Heat capacity of a liquid is [tex]C=T^4[/tex] and the state function is [tex]V(T,P) = Aexp(aT-bP)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Derive an equation for entropy. Use the relevant Maxwell relations.

[tex]dU = T dS - PdV[/tex]

[tex]\frac{\partial U}{\partial T}_V = C = T^4 \Rightarrow U = \frac{T^5}{5} + f(V)[/tex]

Since it's a liquid, and there're no separate [tex]C_V[/tex] and [tex]C_P[/tex], I assumed that expansion can be ignored, so [tex]dU \approx TdS[/tex] and

[tex]dS = \frac{dU}{T} = T^3 dT[/tex]

but it's unlikely to be true since I haven't used the state function or Maxwell relation at all. My assumption is probably wrong. Anyone solve the problem?

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# Homework Help: Equation for S from state func and C

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