# Is the third law of thermodynamics valid for nanoparticles?

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The third law of thermodynamics is deduced in the thermodynamic limit, which includes a material of infinite size.

Nanoparticles have a small finite size. Do the still obey the third law of thermodynamics?

Are there any experimental tests foe the issue?

(Can a temperature be assigned to them at all?)

One can still use the canonical ensemble, hence there is a well-defined temperature. But the equilibrium state is now much more fragile, so that fluctuations are far more important than in the macroscopi case.

You might find the following recent article interesting:

Loukhovitski, B. I., Pelevkin, A. V., & Sharipov, A. S., Toward size-dependent thermodynamics of nanoparticles from quantum chemical calculations of small atomic clusters: a case study of $(B_2O_3)_n$, Physical Chemistry Chemical Physics 24 (2022), 13130–13148.

Thank you - this is interesting!

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Nanoparticles have a small finite size. Do the still obey the third law of thermodynamics?

Can a temperature be assigned to them at all?

It really depends on the environement. If your nanoparticle is alone in a cold vacuum, it will undergo radiative cooling up to $T=0$.

If it is inside a huge thermostat with a certain temperature, then it will have the same temperature due to energy exchange with the termostat.

Microscopic scale energy density fluctuations happen even in an infinite system, thus a thermometer must be sufficiently macroscopic to avearge those fluctuations.

Above I implied that the temperature is low enough in order to speak of your nanoparticle. If the temperature is high enough, then your nanoparticle may melt or evaporate. You see, in Physics many things are implied. Matematically these things are expressed with some inequalities.

answered Jan 19 by (102 points)
edited Jan 22

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