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Let's say we have an ice water solution in an ambience with room temperature, i.e. there is a permanent exchange of energy. Let's suppose the ice cubes were from the freezer, which is at $-18°C$. The ice water has already reached its equilibrium at $0°$. Now, through energy transfer into the system, the ice is melting. The energy is used up on the phase transition while the ice is melting.

(I'm also referring to the answers to the question Why does ice water get colder when salt is added?)

The question is: Will the core temperature of the ice remain the same ($-18°C$) until it melts completely, as the energy it absorbs from the ambience is used up on the phase transition until there is no more solid water? Or will a temperature gradient form within the ice cube? (For this question, the water isn't really needed; we can also suppose we just have an ice cube in a room temperature ambience.)

EDIT for disambiguation: I'm perfectly aware that a body that absorbs energy will radiate the energy by forming a gradient from its center to the outside that is the connecting point to the ambience it exchanges energy with. But: When a mass is undergoing phase transition, all invested energy (or radiated energy, depending on the direction it is going) will be used up on the phase transition. E.g., when you cool water below $0°C$, it will not get colder (let's leave out supercooled water here) until it has frozen completely (thus the ice water equilibrium). Same happens when you heat water that has a temperature of $100°C$. It will not get warmer unless all has evaporated.

Now we have our ice cube with $-18°C$ in its core. We heat it. On its surface, a dynamic equilibrium of freezing and melting is formed, with more water melting than freezing. The water always has a temperature of $0°C$. Now if we add some more energy to the cube, will the additional energy contribute completely to the phase transition, resulting in less freezing and thus more melting in the dynamic equilibrium - or will some of the energy contribute to heating the ice cube itself? If so, why is not all the energy used on the phase transition, and how much is not used on the phase transition? For a thorough answer, I feel that it is this point that has to be answered.

Of course, size matters here. Directly adjacent to the surface, a small gradient may take place; and when the surface gets closer to the core, at some point, it will affect it anyway. But - and that's the big but here: According to the above mentioned phase transition energy absorption, you could argue that it will differ a lot from a temperature gradient in a solid body, because of the energy "drained" by the phase transition.

Note to the moderators: Feel free to move the question to chemistry.SE if you think that it better fits there; many questions on the ice-water-salt-topic have already been asked in chemistry.SE, but I posted it here as I felt that general thermodynamics contribute more to the whole ice-water-system than chemical processes; but then again, rethinking it, it's hard to tell!

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    $\begingroup$ To answer this question exactly, one needs to know how quickly heat is being transferred to the subject. The rules that are generally taught in an introductory course contains the (sometimes hidden) assumption that the heat transfers slowly compared to the time needed for conduction throughout the system. $\endgroup$ – dmckee Jul 27 '15 at 22:29
  • $\begingroup$ "Will a temperature gradient form within the ice cube?" If you've ever poured a drink over ice (or dropped ice cubes in a drink) and noticed the ice suddenly cracking, note that that is due to a density gradient driven by a temperature gradient. $\endgroup$ – Asher Jul 27 '15 at 23:33
  • $\begingroup$ @dmckee No you don't have to know how quickly to know if the center will remain at the same until it melts completely. $\endgroup$ – paparazzo Jul 28 '15 at 0:41
  • $\begingroup$ @Frisbee Certainly not the question from the text, but in general the things we tell introductory students can leave them with an incorrect impression about the question in the title. $\endgroup$ – dmckee Jul 28 '15 at 2:34
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    $\begingroup$ Right here "When a mass is undergoing phase transition, all invested energy (or radiated energy, depending on the direction it is going) will be used up on the phase transition" you have tripped on the simplification usually taught to students. That is only true if the heat transfer takes place on time scales longer than the thermal-relaxation time of the system. Molecules in the melting zone don't lose their connection to the ones just in from that and all thermal processes are stochastic at a microscopic level. Frisbee's answer is correct. $\endgroup$ – dmckee Jul 29 '15 at 0:46
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Yes the core will warm gradually.

Heat transfer in a solid is conduction.

Ice has a known thermal conductivity and will have a linear temperature profile from all paths from surface to center. There will be concentric rings of constant temperature at all times.

It would be impossible to warm just the surface and not warm up the molecules next to the surface.

Surface will warm to $32^\circ\mathrm{F}$ ($0^\circ\mathrm{C}$) and by that time the temperature profile will be established.

The surface at $32^\circ\mathrm{F}$ ($0^\circ\mathrm{C}$) will just migrate inward. The surface will not go above $32^\circ\mathrm{F}$ ($0^\circ\mathrm{C}$) as ice simply melts. As you migrate inward the temperature slope will remain constant. As the path becomes shorter the core temp will increase.

If you raised the temperature up to $30^\circ\mathrm{F}$ ($-1^\circ\mathrm{C}$) and held it there for a while the core would raise to $30^\circ\mathrm{F}$ ($-1^\circ\mathrm{C}$).

Think about a cutting torch on metal. Once you get the surface to melt it just cuts right through the rest.

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  • $\begingroup$ @KyleOman It does not ignore latent heat. Latent heat is not temperature. I clearly state surface at 32. There is heart transfer at the surface with no temperature change. Did you vote me down. I am not making this stuff up. I have a degree in chemical engineering. If you are sure latent latent heat is critical then post and answer. $\endgroup$ – paparazzo Jul 27 '15 at 23:32
  • $\begingroup$ Concerning the units, see meta.physics.stackexchange.com/questions/15/…. This site is run by people in the US and hosted in the US, but I doubt very strongly that the Stack Exchange team would want to have the network considered as being US centric. It's a big internet out there. $\endgroup$ – dmckee Jul 28 '15 at 2:25
  • $\begingroup$ I don't understand the reference to cutting metal. $\endgroup$ – LDC3 Jul 28 '15 at 2:55
  • $\begingroup$ @LDC3 Metal or water the temperature of the core is raised. Have you cut metal with a cutting torch. Even if you have not cut with a torch if someone was cutting metal on one side would you touch the other side before it started to cut? Have your held your hand against the window in the winter - is it the same temp as the outside? $\endgroup$ – paparazzo Jul 28 '15 at 3:07
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    $\begingroup$ @Rococo It is phase change at the surface that holds a temp. But between that and the center is temperature gradient that will transfer heat. $\endgroup$ – paparazzo Jul 28 '15 at 3:38

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