[itex] \tau = k_{B} T [/itex](adsbygoogle = window.adsbygoogle || []).push({});

a) Find the expression for the free energy as a function of the temperature of the system with two states - one iwth eneryg zero and one with energy [itex] \epsilon_{0} [/itex]

b) From the free energy find the expressions for the energy and entropy of the system

c) Plot the average energy and the entropy as a function of tau. [itex] \tau = k_{B} T [/itex]

Ok for a) wek now that

[tex] F = U - T \sigma [/tex]

Partition fun ction [itex] Z = \sum_{s} \exp(-\epsilon_{s}/\tau) = 1 + \exp(-\epsilon_{0}/\tau) [/itex]

so then

[tex] U = \frac{\epsilon_{0} \exp(-\epsilon_{s}/\tau)}{1 + \epsilon_{0} \exp(-\epsilon_{s}/\tau)} [/tex]

but im not quite sure how to proceed with the calculation of the entropy, sigma ...

for b)

for entropy use this

[tex] \sigma = \left(\frac{\partial F}{\partial \tau}\right)_{V} [/tex]

but not sure about how to find the nergy for hte system... is it simply the expression wh9ich doesnt involve tau??

I was thiking a bit more

isnt helmholtz free enryg given by simple

[tex] F- F(0) = -\tau \log Z [/tex]??

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# Homework Help: Helmholtz Free Energy

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