# Why won't there be any transfer of heat energy when ice at 0°C is in contact with water at 0°C in a closed container?

In my book, Concise Physics of Selina Publications for Class IX, it's written there that "If there is no transfer of heat between the two bodies placed in contact, they are said to be at the same temperature, but it doesn't mean that they have equal amount of heat in them." While doing some research on this topic in the internet, I came across various sites which claims that when ice at 0°C is kept in contact with water at 0°C in a closed airtight vessel, there is no transfer of heat energy, due to there same temperature Although, the latter experiment agrees with the statement in the book, I have a doubt regarding why there will not be any transfer of heat even when the internal energy of both the bodies are not same? Water at 0°C has more internal energy than ice at 0°C because the water has absorbed latent heat. Latent heat is the energy absorbed or released by a substance during a change in its physical state (phase) that occurs without changing its temperature.When the 1 g of ice at 0°C changes to 1 g of water at 0°C , there is absorption of about 334 J(This is the value of latent heat of fusion of ice).

When the ice at 0°C is in contant with water at 0°C, there is a chance that the extra heat (latent heat) gets equally distributed between ice and water. But this doesn't occur. What should be the reason?

• It is not really meaningful to say that an object has heat. Heat is the term used for energy in thermal transit and is associated with a process, not a body. It surprises me a bit that your textbook uses this phrasing. Commented Jul 16 at 16:23
• "Latent heat" is the amount of heat that it takes to melt a given mass of ice, and that heat must come from outside the ice. The ice does not contain latent heat. Commented Jul 16 at 16:30
• @DavidWhite No, the ice at 0°C doesn't have latent heat...but the water which is at 0°C does (during its state change but it didn't take place in that closed airtight vessel) Commented Jul 16 at 16:35
• @Steeven I think you should read this book by Bronsted: "Principer og Problemer i Energetiken," published by Bianco Lunas Bogtrykkeri, Copenhagen, 1946; it gives a very interesting view of that subject that is completely along the ideas of Carnot, le Chatelier, Gouy, etc. It is a linguistic not physical issue to define what "heat" is or not; as a francophile I like Carnot's calorique. Commented Jul 16 at 16:47
• What are you calling your system? Commented Jul 16 at 22:46

The other answers have hammered quite well that

1. There is no such thing as heat inside a thing; heat is the name for the spontaneous transfer of energy due to temperature differences and so if it is not being transferred, then there is no heat.
2. You need a temperature difference to have a net flow of heat.
3. jwimberley correctly also covers a sloppiness in your use of language but I left a comment there too.

Instead, I want to focus upon the details needed to answer the essence of your question, namely:

When the ice at 0°C is in contant with water at 0°C, there is a chance that the extra heat (latent heat) gets equally distributed between ice and water. But this doesn't occur. What should be the reason?

There is a chance for a water molecule to freeze onto the ice, and in so doing, give enough latent heat to kick an ice molecule out, breaking the molecular bonds. The problem is that, how would you delineate which is ice and which is water when something changes so little? This very quickly runs into the Ship of Theseus philosophical problem and have very little to do with physics.

But actually we have an even better answer. It is really that the level of basic analysis that you are currently doing, that there is no reason why your ice-water mixture does not suddenly turn into a slurry, and turn back. This means that if we really want to explain why this does not happen, we have to go into greater details. You could put in gravitational interaction, and show that the ice should float to the top, and so a slurry is not stable as it is. Or you can take into account the tiny surface tension effects---the water and the ice will have different surface tensions, and that tips the balance so that you don't get a spontaneous diffusing out of the ice-water mixture so that you get a slurry.

As others have said, systems don't contain heat but contain internal energy. So, let's pretend your textbook used the correct term.

To socratically answer your question -- why there is not heat transferred when the ice and water are at the same temperature but have different internal energies -- first consider this simpler system: drop the ice and just look at an isolated volume of water at some temperature. Chop the volume into two unequal parts with an imaginary plane. The bigger part has more internal energy than the smaller part. Do you think energy would move across your imaginary plane because of that? If so, what would happen to the temperature on the two sides of the imaginary plane? And if not, why would the ice and water mixture be any different?

• That's just moves the problem from "absolute value of internal energy" to "energy density"; The water has more energy density than the ice, so there is some reason to argue that the OP's question does require answering. Commented Jul 17 at 4:34

"If there is no transfer of heat between the two bodies placed in contact, they are said to be at the same temperature, but it doesn't mean that they have equal amount of heat in them."

Heat is defined as the transfer of energy due solely to temperature difference. Things do not "contain" heat in them. The proper term for the energy of the atoms and molecules within a substance is "internal energy". I suggest you get yourself another book.

It is true that when you have ice and water at the same temperature, and isolated from everything else, there is no net energy being transfer occurring between the ice and water in the form of heat.

I have a doubt regarding why there will not be any transfer of heat even when the internal heat energy of both the bodies are not same?

As already stated, things don't contain heat. So don't refer to "internal heat energy". That said, the internal energy of bodies having the same temperature can be equal to or different from each other. You can roughly think of temperature as a measure of the average kinetic energy of the atoms and molecules of the body. If two bodies have the same average molecular kinetic energy, but one body has more molecules than the other, then the former body will have more internal energy than the former, everything else being equal.

Water at 0°C has more heat than ice at 0°C

For the same mass of water at 0$$^0$$C and ice at 0$$^0$$ C, the internal energy of the water will be greater than the ice. Thats because energy, normally in the form of heat (which we call latent heat"), has to be added to the portion of the mixture to form water.

Latent heat is the energy absorbed or released by a substance during a change in its physical state (phase) that occurs without changing its temperature.

Correct. But that latent heat has to come from something else having a temperature greater than 0$$^0$$C.

When the ice at 0°C is in contant with water at 0°C, there is a change that the extra latent heat gets equally distributed between ice and water.

I don't understand what you mean by "the extra latent heat". But if the heat transfer from the external source to the mixture occurs very slowly and evenly, then the phase change should occur with no temperature gradients in the mixture. This can be accomplished by immersing the mixture in a constant temperature environment whose temperature is only slightly greater than 0$$^0$$ C.

Hope this helps.

• Actually I tend to say that when the water had formed at some point (which is outside the system of closed container) it absorbed latent heat provided to it from external source. When this water is kept with ice in a closed container ( let the mass of ice and water be same and the temperature for both be 0°C) some part of that latent heat absorbed by water should have transferred from water to ice such that the energy content for both ice and water equal. Commented Jul 16 at 18:00
• And if it could really happen the water should have been in a partial frozen state but not completely an ice and ice should have been partially liquified (because after we have halved the latent heat and distributed it among both ice and water; the heat absorbed won't be sufficient to change state completely). However the temperature would still remain the same (0°C) Commented Jul 16 at 18:04
• Sorry, but I can't make sense of your first comment. You seem to think of latent heat as something that is "contained" in the water. You've got to get rid of the idea of something containing heat. As long as the water was 0C before mixing with 0C ice, there can't be any energy transfer from the water to the ice in the form of heat. Commented Jul 16 at 18:21

Heat transfer only occurs when there is a temperature difference.The heat flux 'q' s.t by$$\vec q =-\lambda \nabla T$$where $$T$$ is temperature and '$$\lambda$$' is coefficient, and if $$T$$ is same in space, the flux must be zero. You can consider it from the opposite perspective: the ocean contains enormous heat, but it is not possible to extract energy from it just by putting in a stick.

• What does “s.t” mean? (I’m familiar with “s.t.” meaning “such that,” but that doesn’t fit here.) Commented Jul 17 at 1:11
• subject to @Chemomechanics Commented Jul 17 at 1:28

It seems that the ambiguity here is not so much in physics as it is in mathematical logic. Buckle up!

Firstly and most importantly, bravo for your effort to understand your textbook. I appreciate your curiosity and encourage you to keep that spirit.

Secondly, as you described, in the case of melting ice in water at $$0^oC$$ there actually is heat transfer, while it is true that the water and ice are at the same temperature. Note that this is not in contradiction with your textbook.

It seems to me that you have interpretted the text of your textbook as a mutual causal association between temperature difference and heat transfer. As if temperature difference implies there is heat transfer and heat transfer implies there is temperature difference. That interpretation is wrong. The association between these two is one-way. If there is teperature difference then we can say there is heat transfer at contact; but if there is heat transfer at contact we cannot necessarily say that there is a temperature difference.

If you haven't already, you will study in mathematical logic that there is a difference between deduction and equivalence. By deduction I mean statements of the form If A then B. By equivalence I mean statements of the form If A then B, and vice versa: if B then A. Equivalence statements are also sometimes written as A if and only if B.

Let us look at a different example that may better show the difference between deduction and equivalence.

Statement 1: If the lion is not hungry, it doesn't eat food.

Statement 2: The lion is not eating food.

Assuming the above statements are true, can we say that the lion is not hungry? Not necessarily! Maybe the lion is hungry but just doesn't have food.

Back to your textbook: you are given an If A then B statement. This is not an If A then B and vice versa statement. It does not mean statements A and B (namely, temperature difference and heat transfer) are necessary and sufficient conditions for one-another.

Hope that helps.

If we heat a fraction of a block of ice at 273 K to get some liquid water at the same temperature, and remove the source of heat, the water doesn't "fall" to its previous solid phase, releasing energy, in spite of being in contact with the remaining ice.

If we suppose the water freezing again (after the heat source is removed) latent heat is transferred to the remaining ice. Which results in melting the same fraction that was frozen. So the total amount of liquid water doesn't change.