T-dependence of heat of vaporization near critical point

[The_Duck]

The Wikipedia page on the heat of vaporization has a nice graph showing the heat of vaporization going to zero at the critical points of various substances. Is there a known form for the heat of vaporization as a function of temperature near the critical point? I imagine it is probably a power law with some exponent, and while there are lists of critical exponents I can't figure out which critical exponent it would be. I could fit the data to a power law by hand but I wonder if there is a more definitive source.

 

[Bystander]

https://en.wikipedia.org/wiki/Critical_exponent
Might point you to something more enlightening; last I knew, Hanley and crew had yet to nail down anything definite.

 

[The_Duck]

I have read that page but unfortunately none of the critical exponents listed seem to be related to the heat of vaporization (or if they are it isn't obvious to me).

Just now I have found some papers that say that empirically it is indeed a power law:
$${\rm heat}\,{\rm of}\,{\rm vaporization} \sim (T - T_c)^{0.38}$$
(where $T_c$ is the critical temperature). Ideally I would like to connect this exponent of $0.38$ to the standard critical exponents on that Wikipedia page, which are known to be universal. I haven't yet figured out how to do this.