contestada

1. Using Pj= e^-BE/Z in the Gibb’s form for
the entropy, show that
F = kb Tln(Z), where F = U – TS is
the Helmholtz free energy. Here Z=
e^-BE is the canonical partition
function..

Respuesta :

Answer:

Explanation:

Solution. The Gibbs formula for the entropy is

S = −KB∑pi ㏑(pi).

Using the Boltzmann probability in the canonical ensemble pi = exp(−βEi)/Z, we have,

S = −kB∑ pi[ -(Ei ÷ KBT) - ㏑(Z)] = (U÷T)+ kBln(Z) so U − T S = −kBTln(Z),

where we used∑ P i = 1 , U= ∑i piEi

Answer:

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Explanation:

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