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Statistical Mechanics (Thermal and Statistical Physics) Instruction: Write ALL the solutions of this (necessary or and not direct answer). Write also the equations that are needed to solve for a certain problem. Thank you.
3. The canonical partition function of the classical monatomic ideal gas is
1 [V]
where λT
h
√2лmkT
Show that in the thermodynamic limit, the Helmholtz free energy per particle is
F(T,V,
F (T, V, N) = - KT [in (VIN) + 1]
N
=
Z(T,V,N) = ·
b. Find the entropy S(T,V,N).
c.
N!
Change the variables S(E,V,N) using E = 3/2 NKT and compare the resulting expression to the
entropy derived through the microcanonical ensemble
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Transcribed Image Text:3. The canonical partition function of the classical monatomic ideal gas is 1 [V] where λT h √2лmkT Show that in the thermodynamic limit, the Helmholtz free energy per particle is F(T,V, F (T, V, N) = - KT [in (VIN) + 1] N = Z(T,V,N) = · b. Find the entropy S(T,V,N). c. N! Change the variables S(E,V,N) using E = 3/2 NKT and compare the resulting expression to the entropy derived through the microcanonical ensemble
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