[alancalverd]

Whatever needed by a measuring device / method to produce conclusive result.

A really tiny thermistor, or literally, a gnat's whisker. Mosquitoes and bed bugs have unbelievably good  temperature sensors built on micron scales.

[Deecart]

If the question is always that of the first post (i have read around 6 pages of 15 so far)  :
What happens if you put on each side in a perfect isolated box half ice and half water at 0 C ? (With no air i suppose ?)

Then my answer would be : You will end up with some sort of icebergs at 0C with liquid water cavity inside, in a water at 0C... but you will have less ice than water (you loose some of the ice).
Because : The dynamic system (ice become liquid and reversa) try to maximise the heat exchange, so the surface will be maximum.
So could think, huu, so we end up with isolaed icebergs.
But there is not enought room for that.
And furthermore... immediatly when water can mix with the ice (initialy the ice is stucked to the walls) the Archimed force will add some energy at the system.
So perhaps ice could gain some temperature (0 C at the border but a little bit more inside the ice, heat conduction lowers when the ice is thick (with no proportionality to the tickness of ice).
I dont know exactly how we have to take entropy in account here, but the mixed ice and water block could represent some gain in entropy (disorder) : Therefore this energy is taken from the whole other energys stored in the system (so temperature lowers a bit)
Therefore i have no real clue what will happens finally (not sure if we can really do the calculation in such a complex system).

[alancalverd]

The dynamic system (ice become liquid and reversa) try to maximise the heat exchange,

What heat exchange? Heat flow only occurs if there is a temperarture difference. If not, how would the heat know which way to flow, and when to stop? 

[Bored chemist]

Therefore i have no real clue what will happens finally

Nothing- as Alan pointed out.

(not sure if we can really do the calculation in such a complex system).

We can.
We did.

[Deecart]

What heat exchange? Heat flow only occurs if there is a temperarture difference. If not, how would the heat know which way to flow, and when to stop? 

Sure there is heat exchange, or kinetic energy flow if you prefer.
If you had two molecules that could not interact, i would agree with you : You could in this case say that there is some heat exchange only if you take some very small volume, due to the variability of vibration (very small so very small heat exchange, even with small volume).

But here, we have something else and it is very interesting in term of interaction.
You have only water but in 2 states.
And the two states are at the limit where (statisticaly...) they can become liquid or solid.

You surely know the fact that if you let some liquid water in a pot at room temperature, it evaporate.
There is no need to reach the 100°C boiling temperature to have the liquid water become vapor water.
Same with ice, wich can become liquid or even vapor at 0°C.
It is due to the fact that the speed of the molecules match statisticaly to the average temperature, but individualy they can be slower or faster (i take here the simple representation) and therefore interact to become ice, liquid or vapor.

And moreover, every time such a molecule change its state, it will also add or remove some kinetic energy !
 

Phase changes are always accompanied by a change in the energy of a system. For example, converting a liquid, in which the molecules are close together, to a gas, in which the molecules are, on average, far apart, requires an input of energy (heat) to give the molecules enough kinetic energy to allow them to overcome the intermolecular attractive forces. The stronger the attractive forces, the more energy is needed to overcome them. Solids, which are highly ordered, have the strongest intermolecular interactions, whereas gases, which are very disordered, have the weakest.

Thus any transition from a more ordered to a less ordered state (solid to liquid, liquid to gas, or solid to gas) requires an input of energy; it is endothermic.

Conversely, any transition from a less ordered to a more ordered state (liquid to solid, gas to liquid, or gas to solid) releases energy; it is exothermic.

https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/11%3A_Liquids_and_Intermolecular_Forces/11.04%3A_Phase_Changes

So solid to liquid phase transformation is endothermic (it lower the kinetic energy available to the system).
And liquid to solid phase transformation is exothermic (it upgrade the kinetic energy available to the system).

When ice form, it add heat and when ice melt it lower heat.
Therefore, these transformations (you can not avoid) will produce the flow of the heat we are talking about, even if the average temperature of both phases are equal.

[alancalverd]

It is due to the fact that the speed of the molecules match statisticaly to the average temperature,

If you start with an incorrect statement, you can confuse yourself.

Temperature is a measure of the average kinetic energy of the molecules in a sample, not the other way around.

[Deecart]

If you start with an incorrect statement, you can confuse yourself.

Temperature is a measure of the average kinetic energy of the molecules in a sample, not the other way around.

I am not confused : "match" is equivalent to "be linked".
But this was only to say (i sbould not have talked about temperature in my sentence) : The kinetic energy of every individual molecule differ randomly, thats all.

[hamdani yusuf (OP)]

My plan to improve the signal over noise ratio of the experiment is by improving heat insulation between the system and its surrounding. I'll build a multilayer styrofoam box, closed in all six sides. The box will be divided into 3 compartments.

Between first and second compartment is a thermal conductor, such as aluminum plate. While second compartment is separated from third compartment by thermal insulator, such as Styrofoam plate.

Second compartment will be filled by 90% ice & 10% water, while first and third compartment will be filled by 10% ice & 90% water. Heat transfer with the environment should be equal between first and third compartment. If there are different result, it must come from heat transfer with second compartment.

Is there any objection to this plan?

I finally finished the experiment, after some unexpected challenges. The Styrofoam board I used turned out to be leaky. I covered the internal sides of the Styrofoam box using the hot melt glue used to stick the boards to form the box. But it was still leaky, and the Styrofoam shrunk when overheated. Finally the problem was solved by applying wax layer on top of the glue layer, using candles and hot air gun.

The experiment itself brought its own problems. But they can finally be solved. I'll upload the video when I'm done editing it.

[Origin]

I finally finished the experiment, after some unexpected challenges. The Styrofoam board I used turned out to be leaky. I covered the internal sides of the Styrofoam box using the hot melt glue used to stick the boards to form the box. But it was still leaky, and the Styrofoam shrunk when overheated. Finally the problem was solved by applying wax layer on top of the glue layer, using candles and hot air gun.

The experiment itself brought its own problems. But they can finally be solved. I'll upload the video when I'm done editing it.

What a silly waste of time and energy.  Your time would be much better spent learning some physics.

[hamdani yusuf (OP)]

What a silly waste of time and energy.  Your time would be much better spent learning some physics.

You can't learn new things if you think you already know the answer.

[Origin]

You can't learn new things if you think you already know the answer.

Yes, we do know the answer.  You're not learning anything new, you are just wasting time.
The answer was given to you in the first reply and you have wasted your time and others in this never ending merry-go-round thread.

[alancalverd]

Let's go back to everyone's first physics lesson, or thereabouts. We learned that "temperature is the measure of hotness or coldness" (definition), and "heat flows from a hotter body to a colder body" (observation). Therefore if two bodies are at the same temperature, there can be no heat flow between them.

[hamdani yusuf (OP)]

You can't learn new things if you think you already know the answer.

Yes, we do know the answer.  You're not learning anything new, you are just wasting time.
The answer was given to you in the first reply and you have wasted your time and others in this never ending merry-go-round thread.

You can't learn new things if you think you already know the answer.

Yes, we do know the answer.  You're not learning anything new, you are just wasting time.
The answer was given to you in the first reply and you have wasted your time and others in this never ending merry-go-round thread.

You won't know that your beliefs are false until experimental evidence contradicts them.
You won't know what factors can affect experimental results which will make you have inaccurate predictions. 

[hamdani yusuf (OP)]

Let's go back to everyone's first physics lesson, or thereabouts. We learned that "temperature is the measure of hotness or coldness" (definition), and "heat flows from a hotter body to a colder body" (observation). Therefore if two bodies are at the same temperature, there can be no heat flow between them.

My experiment tests the prediction made with following assumptions :
1. No heat flow without temperature difference.
2. Water-ice mixture at equilibrium in atmospheric pressure has temperature around 0 degree Celsius, irrespective of the ratio.

My experimental result indicates that at least one of them must be false.

[alancalverd]

It is not a prediction, it is a definition.
If heat flows from A to B then by definition A is at a higher temperature than B.
At equilibrium, by definition of "equilibrium", there is no heat flow.

[hamdani yusuf (OP)]

It is not a prediction, it is a definition.
If heat flows from A to B then by definition A is at a higher temperature than B.
At equilibrium, by definition of "equilibrium", there is no heat flow.

Do you think that the second assumption is false?

[Bored chemist]

It is not a prediction, it is a definition.
If heat flows from A to B then by definition A is at a higher temperature than B.
At equilibrium, by definition of "equilibrium", there is no heat flow.

Do you think that the second assumption is false?

What "assumption"?

Incidentally:
https://en.wikipedia.org/wiki/Zeroth_law_of_thermodynamics

[alancalverd]

A definition is not an assumption.

[Origin]

My experiment tests the prediction made with following assumptions :
1. No heat flow without temperature difference.

So then you have your answer to this thread, which is, "Is there a net heat exchange between water and ice at 0 degree C?"

[hamdani yusuf (OP)]

What "assumption"?

My experiment tests the prediction made with following assumptions :
1. No heat flow without temperature difference.
2. Water-ice mixture at equilibrium in atmospheric pressure has temperature around 0 degree Celsius, irrespective of the ratio.

My experimental result indicates that at least one of them must be false.