# Equation of State from Partition Function

#### howin

1. The problem statement, all variables and given/known data

Find the partition function for a two-dimensional nonrelativistic classical gas. Find the equation of state. Calculate the specific heat at constant volume cv and the entropy S.

2. Relevant equations

The partition function is Z = (A^N / N!) [(2 pi m k T / h^2)^N] e^NE/kT

Cv = partial derivative of U w/ respect to T = kB^2 (partial ^2 ln Z / Partial B^2)

S = - partial F w/ respect to T

3. The attempt at a solution

From the partition function, get G=F + pA = -Nkt [ln A/N + ln (2 pi m k T/h^2) + E/kT]

mu = -kT [ln A/N + ln (2 pi m k T/h^2) + E/kT]

I think I have the right equations and can get the partition function, but can't figure out how to get the equation of state from the partition function. I've looked through books but they all refer to experimental calculations of the equation of state for a two-D gas.

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