[hamdani yusuf (OP)]

You seem to have forgotten to answer the questions.

I thought you are smart enough to conclude based on those considerations.

Did you consider the idea that, no matter how smart I may or may not be, you didn't provide enough information.
So, for the third time

"Is there a net heat exchange between water and ice at 0 degree C?"
If you think there is, which way does it go?
When does it stop?

I don't have enough convincing information to confidently predict the results. That's why I started the thread and did the experiments.
If it turns out that there's a net heat transfer, it would be from higher heat content to the lower one, i. e.  from water to ice.
It would stop when both containers have the same ratio of water and ice. Hence energy transfer rate would be balanced in both directions.

Do you have any objections to the consideration points I mentioned earlier?

[hamdani yusuf (OP)]

Does anyone considered this to make their predictions?
https://en.m.wikipedia.org/wiki/Freezing-point_depression

Here I used tap water to avoid supercooling which might occur if pure water is used instead. But it might generate another problem which is not negligible.

[alancalverd]

All analogies break down at some points, where they don't resemble the things that they are supposed to represent anymore. Your batteries don't experience phase changes. Hence they are more like two ice blocks with the same temperature.

I haven't specified the nature of either battery, only its potential. One could be a capacitor with a solid dielectric, the other a wet chemical cell with the same terminal voltage. That's all we know or need to know about the temperature of a body: its ability to transfer energy to or from another body. Equilibrium is equilibrium!

[Bored chemist]

It would stop when both containers have the same ratio of water and ice.

How would they "know" when the ratio was 50%50?
The simple answer is that they can't.
And that's why we know that there's no heat transfer.
But we have been telling you that for 9 pages now, so I doubt you will accept it.

[Bored chemist]

Does anyone considered this to make their predictions?

No.
Because it's irrelevant to the question which you actually asked which was about water and ice not "some random solution of stuff".

[alancalverd]

If it turns out that there's a net heat transfer, it would be from higher heat content to the lower one, i. e.  from water to ice.

No!

Heat transfers from a hotter body to a colder one, nothing to do with the heat content of either.

If it were otherwise, you would boil every time you (70 kg of water at 37°C) swam in the sea (bazillions of tonnes at 17°C)!

[hamdani yusuf (OP)]

All analogies break down at some points, where they don't resemble the things that they are supposed to represent anymore. Your batteries don't experience phase changes. Hence they are more like two ice blocks with the same temperature.

I haven't specified the nature of either battery, only its potential. One could be a capacitor with a solid dielectric, the other a wet chemical cell with the same terminal voltage. That's all we know or need to know about the temperature of a body: its ability to transfer energy to or from another body. Equilibrium is equilibrium!

One factor might be in equilibrium, while other factors may shift it. Are these columns in equilibrium?

[Bored chemist]

Water has higher heat content than ice, when they are at the same temperature and pressure.

Not really.
The heat- in particular, the free energy- of the two can be calculated at any temperature you like.
And the important bit is that the freezing/ melting point is the temperature at which the two phases have the same free energy.
They have the same "heat content". That's exactly why heat isn't transferred from one to the other (And, that also is the definition of being at thermal equilibrium).

(The problem is your idea of a "heat content" isn't well defined: but the Gibbs free energies is well defined)

[hamdani yusuf (OP)]

It would stop when both containers have the same ratio of water and ice.

How would they "know" when the ratio was 50%50?
The simple answer is that they can't.
And that's why we know that there's no heat transfer.
But we have been telling you that for 9 pages now, so I doubt you will accept it.

How would a light beam know where to bend when going through an interface between two media?  How would it know that it will get the  fastest route?  There's a problem with anthropomorphising physical phenomena.

We are comparing two ratios, and they don't have to be 50/50.

[alancalverd]

Are these columns in equilibrium?

Obviously not. But if they were all the same height (and the bath at the bottom was enclosed, of course), they would be in equilibrium but with different total potential energies.

[Bored chemist]

How would a light beam know where to bend when going through an interface between two media? 

Because the light beam is in the right place to be affected by the change in medium.

they don't have to be 50/50.

Did you deliberately miss the point?
How does the system know what the ratios are?

There's a problem with anthropomorphising physical phenomena.

And the problem is that you don't understand it.
But, if it makes you heel happier.

What is the mechanism by which the system is driven towards the same ratio?
What parameter does the ratio affect?

[Bored chemist]

Are these columns in equilibrium?

Possibly, but if they are meant to demonstrate capillary action, they aren't well drawn. The meniscuses are missing.

[hamdani yusuf (OP)]

Did you deliberately miss the point?
How does the system know what the ratios are?

Some of us prefer to be pedantic.

Just like diffusion.

[Bored chemist]

Some of us prefer to be pedantic.

Fine,
Answer the pedantic version of the same question.

What is the mechanism by which the system is driven towards the same ratio?
What parameter does the ratio affect?

[hamdani yusuf (OP)]

And the problem is that you don't understand it.
But, if it makes you heel happier.

I was pointing out your problem, not mine.

[Bored chemist]

Some of us prefer to be pedantic.

Fine,
Answer the pedantic version of the same question.

What is the mechanism by which the system is driven towards the same ratio?
What parameter does the ratio affect?

[hamdani yusuf (OP)]

What is the mechanism by which the system is driven towards the same ratio?
What parameter does the ratio affect?

With different ratio between two sides of the system, heat transfer rate in one direction will be higher than its opposite direction. When the ratio is equal, the transfer rate would be the same.

[Bored chemist]

heat transfer rate in one direction will be higher than its opposite direction.

Why?
There's no driving force for the transfer.

[Bored chemist]

Changes happen for a reason.
If I fill a U shaped tube with water, and I pour more water into one side than the other, the water will flow to equalise the heights.
You can call the parameter "height" or "potential energy" or "pressure", but there is something which starts off unequal, and ends up equal.
Similarly, if I put a hot stone into cold water, heat is transferred from the stone to the water.
The parameter that starts off different  but ends up equal is temperature.
If I put iron into copper sulphate solution the iron dissolves and copper is precipitated.
In this case you can consider the parameter to be "electrode potential" or , more formally a parameter called "chemical potential".

In almost every case where something changes, there's a reason for that change, and it stops when some parameter that was previously unequal becomes equal.

So, for about the 4th time, what do you think it is in the case of the ice and water?

[hamdani yusuf (OP)]

Heat transfers from a hotter body to a colder one, nothing to do with the heat content of either.

If it were otherwise, you would boil every time you (70 kg of water at 37°C) swam in the sea (bazillions of tonnes at 17°C)!

If you want to be pedantic, it's heat content per unit mass. Perhaps it can be called specific heat content.