## 8677 #51

Maxwells_Demon
Posts: 101
Joined: Fri Dec 21, 2007 6:09 am

### 8677 #51

http://grephysics.net/ans/8677/51

I'm torn between A and B. How is A incorrect?

BTW, if it's annoying for me to post this here then let me know. Thanks in advance

-Maxwell's Demon

Imperate
Posts: 105
Joined: Thu Jul 03, 2008 7:01 am

### Re: 8677 #51

Hey, I thought exactly the same thing when I first did this question. Whilst I accept B is true, I find it hard to negate choice A. Since by equipartition, each degree of freedom has 1/2kT, and each atom has 3 kinetic degrees of freedom, 3 potential degrees of freedom, suggesting its average energy is 6*1/2kT=3kT.
Maybe it has something to do with the fact equipartition only applies at high temperatures, and is not a general feature of the Einstein or Debye model, rather just a limit.

Maxwells_Demon
Posts: 101
Joined: Fri Dec 21, 2007 6:09 am

### Re: 8677 #51

For Debye, A is only true for T >> Td where Td is Debye temperature. that's why...

-Maxwell's Demon

muonman
Posts: 29
Joined: Wed Aug 27, 2008 7:19 pm

### Re: 8677 #51

Choice (A) would be correct if we were talking about ideal gases. Except, we're not dealing with gases! We're dealing with a solid. In a solid, think of a 3 dimensional spring mattress. You have an atom in the middle forked by six springs in the three dimensions. Thus you don't have "3 translational" + "3 vibrational" degrees of freedom, which would lead us to the incorrect choice (A). You only have 3 vibrational.