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The Grand Canonical Ensemble — R. K. Pathria
Physics — Statistical Mechanics · heat-capacities-difference
Problem Prove that, quite generally,
C P − C V = − k [ ∂ ∂ T { T ( ∂ ln Q ∂ V ) T } ] V 2 ( ∂ 2 ln Q ∂ V 2 ) T > 0. C_P - C_V = -k \frac{\left[\dfrac{\partial}{\partial T}\left\{T\left(\dfrac{\partial \ln Q}{\partial V}\right)_T\right\}\right]_V^2}{\left(\dfrac{\partial^2 \ln Q}{\partial V^2}\right)_T} > 0. C P − C V = − k ( ∂ V 2 ∂ 2 ln Q ) T [ ∂ T ∂ { T ( ∂ V ∂ ln Q ) T } ] V 2 > 0. N k Nk N k Browse the problem library