socolenco_ 20150918 23:21:35  You have [] for entropy and [] for internal energy and their ratio is, which is exactly the reciprocal of the Kelvin temperature TÂ°.\r\n  
ryanjsfx 20140921 13:08:27  I'm not sure my logic is sound but I got this just by process of elimination.
We're looking for inverse of T, so eliminate A and B since they look normal (not inverted) expressions.
If T changes, so does U [U = U(T)]. Eliminate C and D.
That leaves E.  
spacemanERAU 20091018 18:22:02  how do you know the volume is constant?
neon37 20101103 11:30:43 
because needs to be zero in So that we can use . Otherwise, the answer would be complicated and you would have to reciprocate the whole thing. And there is no complicated answer in the question.

flyboy621 20101114 22:13:36 
You don't know the volume is constant. What you know is that IF you hold the volume constant while differentiating the entropy with respect to internal energy, you get the inverse of the temperature. Whenever you take a partial derivative, you have to hold something constant.

 
Hardik 20081106 13:11:39  Use statistical definition of temperature and entropyrnrnvoila  
student2008 20081012 06:31:38  Actually, one can recall the general differential expression for the energy of a system . Thus, .
flyboy621 20101114 22:14:45 
Perfect solution!

 
carlospardo 20071003 13:10:49  All this is unnecessary. When obvious, select the answer with correct units.
djh101 20140828 13:46:39 
I can recall dU = TdS  PDV off the top of my head better than units of entropy (which I would probably derive from that equation anyway).

 
carlospardo 20071003 13:10:48  All this is unnecessary. When obvious, select the answer with correct units.  
WTarrasque 20061103 19:12:23  In the compiled solutions PDF, the reciprocal is only taken of one side. Thus it has:
instead of  
jax 20051203 10:59:32  You mean is the correct answer, right?
yosun 20051204 23:11:43 
right. note that the above is given in terms of inverse Temperature  a commonly used multiplier quantity in thermo.

jax 20051205 06:51:18 
Doesn't the question ask for inverse temperature? When I worked it out I got

walczyk 20110310 21:54:37 
at extremely low energies, a small change in energy amounts to a huge gain in entropy, so the inverse T is huge, and T is tiny.

 