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Question 5.1: The infinitesimal heat transfer δQ is expressed as a functio...

The infinitesimal heat transfer δQ is expressed as a function of the state variables T and V in equation (5.4). It was done as a function of the state variables T and p in equation (5.17). Express the infinitesimal heat transfer δQ as a function of V and p.

δQ = T dS(T, V) ≡ C_V (T, V) dT + L_V (T, V) dV .

δQ = T dS(T, p) ≡ C_p (T, p) dT + L_p (T, p) dp .

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The infinitesimal heat transfer δQ can be expressed as a function of V and p as,

δQ = T (V, p) dS (V, p) = L_V (V, p) dV + L_p (V, p) dp .

where

L_V (V, p) = T (V, p) \frac{∂S (V, p)}{∂V}        and      L_p (V, p) = T (V, p) \frac{∂S (V, p)}{∂p} .

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