Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Statistical Mechanics · Problem 8.3
Statistical Mechanics of Interacting Systems: The Method of Cluster Expansions — R. K. Pathria
Physics — Statistical Mechanics · ideal-fermi-gas-thermodynamic-relations
Problem Show that for an ideal Fermi gas
1 z ( ∂ z ∂ T ) P = − 5 2 T f 5 / 2 ( z ) f 3 / 2 ( z ) ; \frac{1}{z}\left(\frac{\partial z}{\partial T}\right)_P = -\frac{5}{2T}\frac{f_{5/2}(z)}{f_{3/2}(z)}; z 1 ( ∂ T ∂ z ) P = − 2 T 5 f 3/2 ( z ) f 5/2 ( z ) ; γ ≡ C P C V = ( ∂ z / ∂ T ) P ( ∂ z / ∂ T ) v = 5 3 f 5 / 2 ( z ) f 1 / 2 ( z ) [ f 3 / 2 ( z ) ] 2 . \gamma \equiv \frac{C_P}{C_V} = \frac{(\partial z/\partial T)_P}{(\partial z/\partial T)_v} = \frac{5}{3}\frac{f_{5/2}(z)f_{1/2}(z)}{[f_{3/2}(z)]^2}. γ ≡ C V C P = ( ∂ z / ∂ T ) v ( ∂ z / ∂ T ) P = 3 5 [ f 3/2 ( z ) ] 2 f 5/2 ( z ) f 1/2 ( z ) . γ ≃ 1 + π 2 3 ( k T ε F ) 2 . \gamma \simeq 1 + \frac{\pi^2}{3}\left(\frac{kT}{\varepsilon_F}\right)^2. γ ≃ 1 + 3 π 2 ( ε F k T ) 2 . Browse the problem library