EntropyQ

EntropyQ - Entropy and the Partition Function k Ensemble: S...

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Entropy and the Partition Function Ensemble: S = k N ln W max W = N ! n 1 ! n 2 ! n 3 !... ε ε ε ε ε ε ooooo ooo oo o 3 5 4 2 1 n =5 n =3 n =2 n =1 n =0 1 2 3 4 5 ln W = ln N ! – ln n i ! Sterling's Formula: ln x! = x ln x - x ln W = N ln N – N (n i ln n i - n i ) n i = N so ln W = N ln N n i ln n i n i = N Q e -E i /kT ln n i = ln N - ln Q - E i kT ln W = N ln N i n i ln N + i n i ln Q + i n i E i kT ln W = N ln N - N ln N + N ln Q + ε kT S = k N ln W max = k ln Q + ε N T = k ln Q + U - U(0) T ideal gas: U - U(0) = 3/2 nRT = 3/2 NkT
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This document was uploaded on 02/22/2012.

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