# Validity of Maxwell-Boltzmann distribution for solids [duplicate]

Suppose there is a solid made of avogadro number of, say, aluminium atoms. This solid is kept at 273 K. According to Maxwell-Boltzmann distribution, all the particles or atoms will not have the same thermal energy. Some atoms are cooler than 273 K, some are much warmer than that etc. But is this true?

I mean, according to thermodynamics, heat must flow from warmer to cooler places (or particles) and must arrive at thermal equilibrium so that both places or particles will have same thermal energy or temperature.

So, atleast after some time, all the particles or atoms in a solid as I mentioned above must exchange energy with each other and must arrive at thermal equilibrium so that all the particles will have the same temperature (in the case I mentioned, 273 K), isn't it? But according to Maxwell-Boltzmann distribution, this will not happen.

-Why is this so?

-Or is Maxwell-Boltzmann distribution not valid for solids, so that the atoms will infact have same thermal energy or temperature atleast after some time?

-If it is valid for solids, why don't the atoms all arrive at a state where all of them have same temperature (which should happen from the point of view of thermodynamics)?

Edits:

I could clarify most of my questions from the link of another similar question provided. But, I couldn't find an answer to my last question:

-What might be the approximate value of the thermal energy or the temperature of the particle having maximum energy in the solid I mentioned as predicted by Maxwell-Boltzmann distribution?

• The concept of temperature applies to an ensemble of atoms, not individual atoms. From a solid state physics perspective you have phonons (lattice vibrations) zinging around, just like you have vibrational/rotational states in polyatomic molecules. – Jon Custer Nov 8 '19 at 18:11
• @Ron That's a wrong way to think of it. Consider this: molecules in a gas collide all the time and exchange energy. How come they don't all have the same energy? – Ivan Neretin Nov 8 '19 at 18:32
• Thank you all for helping me. In gases, we can say that a single atom is collided by many atoms, thus the atom aquire more energy than others. This could happen with some other atoms too in a gas. So in gases even if atoms continuously pass on energy by collision, there will be some atoms with more energy because some atoms will be collided by MANY others. But in solids, especially, not many atoms are colliding with a single atom. Only surrounding atoms can vibrate with respect to that single atom. So gradually, in a solid, all atoms will distribute their energy and have same energy, isn't it? – Ron Benny Nov 8 '19 at 19:18
• Thermal vibrations wander through the solid much in the same way as sound does. – Karl Nov 8 '19 at 21:22
• But these thermal vibrations must, over time, become uniformly distributed to all the atoms, must they not? If not, why is it so? Could someone explain it's mechanism? (Like in gases, as I mentioned above, the mechanism is that some atoms may be collided by many others, so that these will have a higher energy). Sorry if I'm asking too complicated questions. – Ron Benny Nov 9 '19 at 7:39