[hamdani yusuf (OP)]

Uhm, your theory sounds interesting, have you tried it?

I have used ice/water calorimetry in the past, and as I keep repeating, it is extremely difficult, even with the resources of a national standards laboratory, to do well. To attempt to use it to disprove the most fundamental statement of thermodynamics using domestic kitchen equipment, is beyond foolish.

Do you cover the top of the system with water and ice mixture?

I have to admit the technique isn't really "mine". It was developed by some "famous names".
https://www.nature.com/scitable/content/ice-calorimeter-developed-by-lavoisier-and-laplace-14898943/

The top side looks uninsulated, which can cause heat leakage.

[JosephCook]

Uhm, your theory sounds interesting, have you tried it?

I have used ice/water calorimetry in the past, and as I keep repeating, it is extremely difficult, even with the resources of a national standards laboratory, to do well. To attempt to use it to disprove the most fundamental statement of thermodynamics using domestic kitchen equipment, is beyond foolish.

Got it. Thanks for your answer. I am impressed even by your trial, good one.

[Bored chemist]

I know what a straw man argument is.
It's irrelevant.
Can you quote the post where you said that you did this experiment properly- well lagged and submerged in well stirred ice and water and told us how you did it and what the results were?

[hamdani yusuf (OP)]

I know what a straw man argument is.
It's irrelevant.
Can you quote the post where you said that you did this experiment properly- well lagged and submerged in well stirred ice and water and told us how you did it and what the results were?

I thought you already knew what the results would be before doing the experiment.
I'm keeping the raw footage of the "failed" experiments. I should  have publised all of them, but editing the video and adding narration are time consuming. I choose to spend that time to do something more productive. Although it's possible that I 'll just compile and upload them as behind the scenes for the conclusive result.

[Bored chemist]

I choose to spend that time to do something more productive.

LOL

[hamdani yusuf (OP)]

It won't.
Because, that would require the transfer of heat to or from teh ice and, because everything is at the same temperature, there is no impetus to drive the energy from one place to another.

Why do you not understand and accept this?
Which bit does not make sense to you?

It seems that the energy flow can be driven by gravity through buoyancy and temperature difference. So, if a liter of ice-water mixture is in an insulated container, and initially well mixed, the top side will gradually become cooler than the bottom side. The ice will be naturally  separated from the water through buoyancy. 
Heat conductance of water will reduce the difference. But given adequately tall container, its effect can be minimized.

[Bored chemist]

It seems that the energy flow can be driven by gravity through buoyancy and temperature difference.

You can only use temperature difference to move energy if you actually have a temperature difference.
Do you not realise that you ruled that out when you asked "Is there a net heat exchange between water and ice at 0 degree C?"?
If it's all at 0C there is no temperature difference.

The ice will be naturally  separated from the water through buoyancy. 

Yes, ice floats

the top side will gradually become cooler than the bottom side.

How?
Where is the energy coming from or going to?
What is providing the impetus to drive that energy transfer?

[hamdani yusuf (OP)]

It seems that the energy flow can be driven by gravity through buoyancy and temperature difference.

You can only use temperature difference to move energy if you actually have a temperature difference.
Do you not realise that you ruled that out when you asked "Is there a net heat exchange between water and ice at 0 degree C?"?
If it's all at 0C there is no temperature difference.

The ice will be naturally  separated from the water through buoyancy.

Yes, ice floats

the top side will gradually become cooler than the bottom side.

How?
Where is the energy coming from or going to?
What is providing the impetus to drive that energy transfer?

The energy is provided by the environment, because practically, insulations can't be perfect. Even if the insulation is also made of a bath of ice-water mixture, to several layer like Russian dolls. The outer most layer will still interact with environment, which is then propagated to the inner layers.
The other factor is temperature variation inside the system itself. Slight temperature difference due to quantum fluctuation might make slight difference of density, which makes hotter molecules tend to move downward. This effect can be nullified by heat conductance of water. Which effect is stronger can be shown by an experiment.

[alancalverd]

The energy is provided by the environment, because practically, insulations can't be perfect.

And that's most of the problem with heat experiments. Electrical insulators are zillions of times less conductive than heat insulators even if they are made of the same stuff.

So, if a liter of ice-water mixture is in an insulated container, and initially well mixed, the top side will gradually become cooler than the bottom side. The ice will be naturally  separated from the water through buoyancy.

Told you so, many times. Which is why you need a continuously-stirred slush. Melting snow is a good start.

[Bored chemist]

The energy is provided by the environment, because practically, insulations can't be perfect.

In which case, you do not meet the requirement stated in the title
"Is there a net heat exchange between water and ice at 0 degree C?"

Why do you keep going round in circles about this?

which is then propagated to the inner layers.

Are you deliberately missing the point?
Heat leaks in through the outermost layer.
And it melts ice.
So the temperature there stays at 0C.
So the inner layers are totally isolated.
Now, I realise that, in practice, this is difficult.
But, in principle, the process works.

Which effect is stronger can be shown by an experiment.

Or by calculation.
Quantum effects are small.

[hamdani yusuf (OP)]

Told you so, many times. Which is why you need a continuously-stirred slush. Melting snow is a good start.

I'm thinking about circulating the cool water using a small pump, like the one used in aquariums.

[Bored chemist]

Told you so, many times. Which is why you need a continuously-stirred slush. Melting snow is a good start.

I'm thinking about circulating the cool water using a small pump, like the one used in aquariums.

Don't forget to allow for the heat it adds.

[alancalverd]

I'm thinking about circulating the cool water using a small pump, like the one used in aquariums.

Better to use BC's suggestion of an"extracorporeal" pump and chiller. You can get a good one from a cardiac surgical unit, though we generally run them at something closer to body temperature.

[hamdani yusuf (OP)]

Told you so, many times. Which is why you need a continuously-stirred slush. Melting snow is a good start.

I'm thinking about circulating the cool water using a small pump, like the one used in aquariums.

Don't forget to allow for the heat it adds.

Alternatively, I can use ice blocks held to the bottom of the container using a cage. Slightly warmer water coming down to the bottom will be cooled down by the ice, and flow back up again, producing a natural circulation that stabilizes temperature and makes it more uniform.

[Bored chemist]

Do you really not understand that, if you have convection currents your system is not at 0^oC?

What do you think dives the currents?
Did you think it was magic?

[alancalverd]

To repeat the obvious answer to the original question: No, by definition.

[hamdani yusuf (OP)]

Do you really not understand that, if you have convection currents your system is not at 0^oC?

What do you think dives the currents?
Did you think it was magic?

It looks like you have difficulties to understand more than one layer of conversation. Why do you think I need to use a pump in the first place?

[hamdani yusuf (OP)]

To repeat the obvious answer to the original question: No, by definition.

How does it help to predict experimental results?

[Bored chemist]

Why do you think I need to use a pump in the first place?

Because you can't rely on convection currents, and the ice/ water system needs to be well stirred.

Now, try actually answering this.

Do you really not understand that, if you have convection currents your system is not at 0oC?

What do you think dives the currents?
Did you think it was magic?

Especially in the context of

I can use ice blocks held to the bottom of the container using a cage. Slightly warmer water coming down to the bottom will be cooled down by the ice, and flow back up again, producing a natural circulation

Once you have "slightly warmer water" you are no longer at 0^oC

[alancalverd]

To repeat the obvious answer to the original question: No, by definition.

How does it help to predict experimental results?

It predicts them absolutely, fully, and completely.
But only if you do a very good experiment, and that's very difficult with water.