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In the case of a Van der Walls gas where I could say that $S = C_v \ln(T) + R\ln(V - b) + cte$, noting it is stated on "Concepts in Thermal Physics" of Blundell:

Note that the entropy depends on the constant $b$, but not $a$. Entropy 'cares' about the volume occupied by the molecules in the gas(because this determines how much available space there is for the molecules to move around in, and this in turn determines the number of possible microstates of the system) but not about the intermolecular interactions.

So, in a phase transition of a gas at temperature $T_c$, where $L = \Delta Q_r = T_c(S_f - S_i)$ implies that (1) $\Delta S = \Delta U_{pot} / T_c$. However, according to the above quote and equation for $S$, I don't understand formula (1). Furthermore, is it right?

Could someone explain me what is missing in my reasoning?

Thanks in advance.

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Applying the VDW approximation to this phase change at constant temperature, the entropy change would be $$\Delta S=R\ln{\left(\frac{V_V-b}{V_L-b}\right)}$$and the latent heat of vaporization would be $$L=T_c\Delta S=T_c R\ln{\left(\frac{V_V-b}{V_L-b}\right)}$$where $V_V$ and $V_L$ are the specific volumes of the saturated liquid and saturated vapor, respectively, at temperature Tc. The parameter b captures the effects of molecular interactions, just as the parameter a does.

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  • $\begingroup$ Are you aware of what the curve of P vs V for a VDW fluid at a constant temperature below the critical temperature looks like? $\endgroup$ – Chet Miller Dec 25 '20 at 16:00
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    $\begingroup$ Like a cubic polynomial for the P(V), which corresponds to a multi-valued function for G(P,T) $\endgroup$ – JoseAf Dec 25 '20 at 21:45

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