[hamdani yusuf (OP)]

In practice, it's hard to get 100% ice or 100% water at exactly 0°C. It's easier to have ice at less than 0 and water at higher than 0°C.
Let's say that initially, the ice is -0.1°C while the water is 0.1°C. Temperature difference will cause energy transfer from water side to ice side until they have the same temperature, 0°C in this case. What will happen next? Will the energy transfer suddenly stop? Or it continues until reaching equilibrium, where both sides have the same water/ice ratio?

[Bored chemist]

In practice, it's hard to get 100% ice or 100% water at exactly 0°C.

Not really. Get some ice, a little below freezing , put it in a closed container and put that in a slurry of crushed ice and water.
It will warm up to exactly 0C
Get some water, just above freezing, Seal it in a container and put it in a slurry of ice and water, it will cool down to exactly 0C.

Will the energy transfer suddenly stop?

No, it will gradually stop.
After a while, the difference will be smaller than the random thermal variation.

[hamdani yusuf (OP)]

If it takes an hour to notice any melting, but the fluctuations only last a nanosecond, will you notice any melting due to the fluctuations?

What I really can't understand is how you didn't realise that this was important.

We will notice the melting and freezing after the imbalanced fluctuations accumulate in both sides. If each fluctuation lasts longer, then there will be fewer number of them in an hour,  and vice versa.

[Eternal Student]

Hi.

ES Said:    Sadly, that's still a minor issue.   Work,  pΔV,   is done on a system if there's a volume change ΔV  while maintaining constant pressure p.
Hamdani replied:    Where does the energy come from, and where does it go to?

Where the container expands,  work is done on the container by the system (the water region with net freezing).   The container walls acquire the energy, the system loses that energy.   If it's a container of the type you described (something elastic that tried to maintain a a constant pressure) most of the energy in the walls would be described as elastic potential.  In the more general case, we don't care what form the energy takes in the walls of the container, it's usually heat which ultimately escapes to the outer environment.  All that's important is that the system has done work on something external to the system.
     Opposite idea where the container walls contract.   Here the external environment has done work on the system.

Here is what I found in Wikipedia. Does it also apply to liquid and solid?
Quote
    (Integral formula appeared here) 

   Yes, for a container that maintains constant pressure, which is what you suggested, that integral reduces to p.ΔV.
This is some work done on the environment by the system (or vice versa if its negative).   There can also be other ways of doing work on the system but that doesn't matter.   Changing the volume of the container while the system was exerting pressure on the container walls is certainly one way.  It doesn't matter if the system is a mixture of solid and liquid, an ideal gas, or something else.
   
Best Wishes.

[Bored chemist]

We will notice the melting and freezing after the imbalanced fluctuations accumulate in both sides.

Why do you imagine that the fluctuations are not balanced?
Do you not understand what equilibrium means?

[hamdani yusuf (OP)]

Not really. Get some ice, a little below freezing , put it in a closed container and put that in a slurry of crushed ice and water.
It will warm up to exactly 0C
Get some water, just above freezing, Seal it in a container and put it in a slurry of ice and water, it will cool down to exactly 0C.

What's hard is getting the left compartment filled with pure ice while the right compartment contains pure water. We will need to maintain air temperature at 0°C, so is the tools we use to transport the water and ice. The lighting  should also be taken into account, as well as body temperature of the experimenter.

[Bored chemist]

Not really. Get some ice, a little below freezing , put it in a closed container and put that in a slurry of crushed ice and water.
It will warm up to exactly 0C
Get some water, just above freezing, Seal it in a container and put it in a slurry of ice and water, it will cool down to exactly 0C.

What's hard is getting the left compartment filled with pure ice while the right compartment contains pure water. We will need to maintain air temperature at 0°C, so is the tools we use to transport the water and ice. The lighting  should also be taken into account, as well as body temperature of the experimenter.

It is easy.
You do everything in a tank of ice cold water.

[hamdani yusuf (OP)]

It is easy.
You do everything in a tank of ice cold water.

Easy to say, but hard to do. Otherwise, someone must have done it already, and we can just watch the video.

[alancalverd]

This sort of experiment has been done hundreds of times, to establish the triple point and phase diagram of water.

[Bored chemist]

Otherwise, someone must have done it already

How the  **** do you think we know what the melting point of water is?
Messieurs Laplace and Lavoisier didn't video it, because they did the experiment in 1782.
https://www.nature.com/scitable/content/ice-calorimeter-developed-by-lavoisier-and-laplace-14898943/

[hamdani yusuf (OP)]

This sort of experiment has been done hundreds of times, to establish the triple point and phase diagram of water.

How are the results? Are they consistent with each other?
Does the ice side still free from water, and the water side free from ice?

[Bored chemist]

How are the results?

Extremely good.

Are they consistent with each other?

Obviously, yes.

Does the ice side still free from water, and the water side free from ice?

Yes.

Do you realise that you are asking "Does basic science work?"?

[Bored chemist]

https://www.nist.gov/video/triple-point-cell

https://isotech.co.uk/wp-content/uploads/2020/09/The-Establishment-of-ITS-90-Water-Triple-Point-References-to-%C2%B12uK-and-the-Assessment-of-100-Water-Triple-Point-Cells-Made-Between-2001-and-2006.pdf

[hamdani yusuf (OP)]

Otherwise, someone must have done it already

How the  **** do you think we know what the melting point of water is?
Messieurs Laplace and Lavoisier didn't video it, because they did the experiment in 1782.
https://www.nature.com/scitable/content/ice-calorimeter-developed-by-lavoisier-and-laplace-14898943/

Did the experiment initially separate the ice from water?

[alancalverd]

A rotating magnet and an aluminum disk can have the same initial temperature. But when they are brought close to each other, some temperature increase is observed on the aluminum disk.

because you are supplying energy to rotate the magnet. If you don't, no heat is generated.

[hamdani yusuf (OP)]

A rotating magnet and an aluminum disk can have the same initial temperature. But when they are brought close to each other, some temperature increase is observed on the aluminum disk.

because you are supplying energy to rotate the magnet. If you don't, no heat is generated.

What if it's the aluminum disk which was initially rotating,  while the magnet was stationary?  I think that energy transfer and conversion still happen. Similar case would happen if the aluminum disk was attached to a spring and vibrate at resonance frequency.

My point is that equality in temperature doesn't guarantee the absent of energy transfer, especially when some other forms of energy are involved. 

[Bored chemist]

What if it's the aluminum disk which was initially rotating,

then you would be supplying energy.

My point is that equality in temperature doesn't guarantee the absent of energy transfer, especially when some other forms of energy are involved. 

It guarantees that you don't get heat transfer.

[alancalverd]

What if it's the aluminum disk which was initially rotating,  while the magnet was stationary? 

Makes no difference - all the disc "sees" is relative rotation.

[hamdani yusuf (OP)]

Similar case would happen if the aluminum disk was attached to a spring and vibrate at resonance frequency.

What if the magnet is replaced by an electret?

[Bored chemist]

Similar case would happen if the aluminum disk was attached to a spring and vibrate at resonance frequency.

What if the magnet is replaced by an electret?

You still would not be talking about exchange of heat, so it still wouldn't be anything to do with the title of the thread.