- #1
gulsen
- 217
- 0
Heat capacity of a liquid is [tex]C=T^4[/tex] and the state function is [tex]V(T,P) = Aexp(aT-bP)[/tex]
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?
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?