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Question 3 (Ideal Gas (Part 1)) The canonical partition function of an ideal gas consisting of monoatomic particles is equal to Q(N,V,T) = 1/Lambda^{3N}N! int dGamma exp(-eta H) = V^N/Lambda^{3N}N! in which Lambda = h/sqrt{2pi m k_B T} and dGamma = dq_1...dq_N dp_1...dp_N. Derive expressions for the following thermodynamic properties: - F(N,V,T) (hint: ln(N!) approx N ln N - N) - p(N,V,T) (which leads to the ideal gas law) - mu(N,V,T) (which leads to mu = mu_0 + RT ln p) - U(N,V,T) and S(N,V,T) - C_V (heat capacity at constant volume) - C_p (heat capacity at constant pressure)

          Question 3 (Ideal Gas (Part 1)) The canonical partition function of an ideal gas consisting of monoatomic particles is equal to
Q(N,V,T) = 1/Lambda^{3N}N! int dGamma exp(-eta H) = V^N/Lambda^{3N}N!

in which Lambda = h/sqrt{2pi m k_B T} and dGamma = dq_1...dq_N dp_1...dp_N.
Derive expressions for the following thermodynamic properties:
- F(N,V,T) (hint: ln(N!) approx N ln N - N)
- p(N,V,T) (which leads to the ideal gas law)
- mu(N,V,T) (which leads to mu = mu_0 + RT ln p)
- U(N,V,T) and S(N,V,T)
- C_V (heat capacity at constant volume)
- C_p (heat capacity at constant pressure)

Question 3 (Ideal Gas (Part 1)) The canonical partition function of an ideal gas consisting of monoatomic particles is equal to
Q(N,V,T) = 1/Lambda^3NN! int dGamma exp(-eta H) = V^N/Lambda^3NN!

in which Lambda = h/sqrt2pi m kB T and dGamma = dq1...dqN dp1...dpN.
Derive expressions for the following thermodynamic properties:
- F(N,V,T) (hint: ln(N!) approx N ln N - N)
- p(N,V,T) (which leads to the ideal gas law)
- mu(N,V,T) (which leads to mu = mu0 + RT ln p)
- U(N,V,T) and S(N,V,T)
- CV (heat capacity at constant volume)
- Cp (heat capacity at constant pressure)

Added by Kimberly O.

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