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., N) = -KT [in (1/4) + 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
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., N) = -KT [in (1/4) + 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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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a71a866-3c53-44fa-b400-40d874475a4f%2Fafd47d4c-e416-4235-9184-742c9250d393%2F6zqlxin.jpeg&w=3840&q=75)
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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