GR9277 #73



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Comments 
QuantumCat 20140925 13:22:16  = ln
At any arbitrarily high temperature, the system only has two accessible states, so = ln(). C is the only answer choice with this.
The third law of thermodynamics says that the in entropy of a system approaches zero at absolute zero. Also because we cannot directly measure entropy, I think it is a bit of a misnomer to say that entropy is 0 at T = 0, but not according to ETS...   Ami 20091008 06:44:31  the partition function is not as mantiond but:
.
carle257 20100410 01:14:01 
Why do we not just choose E1 to be zero? Simplifies things a bit.

flyboy621 20101022 16:23:49 
Ami,
You are correct, but it's simpler to set , which is perfectly OK and simplifies the algebra. Then

  le.davide 20091005 00:03:34  What about the degrees of degeneracy in the partition function?
Ami 20091008 16:00:41 
one for each energy level for each system...
what's wrong with that?

  Poop Loops 20081025 17:38:11  You can also look at this conceptually. Remembering that as , you already eliminate all but 2 choices.
It's tempting to think that Entropy can increase indefinitely, but think about what's going on here. Say this system is a perfect gas. As temperature increases, so does entropy because everything is getting more and more disordered. But, at really high temperatures, every particle is already zooming around everywhere really fast, so you can't really get *more* disorder.   Imperate 20081016 12:54:18  A simple way to see that C is the correct answer is that at low temps all the subsystems reduce into the lowest state E_1, and thus the number of accessible microstates of the whole system is just one at abs zero (so S=klnW=kln(1)=0). But at arb high temps, each system is equally likely to be in E_1 or E_2, so you have a two level system (just like the isolated spin1/2 paramagnet at high temps), and to find the microstates of the whole system it's like finding how many ways to arrange O's and X's on a checkboard with N places. Thus there are W=2^N microstates at high temps, and entropy is S=kln2^N=kNln2.
  sharpstones 20070326 18:39:34  Not to be too nitty gritty but . In our case at high T where Z = 2 then it reduces to the right answer.
insertphyspun 20110628 14:33:53 
Yes, that was my problem with the original solution! Don't confuse the microcanonical partition function with the canonical partition function (or the grandcanonical for that matter).

 




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