[hamdani yusuf (OP)]

And there is no reason why a single molecular interaction should depend (at least to the first order) on the kinetic energy of any other molecules.

That's precisely why I said that perhaps the variation can produce observable effects, which was the reason I made the experiment in the first place. I wouldn't waste my time if I was sure that there would be no variation, nor if I thought that it's impossible to observe the effects.

[alancalverd]

It would be impossible to observe any effect because for every interaction A -> B there will be, somewhere, an equal and opposite B->A, due to the definition of temperature. So how do you choose which molecule to observe?

[hamdani yusuf (OP)]

It would be impossible to observe any effect because for every interaction A -> B there will be, somewhere, an equal and opposite B->A, due to the definition of temperature. So how do you choose which molecule to observe?

There are at least 4 processes may accompany thermal fluctuation in the experiment:
increase of local temperature.
decrease of local temperature.
melting.
freezing.
The first two involve changing of kinetic energy. The last two involve changing of potential energy.
I choose to observe the molecules which undergo freezing. Ice is less dense than water. It tends to float and accumulates on the water surface.

[alancalverd]

"Thermal fluctuation" implies a change in temperature.
Either you are going to alter the average internal kinetic energy of something (i.e. change its temperature) or not.
If you alter any temperature your result will not be an answer to the question.
If you don't, you have simply confirmed that you understand the meaning of "temperature". 

[hamdani yusuf (OP)]

"Thermal fluctuation" implies a change in temperature.
Either you are going to alter the average internal kinetic energy of something (i.e. change its temperature) or not.

One part of an object can increase its temperature while another part decrease its temperature, thus the average temperature doesn't change.

[alancalverd]

You are beginning to grasp the meanings of "internal" "kinetic", "net" and "average". So far so good.

Except for the anthropic "can increase its temperature". Not spontaneously or idiogenically, unless you are talking about yogic physiology or hibernating mammals. Or maybe dragonflies, who warm up their engines before takeoff.

[hamdani yusuf (OP)]

Have you heard about cosmic rays, microwave background, quantum fluctuation, Heisenberg uncertainty, and zero point energy?

[alancalverd]

Frequently. I  am a physicist.

[Bored chemist]

One part of an object can increase its temperature while another part decrease its temperature, thus the average temperature doesn't change.

The problem with sating that (well one problem) is the temperature of something is always an average.

So what you are saying is that the average changes, but the average doesn't change.

[hamdani yusuf (OP)]

One part of an object can increase its temperature while another part decrease its temperature, thus the average temperature doesn't change.

The problem with sating that (well one problem) is the temperature of something is always an average.

So what you are saying is that the average changes, but the average doesn't change.

You forget to distinguish between local and global temperature.

[alancalverd]

There is no such thing as "local" temperature at the molecular level. Temperature is a property of an assembly, not a single particle or even a small sample.

[Eternal Student]

Hi.

   I don't suppose I've managed to read every post since I was last here but I think I've got the gist.
I have to strongly agree with what @alancalverd and @Bored chemist  have just tried to say:

   It is dangerous and difficult to try and consider "local temperature" when you're considering a volume so small that you have only a few molecules.   It makes very little sense to model that volume as one homogeneous body with many particles that have an average kinetic energy corresponding to the given temperature (because it just does not have many particles - so by assuming it has you're almost bound to get nonsense results and consequences).

    Yes, the phrase "local temperature" is used frequently but not on those small scales.  The weather presenter will tell you that the temperature of the air in Spain is different to the temperature in Canada.   However that's still millions of particles of Nitrogen that exist in a given region.  It is reasonable to model that volume and number of particles as one homogeneous body with a well defined temperature.

Best Wishes.

[Bored chemist]

One part of an object can increase its temperature while another part decrease its temperature, thus the average temperature doesn't change.

The problem with sating that (well one problem) is the temperature of something is always an average.

So what you are saying is that the average changes, but the average doesn't change.

You forget to distinguish between local and global temperature.

You invented a distinction that does not actually exist.

[hamdani yusuf (OP)]

Hi.

   I don't suppose I've managed to read every post since I was last here but I think I've got the gist.
I have to strongly agree with what @alancalverd and @Bored chemist  have just tried to say:

   It is dangerous and difficult to try and consider "local temperature" when you're considering a volume so small that you have only a few molecules.   It makes very little sense to model that volume as one homogeneous body with many particles that have an average kinetic energy corresponding to the given temperature (because it just does not have many particles - so by assuming it has you're almost bound to get nonsense results and consequences).

    Yes, the phrase "local temperature" is used frequently but not on those small scales.  The weather presenter will tell you that the temperature of the air in Spain is different to the temperature in Canada.   However that's still millions of particles of Nitrogen that exist in a given region.  It is reasonable to model that volume and number of particles as one homogeneous body with a well defined temperature.

Best Wishes.

Can we measure the temperature of water in a 1 cubic micron?
What's the guarantee that its temperature is exactly the same as its neighboring water body?

[alancalverd]

(a) probably
(b) negligible

But the answer to the OP remains "no".

[Bored chemist]

Can we measure the temperature of water in a 1 cubic micron?
What's the guarantee that its temperature is exactly the same as its neighboring water body?

Over what timescale?

[Eternal Student]

Hi.

Can we measure the temperature of water in a 1 cubic micron?

    I'm going to say no, not reliably or meaningfully.
There's no set scale at which everyone declares that it's unreasonable to assign a temperature, instead the approximation (treating the region as a homogeneous body with many particles, having average energy corresponding to the temperature) just becomes progressively less useful. 

Best Wishes.

[Bored chemist]

I'm going to say no, not reliably or meaningfully.

Others may differ
http://users.mrl.illinois.edu/cahill/intel08.pdf

But if you asked about a nanometre cubed, it would be tricky.

[hamdani yusuf (OP)]

Can we measure the temperature of water in a 1 cubic micron?
What's the guarantee that its temperature is exactly the same as its neighboring water body?

Over what timescale?

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

[Bored chemist]

Can we measure the temperature of water in a 1 cubic micron?
What's the guarantee that its temperature is exactly the same as its neighboring water body?

Over what timescale?

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

Good.
That means that the answer is simple. If the water you are seeking to measure the temperature of is in equilibrium with ice then the temperature is (on average) 0C.