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2. An ideal gas expands and contracts. The process can be shown on the Carnot cycle. Give a detailed explanation of what is happening in each process. 3. An ideal fermion gas can be described by the density of states ?_0(E) = { d?????? if E ? 0 0, otherwise If the normalization d = V / (2?^2) ? (2m / ?^2)^(3/2) i. Calculate its Fermi energy ?_F. ii. Calculate the internal energy U(T = 0) of the ideal fermion gas. 4. The probability of observing the system in energy state E_s, in the canonical ensemble is given by P_s = 1/Z ? e^(-?E_s), where Z = ?_s e^(-?E_s) is the canonical partition function. Show that the Helmholtz free energy is given by F = U - TS

          2. An ideal gas expands and contracts. The process can be shown on the Carnot cycle. Give a detailed explanation of what is happening in each process.
3. An ideal fermion gas can be described by the density of states
?_0(E) = { d?????? if E ? 0
0, otherwise
If the normalization
d = V / (2?^2) ? (2m / ?^2)^(3/2)
i. Calculate its Fermi energy ?_F.
ii. Calculate the internal energy U(T = 0) of the ideal fermion gas.
4. The probability of observing the system in energy state E_s, in the canonical ensemble is given by
P_s = 1/Z ? e^(-?E_s),
where Z = ?_s e^(-?E_s) is the canonical partition function.
Show that the Helmholtz free energy is given by
F = U - TS

2. An ideal gas expands and contracts. The process can be shown on the Carnot cycle. Give a detailed explanation of what is happening in each process.
3. An ideal fermion gas can be described by the density of states
?0(E) = d?????? if E ? 0
0, otherwise
If the normalization
d = V / (2?^2) ? (2m / ?^2)^(3/2)
i. Calculate its Fermi energy ?F.
ii. Calculate the internal energy U(T = 0) of the ideal fermion gas.
4. The probability of observing the system in energy state Es, in the canonical ensemble is given by
Ps = 1/Z ? e^(-?Es),
where Z = ?s e^(-?Es) is the canonical partition function.
Show that the Helmholtz free energy is given by
F = U - TS

Added by Laura W.

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