Question

Calculation of thermodynamic properties in terms of partition function

Answer 1

Using the partition function various thermodynamic properties can be defined:

• U = − ( ∂ ln Q ∂ β ) N , V = k B T 2 ( ∂ ln Q ∂ T ) N , V.
• P = − k B T ( ∂ ln Q ∂ V ) N , T = k B T Q ( ∂ Q ∂ V ) N , T.
• S = k B ln Q + k B T ( ∂ ln Q ∂ T ) N , V.
• H = U + P V = k B T 2 ( ∂ ln Q ∂ T ) N , V + k B T V ( ∂ ln Q ∂ V ) T , N.

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Answer 2

Answer:

Using the partition function various thermodynamic properties can be defined:

U = − ( ∂ ln Q ∂ β ) N , V = k B T 2 ( ∂ ln Q ∂ T ) N , V.

P = − k B T ( ∂ ln Q ∂ V ) N , T = k B T Q ( ∂ Q ∂ V ) N , T.

S = k B ln Q + k B T ( ∂ ln Q ∂ T ) N , V.

H = U + P V = k B T 2 ( ∂ ln Q ∂ T ) N , V + k B T V ( ∂ ln Q ∂ V ) T , N