit percent?
$endgroup$
– Peter A. Schneider
Apr 13 at 17:24




$begingroup$
Can you give an estimate about the ratio of infrared? It's certainly minor, but how minor? Single-digit percent?
$endgroup$
– Peter A. Schneider
Apr 13 at 17:24




2




2




$begingroup$
@PeterA.Schneider It should be much less than single digit percents. Consider the heat we get from the sun, at 6000K. If you have an object that's around 300K, that's 20 lower temperatures. Radiation is a 4th power effect, so that means the effects will be 20^4 less. That's 160,000 times less than the effect of the sun. The areas wont line up, obviously, so you'd have to do some conversions, but we're talking 5 orders of magnitude weaker than the sun. How long does it take the sun to melt an ice cube?
$endgroup$
– Cort Ammon
Apr 14 at 3:23




$begingroup$
@PeterA.Schneider It should be much less than single digit percents. Consider the heat we get from the sun, at 6000K. If you have an object that's around 300K, that's 20 lower temperatures. Radiation is a 4th power effect, so that means the effects will be 20^4 less. That's 160,000 times less than the effect of the sun. The areas wont line up, obviously, so you'd have to do some conversions, but we're talking 5 orders of magnitude weaker than the sun. How long does it take the sun to melt an ice cube?
$endgroup$
– Cort Ammon
Apr 14 at 3:23




1




1




$begingroup$
@CortAmmon Thanks, this was the kind of estimate I had in mind -- I missed the 4th power in the Boltzmann equation.
$endgroup$
– Peter A. Schneider
Apr 14 at 9:35




$begingroup$
@CortAmmon Thanks, this was the kind of estimate I had in mind -- I missed the 4th power in the Boltzmann equation.
$endgroup$
– Peter A. Schneider
Apr 14 at 9:35











3












$begingroup$

Thermal energy transfer is in the form of heat from the water to the ice cube by natural convection.



If the cube and water together form an isolated system (no heat transfer between them and their surroundings) the heat transfer will continue until all the ice is melted, or until the water temperature equals 0 C at which point any ice remaining will be in two phase thermal equilibrium with the water.



Hope this helps






share|cite|improve this answer









$endgroup$












  • $begingroup$
    How do you know it's natural convection?
    $endgroup$
    – pentane
    Apr 13 at 21:25










  • $begingroup$
    @pentane There are two kinds of convection: forced and natural. Forced usually involves some kind of forced movement of the fluid over a surface. Say, by way of a fan, the wind, a pump for water, etc. Natural involves movement due to buoyancy, warm fluid rising over cool.
    $endgroup$
    – Bob D
    Apr 13 at 21:53










  • $begingroup$
    no I know what it is but how do you know an ice cube in a glass of water is convection. where's the flow?
    $endgroup$
    – pentane
    Apr 13 at 21:57
















3












$begingroup$

Thermal energy transfer is in the form of heat from the water to the ice cube by natural convection.



If the cube and water together form an isolated system (no heat transfer between them and their surroundings) the heat transfer will continue until all the ice is melted, or until the water temperature equals 0 C at which point any ice remaining will be in two phase thermal equilibrium with the water.



Hope this helps






share|cite|improve this answer









$endgroup$












  • $begingroup$
    How do you know it's natural convection?
    $endgroup$
    – pentane
    Apr 13 at 21:25










  • $begingroup$
    @pentane There are two kinds of convection: forced and natural. Forced usually involves some kind of forced movement of the fluid over a surface. Say, by way of a fan, the wind, a pump for water, etc. Natural involves movement due to buoyancy, warm fluid rising over cool.
    $endgroup$
    – Bob D
    Apr 13 at 21:53










  • $begingroup$
    no I know what it is but how do you know an ice cube in a glass of water is convection. where's the flow?
    $endgroup$
    – pentane
    Apr 13 at 21:57














3












3








3





$begingroup$

Thermal energy transfer is in the form of heat from the water to the ice cube by natural convection.



If the cube and water together form an isolated system (no heat transfer between them and their surroundings) the heat transfer will continue until all the ice is melted, or until the water temperature equals 0 C at which point any ice remaining will be in two phase thermal equilibrium with the water.



Hope this helps






share|cite|improve this answer









$endgroup$



Thermal energy transfer is in the form of heat from the water to the ice cube by natural convection.



If the cube and water together form an isolated system (no heat transfer between them and their surroundings) the heat transfer will continue until all the ice is melted, or until the water temperature equals 0 C at which point any ice remaining will be in two phase thermal equilibrium with the water.



Hope this helps







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Apr 13 at 13:27









Bob DBob D

4,7252318




4,7252318











  • $begingroup$
    How do you know it's natural convection?
    $endgroup$
    – pentane
    Apr 13 at 21:25










  • $begingroup$
    @pentane There are two kinds of convection: forced and natural. Forced usually involves some kind of forced movement of the fluid over a surface. Say, by way of a fan, the wind, a pump for water, etc. Natural involves movement due to buoyancy, warm fluid rising over cool.
    $endgroup$
    – Bob D
    Apr 13 at 21:53










  • $begingroup$
    no I know what it is but how do you know an ice cube in a glass of water is convection. where's the flow?
    $endgroup$
    – pentane
    Apr 13 at 21:57

















  • $begingroup$
    How do you know it's natural convection?
    $endgroup$
    – pentane
    Apr 13 at 21:25










  • $begingroup$
    @pentane There are two kinds of convection: forced and natural. Forced usually involves some kind of forced movement of the fluid over a surface. Say, by way of a fan, the wind, a pump for water, etc. Natural involves movement due to buoyancy, warm fluid rising over cool.
    $endgroup$
    – Bob D
    Apr 13 at 21:53










  • $begingroup$
    no I know what it is but how do you know an ice cube in a glass of water is convection. where's the flow?
    $endgroup$
    – pentane
    Apr 13 at 21:57
















$begingroup$
How do you know it's natural convection?
$endgroup$
– pentane
Apr 13 at 21:25




$begingroup$
How do you know it's natural convection?
$endgroup$
– pentane
Apr 13 at 21:25












$begingroup$
@pentane There are two kinds of convection: forced and natural. Forced usually involves some kind of forced movement of the fluid over a surface. Say, by way of a fan, the wind, a pump for water, etc. Natural involves movement due to buoyancy, warm fluid rising over cool.
$endgroup$
– Bob D
Apr 13 at 21:53




$begingroup$
@pentane There are two kinds of convection: forced and natural. Forced usually involves some kind of forced movement of the fluid over a surface. Say, by way of a fan, the wind, a pump for water, etc. Natural involves movement due to buoyancy, warm fluid rising over cool.
$endgroup$
– Bob D
Apr 13 at 21:53












$begingroup$
no I know what it is but how do you know an ice cube in a glass of water is convection. where's the flow?
$endgroup$
– pentane
Apr 13 at 21:57





$begingroup$
no I know what it is but how do you know an ice cube in a glass of water is convection. where's the flow?
$endgroup$
– pentane
Apr 13 at 21:57












3












$begingroup$

I am in complete disagreement with previous answers which consider convection as the main mechanism for heat transfer from liquid water to the ice cube.



Convection is an important and dominant mechanism to maintain the liquid layers close to the ice surface at higher temperature. Thus, its main role is to ensure that at the surface between liquid and solid a constant difference of temperature is maintained. However, as a mechanism to carry energy from the liquid into the solid, convection simply does not exist! Unless one would think of fluid streams penetrating into the solid, which is not the case.



Therefore we are left with conduction or radiation as possible ways to tranfer thermal energy from liquid water to the ice. A simple order-of-magnitude estimate, based on the formulae of the Stefan-Boltzmann's law and Fourier's law, taking into account the SI values of about $10^-7$ for $sigma_s$, of about $2$ for $kappa$ of ice, the values of the two temperatures and a value of $Delta x$ of the order of a few interatomic distances, shows that the radiation contribution is negligible.



An additional remark could be added on the microscopic description of the melting process.
It is a well established observation that pre-melting, i.e. the melting of a solid starting from the surface layers, instead of than from the bulk, is a phenomenon present even in the case of ice. This observation would exclude the possibility that the melting process in the present case could start in the bulk of the ice.






share|cite|improve this answer











$endgroup$












  • $begingroup$
    So convection according to you is only the maintenance of a constant temperature of the liquid layers around the ice cube (in this case)? Then what actually is the mechanism of heat transfer to the ice cube from water?
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 21:44






  • 1




    $begingroup$
    I wrote it above. Thermal conduction prevails by orders of magnitude on radiation. That is the only relevant mechanism to transfer thermal energy across the liquid solid border. Convection cennot play a direct role by definition. It plays an indirect role, as I tryed to explain.
    $endgroup$
    – GiorgioP
    Apr 13 at 22:17







  • 1




    $begingroup$
    I have added an explicit statement at the beginning of the third paragraph. In the original post it was implicit since, after exclusion of convection, I was considering the relative role played by conduction and radiation.
    $endgroup$
    – GiorgioP
    Apr 13 at 22:29










  • $begingroup$
    To provide a counterpoint, convection exists in the same way the sound barrier exists. While, at the microscopic level, convection is merely conduction, the macroscopic fluid flow in convection makes it so much more effective at transfering heat that we have to use entirely different equations to model it. Likewise, gas molecules simply move according to the equations of motion at any speed. However, there's a key point where the momentum of the gas particles becomes substantially more anisotropic (starts to have a direction), and when that happens we see shock waves anda "sound barrier."
    $endgroup$
    – Cort Ammon
    Apr 14 at 16:48










  • $begingroup$
    While you are right that convection and the sound barrier do not exist in the most strict of technical senses, I just wanted to make sure somebody doesn't get the wrong idea from the words.
    $endgroup$
    – Cort Ammon
    Apr 14 at 16:49















3












$begingroup$

I am in complete disagreement with previous answers which consider convection as the main mechanism for heat transfer from liquid water to the ice cube.



Convection is an important and dominant mechanism to maintain the liquid layers close to the ice surface at higher temperature. Thus, its main role is to ensure that at the surface between liquid and solid a constant difference of temperature is maintained. However, as a mechanism to carry energy from the liquid into the solid, convection simply does not exist! Unless one would think of fluid streams penetrating into the solid, which is not the case.



Therefore we are left with conduction or radiation as possible ways to tranfer thermal energy from liquid water to the ice. A simple order-of-magnitude estimate, based on the formulae of the Stefan-Boltzmann's law and Fourier's law, taking into account the SI values of about $10^-7$ for $sigma_s$, of about $2$ for $kappa$ of ice, the values of the two temperatures and a value of $Delta x$ of the order of a few interatomic distances, shows that the radiation contribution is negligible.



An additional remark could be added on the microscopic description of the melting process.
It is a well established observation that pre-melting, i.e. the melting of a solid starting from the surface layers, instead of than from the bulk, is a phenomenon present even in the case of ice. This observation would exclude the possibility that the melting process in the present case could start in the bulk of the ice.






share|cite|improve this answer











$endgroup$












  • $begingroup$
    So convection according to you is only the maintenance of a constant temperature of the liquid layers around the ice cube (in this case)? Then what actually is the mechanism of heat transfer to the ice cube from water?
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 21:44






  • 1




    $begingroup$
    I wrote it above. Thermal conduction prevails by orders of magnitude on radiation. That is the only relevant mechanism to transfer thermal energy across the liquid solid border. Convection cennot play a direct role by definition. It plays an indirect role, as I tryed to explain.
    $endgroup$
    – GiorgioP
    Apr 13 at 22:17







  • 1




    $begingroup$
    I have added an explicit statement at the beginning of the third paragraph. In the original post it was implicit since, after exclusion of convection, I was considering the relative role played by conduction and radiation.
    $endgroup$
    – GiorgioP
    Apr 13 at 22:29










  • $begingroup$
    To provide a counterpoint, convection exists in the same way the sound barrier exists. While, at the microscopic level, convection is merely conduction, the macroscopic fluid flow in convection makes it so much more effective at transfering heat that we have to use entirely different equations to model it. Likewise, gas molecules simply move according to the equations of motion at any speed. However, there's a key point where the momentum of the gas particles becomes substantially more anisotropic (starts to have a direction), and when that happens we see shock waves anda "sound barrier."
    $endgroup$
    – Cort Ammon
    Apr 14 at 16:48










  • $begingroup$
    While you are right that convection and the sound barrier do not exist in the most strict of technical senses, I just wanted to make sure somebody doesn't get the wrong idea from the words.
    $endgroup$
    – Cort Ammon
    Apr 14 at 16:49













3












3








3





$begingroup$

I am in complete disagreement with previous answers which consider convection as the main mechanism for heat transfer from liquid water to the ice cube.



Convection is an important and dominant mechanism to maintain the liquid layers close to the ice surface at higher temperature. Thus, its main role is to ensure that at the surface between liquid and solid a constant difference of temperature is maintained. However, as a mechanism to carry energy from the liquid into the solid, convection simply does not exist! Unless one would think of fluid streams penetrating into the solid, which is not the case.



Therefore we are left with conduction or radiation as possible ways to tranfer thermal energy from liquid water to the ice. A simple order-of-magnitude estimate, based on the formulae of the Stefan-Boltzmann's law and Fourier's law, taking into account the SI values of about $10^-7$ for $sigma_s$, of about $2$ for $kappa$ of ice, the values of the two temperatures and a value of $Delta x$ of the order of a few interatomic distances, shows that the radiation contribution is negligible.



An additional remark could be added on the microscopic description of the melting process.
It is a well established observation that pre-melting, i.e. the melting of a solid starting from the surface layers, instead of than from the bulk, is a phenomenon present even in the case of ice. This observation would exclude the possibility that the melting process in the present case could start in the bulk of the ice.






share|cite|improve this answer











$endgroup$



I am in complete disagreement with previous answers which consider convection as the main mechanism for heat transfer from liquid water to the ice cube.



Convection is an important and dominant mechanism to maintain the liquid layers close to the ice surface at higher temperature. Thus, its main role is to ensure that at the surface between liquid and solid a constant difference of temperature is maintained. However, as a mechanism to carry energy from the liquid into the solid, convection simply does not exist! Unless one would think of fluid streams penetrating into the solid, which is not the case.



Therefore we are left with conduction or radiation as possible ways to tranfer thermal energy from liquid water to the ice. A simple order-of-magnitude estimate, based on the formulae of the Stefan-Boltzmann's law and Fourier's law, taking into account the SI values of about $10^-7$ for $sigma_s$, of about $2$ for $kappa$ of ice, the values of the two temperatures and a value of $Delta x$ of the order of a few interatomic distances, shows that the radiation contribution is negligible.



An additional remark could be added on the microscopic description of the melting process.
It is a well established observation that pre-melting, i.e. the melting of a solid starting from the surface layers, instead of than from the bulk, is a phenomenon present even in the case of ice. This observation would exclude the possibility that the melting process in the present case could start in the bulk of the ice.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Apr 13 at 22:27

























answered Apr 13 at 20:52









GiorgioPGiorgioP

4,6741729




4,6741729











  • $begingroup$
    So convection according to you is only the maintenance of a constant temperature of the liquid layers around the ice cube (in this case)? Then what actually is the mechanism of heat transfer to the ice cube from water?
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 21:44






  • 1




    $begingroup$
    I wrote it above. Thermal conduction prevails by orders of magnitude on radiation. That is the only relevant mechanism to transfer thermal energy across the liquid solid border. Convection cennot play a direct role by definition. It plays an indirect role, as I tryed to explain.
    $endgroup$
    – GiorgioP
    Apr 13 at 22:17







  • 1




    $begingroup$
    I have added an explicit statement at the beginning of the third paragraph. In the original post it was implicit since, after exclusion of convection, I was considering the relative role played by conduction and radiation.
    $endgroup$
    – GiorgioP
    Apr 13 at 22:29










  • $begingroup$
    To provide a counterpoint, convection exists in the same way the sound barrier exists. While, at the microscopic level, convection is merely conduction, the macroscopic fluid flow in convection makes it so much more effective at transfering heat that we have to use entirely different equations to model it. Likewise, gas molecules simply move according to the equations of motion at any speed. However, there's a key point where the momentum of the gas particles becomes substantially more anisotropic (starts to have a direction), and when that happens we see shock waves anda "sound barrier."
    $endgroup$
    – Cort Ammon
    Apr 14 at 16:48










  • $begingroup$
    While you are right that convection and the sound barrier do not exist in the most strict of technical senses, I just wanted to make sure somebody doesn't get the wrong idea from the words.
    $endgroup$
    – Cort Ammon
    Apr 14 at 16:49
















  • $begingroup$
    So convection according to you is only the maintenance of a constant temperature of the liquid layers around the ice cube (in this case)? Then what actually is the mechanism of heat transfer to the ice cube from water?
    $endgroup$
    – Ubaid Hassan
    Apr 13 at 21:44






  • 1




    $begingroup$
    I wrote it above. Thermal conduction prevails by orders of magnitude on radiation. That is the only relevant mechanism to transfer thermal energy across the liquid solid border. Convection cennot play a direct role by definition. It plays an indirect role, as I tryed to explain.
    $endgroup$
    – GiorgioP
    Apr 13 at 22:17







  • 1




    $begingroup$
    I have added an explicit statement at the beginning of the third paragraph. In the original post it was implicit since, after exclusion of convection, I was considering the relative role played by conduction and radiation.
    $endgroup$
    – GiorgioP
    Apr 13 at 22:29










  • $begingroup$
    To provide a counterpoint, convection exists in the same way the sound barrier exists. While, at the microscopic level, convection is merely conduction, the macroscopic fluid flow in convection makes it so much more effective at transfering heat that we have to use entirely different equations to model it. Likewise, gas molecules simply move according to the equations of motion at any speed. However, there's a key point where the momentum of the gas particles becomes substantially more anisotropic (starts to have a direction), and when that happens we see shock waves anda "sound barrier."
    $endgroup$
    – Cort Ammon
    Apr 14 at 16:48










  • $begingroup$
    While you are right that convection and the sound barrier do not exist in the most strict of technical senses, I just wanted to make sure somebody doesn't get the wrong idea from the words.
    $endgroup$
    – Cort Ammon
    Apr 14 at 16:49















$begingroup$
So convection according to you is only the maintenance of a constant temperature of the liquid layers around the ice cube (in this case)? Then what actually is the mechanism of heat transfer to the ice cube from water?
$endgroup$
– Ubaid Hassan
Apr 13 at 21:44




$begingroup$
So convection according to you is only the maintenance of a constant temperature of the liquid layers around the ice cube (in this case)? Then what actually is the mechanism of heat transfer to the ice cube from water?
$endgroup$
– Ubaid Hassan
Apr 13 at 21:44




1




1




$begingroup$
I wrote it above. Thermal conduction prevails by orders of magnitude on radiation. That is the only relevant mechanism to transfer thermal energy across the liquid solid border. Convection cennot play a direct role by definition. It plays an indirect role, as I tryed to explain.
$endgroup$
– GiorgioP
Apr 13 at 22:17





$begingroup$
I wrote it above. Thermal conduction prevails by orders of magnitude on radiation. That is the only relevant mechanism to transfer thermal energy across the liquid solid border. Convection cennot play a direct role by definition. It plays an indirect role, as I tryed to explain.
$endgroup$
– GiorgioP
Apr 13 at 22:17





1




1




$begingroup$
I have added an explicit statement at the beginning of the third paragraph. In the original post it was implicit since, after exclusion of convection, I was considering the relative role played by conduction and radiation.
$endgroup$
– GiorgioP
Apr 13 at 22:29




$begingroup$
I have added an explicit statement at the beginning of the third paragraph. In the original post it was implicit since, after exclusion of convection, I was considering the relative role played by conduction and radiation.
$endgroup$
– GiorgioP
Apr 13 at 22:29












$begingroup$
To provide a counterpoint, convection exists in the same way the sound barrier exists. While, at the microscopic level, convection is merely conduction, the macroscopic fluid flow in convection makes it so much more effective at transfering heat that we have to use entirely different equations to model it. Likewise, gas molecules simply move according to the equations of motion at any speed. However, there's a key point where the momentum of the gas particles becomes substantially more anisotropic (starts to have a direction), and when that happens we see shock waves anda "sound barrier."
$endgroup$
– Cort Ammon
Apr 14 at 16:48




$begingroup$
To provide a counterpoint, convection exists in the same way the sound barrier exists. While, at the microscopic level, convection is merely conduction, the macroscopic fluid flow in convection makes it so much more effective at transfering heat that we have to use entirely different equations to model it. Likewise, gas molecules simply move according to the equations of motion at any speed. However, there's a key point where the momentum of the gas particles becomes substantially more anisotropic (starts to have a direction), and when that happens we see shock waves anda "sound barrier."
$endgroup$
– Cort Ammon
Apr 14 at 16:48












$begingroup$
While you are right that convection and the sound barrier do not exist in the most strict of technical senses, I just wanted to make sure somebody doesn't get the wrong idea from the words.
$endgroup$
– Cort Ammon
Apr 14 at 16:49




$begingroup$
While you are right that convection and the sound barrier do not exist in the most strict of technical senses, I just wanted to make sure somebody doesn't get the wrong idea from the words.
$endgroup$
– Cort Ammon
Apr 14 at 16:49











1












$begingroup$

Heat Transfer Modes



The three forms of heat transfer between a system and the surroundings are as follows:



Conduction



This is the transport of heat by particles exchanging their internal energy. It occurs by one of three modes -- molecular collisions (gases), collisions/vibrations (local in liquids and lattice in solids), and free electron transport (in conductors and semiconductors). Conduction requires (or sets up) a temperature gradient in the material that is transporting the heat.



Convection



This is the transport of heat content by the bulk motion of a fluid over an object. It occurs in one of two modes -- free or forced. In free convection, the fluid moves because it is subject to a buoyancy force. In forced convection, we push the fluid. Convection requires a temperature difference. Convection can be modeled using principles of conduction across a film between the fluid and the object.



Radiation



This is the transport of energy from an object as electromagnetic radiation. Radiation only requires that objects have a temperature.



The Melting Process



To melt, atoms in a solid must gain enough energy to leave their bonds in the solid. Fusion is endothermic.



The energy arrives as heat from the surroundings. It arrives by the motion of the hotter liquid water molecules hitting the colder solid. The energy difference between moving liquid molecules and static (vibrating) solid molecules is a temperature difference in internal energy coordinates. That temperature difference needs only be infinitesimal to support the flow of heat from hot to cold. Liquid water does not support free electrons (of course not!) nor does it support lattice vibrations (that is what is happening in the ice). So, the one mode of transport of heat is conduction by molecular collisions from liquid water to solid ice.



The energy as heat can arrive by convection flow. When the system is in a gravitational field, and when the liquid immediately around the ice might become colder than the bulk water, the colder water will be denser. It will start to flow downward by natural convection. Thus, natural convection can be a factor in the heat flow. When the ice is floating on the water (typical), the colder water below the ice will fall down in the warmer water below it. As an inverse case, when you could put the ice cube at the bottom of a container and have hot water above it, you will shut down the natural convection mode. Think also about a cold penny that sits inserted into an insulated floor with hot air above it. The penny will have no natural convection modes because the cold air that might form around it is already denser than the hot air above it. This same thought is behind the formation of cold and hot fronts with thunderstorms in weather patterns.



You did not say whether the tank was stirred. So we can ignore forced convection.



The ice is radiating from it. The hotter water is radiating to the ice. The net radiation flux is to the ice from the water.



Estimates of Magnitudes



The temperatures of the solid ice and liquid water control the net radiation flux. When the liquid is only infinitesimally above the ice in temperature, the net radiation flux is ... small. Add to this that both ice and water have emissivities well below unity and their emissivities are comparable. At the end, you can pretty much say radiation is ... to be neglected.



Natural convection, when it occurs, swamps conduction heat transfer (well, not literally of course). Presuming the ice is at the top allows for this. Saying the ice is surrounding by water and mixed with it will lower its contribution.



At the end, we have conduction. Those "hotter" liquid water molecules are colliding constantly with those "colder" solid ice molecules (hot and cold as measures of internal energy). The transfer of heat is occurring constantly. A reference graph showing the variations in conductivity is found at this link.



Remaining Clarification



In pure materials (water), fusion occurs at a constant temperature. Never, ever can you discuss fusion as a process where the solid becomes hotter. The solid ice in this case stays pinned at one temperature as it completely melts. Inversely, you might find that when you mistakenly think the ice gets hotter during melting, you will immediately have to shut down any and all net heat transfer from the surroundings (liquid) to the system (ice). It is the second law of thermodynamics at play.






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New contributor




Jeffrey J Weimer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






$endgroup$












  • $begingroup$
    Liquids have a physics much closer to that of solids than gases (it is enough to compare the difference of densities to acknowledge it). Describing transport of energy in a liquid in term of collision is as good or as bad as using the same explanation for conduction in solids.
    $endgroup$
    – GiorgioP
    Apr 14 at 17:13










  • $begingroup$
    No doubt about important differences at level of the numbers. My point was about modeling the atomic dynamics of a liquid as collisions. The term collision is physically justified whenever an important change of momentum is concentrated in a short time interval. This is not the case for liquids. Atomic dynamic in liquids is much more complicate than phonon dynamics but collective modes (the equivalet of phonons in a harmonic solid) are routinely used to describe it.
    $endgroup$
    – GiorgioP
    2 days ago










  • $begingroup$
    A reasonable one-particle description of the atomic dynamics in dense liquids is a kind of superposition between diffusion and the so called cage motion which is the analogous of atomic vibration in a solid. The key point motivating my comment is that neither diffusion nor cage vibrations can be reasonably modeled as simple collisions.
    $endgroup$
    – GiorgioP
    2 days ago










  • $begingroup$
    @GiorgioP Much appreciated. I've modified my description to account for your insights in a manner that keeps it simple without I distorting the truth I hope.
    $endgroup$
    – Jeffrey J Weimer
    2 days ago















1












$begingroup$

Heat Transfer Modes



The three forms of heat transfer between a system and the surroundings are as follows:



Conduction



This is the transport of heat by particles exchanging their internal energy. It occurs by one of three modes -- molecular collisions (gases), collisions/vibrations (local in liquids and lattice in solids), and free electron transport (in conductors and semiconductors). Conduction requires (or sets up) a temperature gradient in the material that is transporting the heat.



Convection



This is the transport of heat content by the bulk motion of a fluid over an object. It occurs in one of two modes -- free or forced. In free convection, the fluid moves because it is subject to a buoyancy force. In forced convection, we push the fluid. Convection requires a temperature difference. Convection can be modeled using principles of conduction across a film between the fluid and the object.



Radiation



This is the transport of energy from an object as electromagnetic radiation. Radiation only requires that objects have a temperature.



The Melting Process



To melt, atoms in a solid must gain enough energy to leave their bonds in the solid. Fusion is endothermic.



The energy arrives as heat from the surroundings. It arrives by the motion of the hotter liquid water molecules hitting the colder solid. The energy difference between moving liquid molecules and static (vibrating) solid molecules is a temperature difference in internal energy coordinates. That temperature difference needs only be infinitesimal to support the flow of heat from hot to cold. Liquid water does not support free electrons (of course not!) nor does it support lattice vibrations (that is what is happening in the ice). So, the one mode of transport of heat is conduction by molecular collisions from liquid water to solid ice.



The energy as heat can arrive by convection flow. When the system is in a gravitational field, and when the liquid immediately around the ice might become colder than the bulk water, the colder water will be denser. It will start to flow downward by natural convection. Thus, natural convection can be a factor in the heat flow. When the ice is floating on the water (typical), the colder water below the ice will fall down in the warmer water below it. As an inverse case, when you could put the ice cube at the bottom of a container and have hot water above it, you will shut down the natural convection mode. Think also about a cold penny that sits inserted into an insulated floor with hot air above it. The penny will have no natural convection modes because the cold air that might form around it is already denser than the hot air above it. This same thought is behind the formation of cold and hot fronts with thunderstorms in weather patterns.



You did not say whether the tank was stirred. So we can ignore forced convection.



The ice is radiating from it. The hotter water is radiating to the ice. The net radiation flux is to the ice from the water.



Estimates of Magnitudes



The temperatures of the solid ice and liquid water control the net radiation flux. When the liquid is only infinitesimally above the ice in temperature, the net radiation flux is ... small. Add to this that both ice and water have emissivities well below unity and their emissivities are comparable. At the end, you can pretty much say radiation is ... to be neglected.



Natural convection, when it occurs, swamps conduction heat transfer (well, not literally of course). Presuming the ice is at the top allows for this. Saying the ice is surrounding by water and mixed with it will lower its contribution.



At the end, we have conduction. Those "hotter" liquid water molecules are colliding constantly with those "colder" solid ice molecules (hot and cold as measures of internal energy). The transfer of heat is occurring constantly. A reference graph showing the variations in conductivity is found at this link.



Remaining Clarification



In pure materials (water), fusion occurs at a constant temperature. Never, ever can you discuss fusion as a process where the solid becomes hotter. The solid ice in this case stays pinned at one temperature as it completely melts. Inversely, you might find that when you mistakenly think the ice gets hotter during melting, you will immediately have to shut down any and all net heat transfer from the surroundings (liquid) to the system (ice). It is the second law of thermodynamics at play.






share|cite|improve this answer










New contributor




Jeffrey J Weimer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






$endgroup$












  • $begingroup$
    Liquids have a physics much closer to that of solids than gases (it is enough to compare the difference of densities to acknowledge it). Describing transport of energy in a liquid in term of collision is as good or as bad as using the same explanation for conduction in solids.
    $endgroup$
    – GiorgioP
    Apr 14 at 17:13










  • $begingroup$
    No doubt about important differences at level of the numbers. My point was about modeling the atomic dynamics of a liquid as collisions. The term collision is physically justified whenever an important change of momentum is concentrated in a short time interval. This is not the case for liquids. Atomic dynamic in liquids is much more complicate than phonon dynamics but collective modes (the equivalet of phonons in a harmonic solid) are routinely used to describe it.
    $endgroup$
    – GiorgioP
    2 days ago










  • $begingroup$
    A reasonable one-particle description of the atomic dynamics in dense liquids is a kind of superposition between diffusion and the so called cage motion which is the analogous of atomic vibration in a solid. The key point motivating my comment is that neither diffusion nor cage vibrations can be reasonably modeled as simple collisions.
    $endgroup$
    – GiorgioP
    2 days ago










  • $begingroup$
    @GiorgioP Much appreciated. I've modified my description to account for your insights in a manner that keeps it simple without I distorting the truth I hope.
    $endgroup$
    – Jeffrey J Weimer
    2 days ago













1












1








1





$begingroup$

Heat Transfer Modes



The three forms of heat transfer between a system and the surroundings are as follows:



Conduction



This is the transport of heat by particles exchanging their internal energy. It occurs by one of three modes -- molecular collisions (gases), collisions/vibrations (local in liquids and lattice in solids), and free electron transport (in conductors and semiconductors). Conduction requires (or sets up) a temperature gradient in the material that is transporting the heat.



Convection



This is the transport of heat content by the bulk motion of a fluid over an object. It occurs in one of two modes -- free or forced. In free convection, the fluid moves because it is subject to a buoyancy force. In forced convection, we push the fluid. Convection requires a temperature difference. Convection can be modeled using principles of conduction across a film between the fluid and the object.



Radiation



This is the transport of energy from an object as electromagnetic radiation. Radiation only requires that objects have a temperature.



The Melting Process



To melt, atoms in a solid must gain enough energy to leave their bonds in the solid. Fusion is endothermic.



The energy arrives as heat from the surroundings. It arrives by the motion of the hotter liquid water molecules hitting the colder solid. The energy difference between moving liquid molecules and static (vibrating) solid molecules is a temperature difference in internal energy coordinates. That temperature difference needs only be infinitesimal to support the flow of heat from hot to cold. Liquid water does not support free electrons (of course not!) nor does it support lattice vibrations (that is what is happening in the ice). So, the one mode of transport of heat is conduction by molecular collisions from liquid water to solid ice.



The energy as heat can arrive by convection flow. When the system is in a gravitational field, and when the liquid immediately around the ice might become colder than the bulk water, the colder water will be denser. It will start to flow downward by natural convection. Thus, natural convection can be a factor in the heat flow. When the ice is floating on the water (typical), the colder water below the ice will fall down in the warmer water below it. As an inverse case, when you could put the ice cube at the bottom of a container and have hot water above it, you will shut down the natural convection mode. Think also about a cold penny that sits inserted into an insulated floor with hot air above it. The penny will have no natural convection modes because the cold air that might form around it is already denser than the hot air above it. This same thought is behind the formation of cold and hot fronts with thunderstorms in weather patterns.



You did not say whether the tank was stirred. So we can ignore forced convection.



The ice is radiating from it. The hotter water is radiating to the ice. The net radiation flux is to the ice from the water.



Estimates of Magnitudes



The temperatures of the solid ice and liquid water control the net radiation flux. When the liquid is only infinitesimally above the ice in temperature, the net radiation flux is ... small. Add to this that both ice and water have emissivities well below unity and their emissivities are comparable. At the end, you can pretty much say radiation is ... to be neglected.



Natural convection, when it occurs, swamps conduction heat transfer (well, not literally of course). Presuming the ice is at the top allows for this. Saying the ice is surrounding by water and mixed with it will lower its contribution.



At the end, we have conduction. Those "hotter" liquid water molecules are colliding constantly with those "colder" solid ice molecules (hot and cold as measures of internal energy). The transfer of heat is occurring constantly. A reference graph showing the variations in conductivity is found at this link.



Remaining Clarification



In pure materials (water), fusion occurs at a constant temperature. Never, ever can you discuss fusion as a process where the solid becomes hotter. The solid ice in this case stays pinned at one temperature as it completely melts. Inversely, you might find that when you mistakenly think the ice gets hotter during melting, you will immediately have to shut down any and all net heat transfer from the surroundings (liquid) to the system (ice). It is the second law of thermodynamics at play.






share|cite|improve this answer










New contributor




Jeffrey J Weimer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






$endgroup$



Heat Transfer Modes



The three forms of heat transfer between a system and the surroundings are as follows:



Conduction



This is the transport of heat by particles exchanging their internal energy. It occurs by one of three modes -- molecular collisions (gases), collisions/vibrations (local in liquids and lattice in solids), and free electron transport (in conductors and semiconductors). Conduction requires (or sets up) a temperature gradient in the material that is transporting the heat.



Convection



This is the transport of heat content by the bulk motion of a fluid over an object. It occurs in one of two modes -- free or forced. In free convection, the fluid moves because it is subject to a buoyancy force. In forced convection, we push the fluid. Convection requires a temperature difference. Convection can be modeled using principles of conduction across a film between the fluid and the object.



Radiation



This is the transport of energy from an object as electromagnetic radiation. Radiation only requires that objects have a temperature.



The Melting Process



To melt, atoms in a solid must gain enough energy to leave their bonds in the solid. Fusion is endothermic.



The energy arrives as heat from the surroundings. It arrives by the motion of the hotter liquid water molecules hitting the colder solid. The energy difference between moving liquid molecules and static (vibrating) solid molecules is a temperature difference in internal energy coordinates. That temperature difference needs only be infinitesimal to support the flow of heat from hot to cold. Liquid water does not support free electrons (of course not!) nor does it support lattice vibrations (that is what is happening in the ice). So, the one mode of transport of heat is conduction by molecular collisions from liquid water to solid ice.



The energy as heat can arrive by convection flow. When the system is in a gravitational field, and when the liquid immediately around the ice might become colder than the bulk water, the colder water will be denser. It will start to flow downward by natural convection. Thus, natural convection can be a factor in the heat flow. When the ice is floating on the water (typical), the colder water below the ice will fall down in the warmer water below it. As an inverse case, when you could put the ice cube at the bottom of a container and have hot water above it, you will shut down the natural convection mode. Think also about a cold penny that sits inserted into an insulated floor with hot air above it. The penny will have no natural convection modes because the cold air that might form around it is already denser than the hot air above it. This same thought is behind the formation of cold and hot fronts with thunderstorms in weather patterns.



You did not say whether the tank was stirred. So we can ignore forced convection.



The ice is radiating from it. The hotter water is radiating to the ice. The net radiation flux is to the ice from the water.



Estimates of Magnitudes



The temperatures of the solid ice and liquid water control the net radiation flux. When the liquid is only infinitesimally above the ice in temperature, the net radiation flux is ... small. Add to this that both ice and water have emissivities well below unity and their emissivities are comparable. At the end, you can pretty much say radiation is ... to be neglected.



Natural convection, when it occurs, swamps conduction heat transfer (well, not literally of course). Presuming the ice is at the top allows for this. Saying the ice is surrounding by water and mixed with it will lower its contribution.



At the end, we have conduction. Those "hotter" liquid water molecules are colliding constantly with those "colder" solid ice molecules (hot and cold as measures of internal energy). The transfer of heat is occurring constantly. A reference graph showing the variations in conductivity is found at this link.



Remaining Clarification



In pure materials (water), fusion occurs at a constant temperature. Never, ever can you discuss fusion as a process where the solid becomes hotter. The solid ice in this case stays pinned at one temperature as it completely melts. Inversely, you might find that when you mistakenly think the ice gets hotter during melting, you will immediately have to shut down any and all net heat transfer from the surroundings (liquid) to the system (ice). It is the second law of thermodynamics at play.







share|cite|improve this answer










New contributor




Jeffrey J Weimer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this answer



share|cite|improve this answer








edited 2 days ago





















New contributor




Jeffrey J Weimer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









answered Apr 13 at 23:15









Jeffrey J WeimerJeffrey J Weimer

1215




1215




New contributor




Jeffrey J Weimer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Jeffrey J Weimer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Jeffrey J Weimer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











  • $begingroup$
    Liquids have a physics much closer to that of solids than gases (it is enough to compare the difference of densities to acknowledge it). Describing transport of energy in a liquid in term of collision is as good or as bad as using the same explanation for conduction in solids.
    $endgroup$
    – GiorgioP
    Apr 14 at 17:13










  • $begingroup$
    No doubt about important differences at level of the numbers. My point was about modeling the atomic dynamics of a liquid as collisions. The term collision is physically justified whenever an important change of momentum is concentrated in a short time interval. This is not the case for liquids. Atomic dynamic in liquids is much more complicate than phonon dynamics but collective modes (the equivalet of phonons in a harmonic solid) are routinely used to describe it.
    $endgroup$
    – GiorgioP
    2 days ago










  • $begingroup$
    A reasonable one-particle description of the atomic dynamics in dense liquids is a kind of superposition between diffusion and the so called cage motion which is the analogous of atomic vibration in a solid. The key point motivating my comment is that neither diffusion nor cage vibrations can be reasonably modeled as simple collisions.
    $endgroup$
    – GiorgioP
    2 days ago










  • $begingroup$
    @GiorgioP Much appreciated. I've modified my description to account for your insights in a manner that keeps it simple without I distorting the truth I hope.
    $endgroup$
    – Jeffrey J Weimer
    2 days ago
















  • $begingroup$
    Liquids have a physics much closer to that of solids than gases (it is enough to compare the difference of densities to acknowledge it). Describing transport of energy in a liquid in term of collision is as good or as bad as using the same explanation for conduction in solids.
    $endgroup$
    – GiorgioP
    Apr 14 at 17:13










  • $begingroup$
    No doubt about important differences at level of the numbers. My point was about modeling the atomic dynamics of a liquid as collisions. The term collision is physically justified whenever an important change of momentum is concentrated in a short time interval. This is not the case for liquids. Atomic dynamic in liquids is much more complicate than phonon dynamics but collective modes (the equivalet of phonons in a harmonic solid) are routinely used to describe it.
    $endgroup$
    – GiorgioP
    2 days ago










  • $begingroup$
    A reasonable one-particle description of the atomic dynamics in dense liquids is a kind of superposition between diffusion and the so called cage motion which is the analogous of atomic vibration in a solid. The key point motivating my comment is that neither diffusion nor cage vibrations can be reasonably modeled as simple collisions.
    $endgroup$
    – GiorgioP
    2 days ago










  • $begingroup$
    @GiorgioP Much appreciated. I've modified my description to account for your insights in a manner that keeps it simple without I distorting the truth I hope.
    $endgroup$
    – Jeffrey J Weimer
    2 days ago















$begingroup$
Liquids have a physics much closer to that of solids than gases (it is enough to compare the difference of densities to acknowledge it). Describing transport of energy in a liquid in term of collision is as good or as bad as using the same explanation for conduction in solids.
$endgroup$
– GiorgioP
Apr 14 at 17:13




$begingroup$
Liquids have a physics much closer to that of solids than gases (it is enough to compare the difference of densities to acknowledge it). Describing transport of energy in a liquid in term of collision is as good or as bad as using the same explanation for conduction in solids.
$endgroup$
– GiorgioP
Apr 14 at 17:13












$begingroup$
No doubt about important differences at level of the numbers. My point was about modeling the atomic dynamics of a liquid as collisions. The term collision is physically justified whenever an important change of momentum is concentrated in a short time interval. This is not the case for liquids. Atomic dynamic in liquids is much more complicate than phonon dynamics but collective modes (the equivalet of phonons in a harmonic solid) are routinely used to describe it.
$endgroup$
– GiorgioP
2 days ago




$begingroup$
No doubt about important differences at level of the numbers. My point was about modeling the atomic dynamics of a liquid as collisions. The term collision is physically justified whenever an important change of momentum is concentrated in a short time interval. This is not the case for liquids. Atomic dynamic in liquids is much more complicate than phonon dynamics but collective modes (the equivalet of phonons in a harmonic solid) are routinely used to describe it.
$endgroup$
– GiorgioP
2 days ago












$begingroup$
A reasonable one-particle description of the atomic dynamics in dense liquids is a kind of superposition between diffusion and the so called cage motion which is the analogous of atomic vibration in a solid. The key point motivating my comment is that neither diffusion nor cage vibrations can be reasonably modeled as simple collisions.
$endgroup$
– GiorgioP
2 days ago




$begingroup$
A reasonable one-particle description of the atomic dynamics in dense liquids is a kind of superposition between diffusion and the so called cage motion which is the analogous of atomic vibration in a solid. The key point motivating my comment is that neither diffusion nor cage vibrations can be reasonably modeled as simple collisions.
$endgroup$
– GiorgioP
2 days ago












$begingroup$
@GiorgioP Much appreciated. I've modified my description to account for your insights in a manner that keeps it simple without I distorting the truth I hope.
$endgroup$
– Jeffrey J Weimer
2 days ago




$begingroup$
@GiorgioP Much appreciated. I've modified my description to account for your insights in a manner that keeps it simple without I distorting the truth I hope.
$endgroup$
– Jeffrey J Weimer
2 days ago










Ubaid Hassan is a new contributor. Be nice, and check out our Code of Conduct.









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대한민국 목차 국명 지리 역사 정치 국방 경제 사회 문화 국제 순위 관련 항목 각주 외부 링크 둘러보기 메뉴북위 37° 34′ 08″ 동경 126° 58′ 36″ / 북위 37.568889° 동경 126.976667°  / 37.568889; 126.976667ehThe Korean Repository문단을 편집문단을 편집추가해Clarkson PLC 사Report for Selected Countries and Subjects-Korea“Human Development Index and its components: P.198”“http://www.law.go.kr/%EB%B2%95%EB%A0%B9/%EB%8C%80%ED%95%9C%EB%AF%BC%EA%B5%AD%EA%B5%AD%EA%B8%B0%EB%B2%95”"한국은 국제법상 한반도 유일 합법정부 아니다" - 오마이뉴스 모바일Report for Selected Countries and Subjects: South Korea격동의 역사와 함께한 조선일보 90년 : 조선일보 인수해 혁신시킨 신석우, 임시정부 때는 '대한민국' 국호(國號) 정해《우리가 몰랐던 우리 역사: 나라 이름의 비밀을 찾아가는 역사 여행》“남북 공식호칭 ‘남한’‘북한’으로 쓴다”“Corea 대 Korea, 누가 이긴 거야?”국내기후자료 - 한국[김대중 前 대통령 서거] 과감한 구조개혁 'DJ노믹스'로 최단기간 환란극복 :: 네이버 뉴스“이라크 "韓-쿠르드 유전개발 MOU 승인 안해"(종합)”“해외 우리국민 추방사례 43%가 일본”차기전차 K2'흑표'의 세계 최고 전력 분석, 쿠키뉴스 엄기영, 2007-03-02두산인프라, 헬기잡는 장갑차 'K21'...내년부터 공급, 고뉴스 이대준, 2008-10-30과거 내용 찾기mk 뉴스 - 구매력 기준으로 보면 한국 1인당 소득 3만弗과거 내용 찾기"The N-11: More Than an Acronym"Archived조선일보 최우석, 2008-11-01Global 500 2008: Countries - South Korea“몇년째 '시한폭탄'... 가계부채, 올해는 터질까”가구당 부채 5000만원 처음 넘어서“‘빚’으로 내몰리는 사회.. 위기의 가계대출”“［경제365］ 공공부문 부채 급증…800조 육박”“"소득 양극화 다소 완화...불평등은 여전"”“공정사회·공생발전 한참 멀었네”iSuppli，08年2QのDRAMシェア・ランキングを発表(08/8/11)South Korea dominates shipbuilding industry | Stock Market News & Stocks to Watch from StraightStocks한국 자동차 생산, 3년 연속 세계 5위자동차수출 '현대-삼성 웃고 기아-대우-쌍용은 울고' 과거 내용 찾기동반성장위 창립 1주년 맞아Archived"중기적합 3개업종 합의 무시한 채 선정"李대통령, 사업 무분별 확장 소상공인 생계 위협 질타삼성-LG, 서민업종인 빵·분식사업 잇따라 철수상생은 뒷전…SSM ‘몸집 불리기’ 혈안Archived“경부고속도에 '아시안하이웨이' 표지판”'철의 실크로드' 앞서 '말(言)의 실크로드'부터, 프레시안 정창현, 2008-10-01“'서울 지하철은 안전한가?'”“서울시 “올해 안에 모든 지하철역 스크린도어 설치””“부산지하철 1,2호선 승강장 안전펜스 설치 완료”“전교조, 정부 노조 통계서 처음 빠져”“［Weekly BIZ］ 도요타 '제로 이사회'가 리콜 사태 불러들였다”“S Korea slams high tuition costs”““정치가 여론 양극화 부채질… 합리주의 절실””“〈"`촛불집회'는 민주주의의 질적 변화 상징"〉”““촛불집회가 민주주의 왜곡 초래””“국민 65%, "한국 노사관계 대립적"”“한국 국가경쟁력 27위‥노사관계 '꼴찌'”“제대로 형성되지 않은 대한민국 이념지형”“［신년기획-갈등의 시대］ 갈등지수 OECD 4위…사회적 손실 GDP 27% 무려 300조”“2012 총선-대선의 키워드는 '국민과 소통'”“한국 삶의 질 27위, 2000년과 2008년 연속 하위권 머물러”“［해피 코리아］ 행복점수 68점…해외 평가선 '낙제점'”“한국 어린이·청소년 행복지수 3년 연속 OECD ‘꼴찌’”“한국 이혼율 OECD중 8위”“［통계청］ 한국 이혼율 OECD 4위”“오피니언 ［이렇게 생각한다］ `부부의 날` 에 돌아본 이혼율 1위 한국”“Suicide Rates by Country, Global Health Observatory Data Repository.”“1. 또 다른 차별”“오피니언 ［편집자에게］ '왕따'와 '패거리 정치' 심리는 닮은꼴”“［미래한국리포트］ 무한경쟁에 빠진 대한민국”“대학생 98% "외모가 경쟁력이라는 말 동의"”“특급호텔 웨딩·200만원대 유모차… "남보다 더…" 호화病, 고질병 됐다”“［스트레스 공화국］ ① 경쟁사회, 스트레스 쌓인다”““매일 30여명 자살 한국, 의사보다 무속인에…””“"자살 부르는 '우울증', 환자 중 85% 치료 안 받아"”“정신병원을 가다”“대한민국도 ‘묻지마 범죄’,안전지대 아니다”“유엔 "학생 '성적 지향'에 따른 차별 금지하라"”“유엔아동권리위원회 보고서 및 번역본 원문”“고졸 성공스토리 담은 '제빵왕 김탁구' 드라마 나온다”“‘빛 좋은 개살구’ 고졸 취업…실습 대신 착취”원본 문서“정신건강, 사회적 편견부터 고쳐드립니다”‘소통’과 ‘행복’에 목 마른 사회가 잠들어 있던 ‘심리학’ 깨웠다“［포토］ 사유리-곽금주 교수의 유쾌한 심리상담”“"올해 한국인 평균 영화관람횟수 세계 1위"(종합)”“［게임연중기획］ 게임은 문화다-여가활동 1순위 게임”“영화속 ‘영어 지상주의’ …“왠지 씁쓸한데””“2월 `신문 부수 인증기관` 지정..방송법 후속작업”“무료신문 성장동력 ‘차별성’과 ‘갈등해소’”대한민국 국회 법률지식정보시스템"Pew Research Center's Religion & Public Life Project: South Korea"“amp;vwcd=MT_ZTITLE&path=인구·가구%20>%20인구총조사%20>%20인구부문%20>%20 총조사인구(2005)%20>%20전수부문&oper_YN=Y&item=&keyword=종교별%20인구& amp;lang_mode=kor&list_id= 2005년 통계청 인구 총조사”원본 문서“한국인이 좋아하는 취미와 운동 (2004-2009)”“한국인이 좋아하는 취미와 운동 (2004-2014)”Archived“한국, `부분적 언론자유국' 강등〈프리덤하우스〉”“국경없는기자회 "한국, 인터넷감시 대상국"”“한국, 조선산업 1위 유지(S. Korea Stays Top Shipbuilding Nation) RZD-Partner Portal”원본 문서“한국, 4년 만에 ‘선박건조 1위’”“옛 마산시,인터넷속도 세계 1위”“"한국 초고속 인터넷망 세계1위"”“인터넷·휴대폰 요금, 외국보다 훨씬 비싸”“한국 관세행정 6년 연속 세계 '1위'”“한국 교통사고 사망자 수 OECD 회원국 중 2위”“결핵 후진국' 한국, 환자가 급증한 이유는”“수술은 신중해야… 자칫하면 생명 위협”대한민국분류대한민국의 지도대한민국 정부대표 다국어포털대한민국 전자정부대한민국 국회한국방송공사about korea and information korea브리태니커 백과사전(한국편)론리플래닛의 정보(한국편)CIA의 세계 정보(한국편)마리암 부디아 (Mariam Budia),『한국: 하늘이 내린 한 폭의 그림』, 서울: 트랜스라틴 19호 (2012년 3월)대한민국ehehehehehehehehehehehehehehWorldCat132441370n791268020000 0001 2308 81034078029-6026373548cb11863345f(데이터)00573706ge128495

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고조선원삼국 시대삼국 시대남북국 시대후삼국 시대고려조선대한제국일제 강점기대한민국 임시 정부한반도 분단미군정개요제1공화국제2공화국제3공화국제4공화국제5공화국제6공화국4.3 사건6.25 전쟁4.19 혁명5.16 쿠테타한강의 기적부마 항쟁10.26 사태12.12 사태광주 민주화 운동6월 항쟁1988년 서울올림픽IMF 외환...
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