Estimate the latent heat of water

[It's me]

Homework Statement

Try to estimate the latent heat of vaporization of water and nitrogen using the Van der Waals model. What happens?

Homework Equations

$$ΔQ=TΔS=L$$

$$S=nR[\ln(\frac{(V−nb)T^{3/2}}{nΦ})+\frac{5}{2}]$$

The Attempt at a Solution

I predict the latent heat of vaporization of water will be wrongly approximated by the Van der Waals model. By looking at the equation for entropy I think the ΔS is going to be zero, so the latent heat would be zero also. But I am not sure if I am looking at the problem in the wrong way.

 

[BvU]

Why would $\Delta S$ be zero ?