$($b$)$ An industrial solvent at boiling conditions $(274K$ and $1$atm $)$ has the following effect of pressure on temperature at saturated conditions.

$(\frac{dT}{dP}{)}^{\text{s}\text{a}\text{t}}=0\mathrm{.}34\frac{K}{mmHg}$

The vapor phase and liquid phase volumes are given as: $V^v=1\mathrm{.}72\frac{m^3}{k}g$ and $V^l=0\mathrm{.}002\frac{m^3}{k}g.$ Calculate the latent heat of vaporization of the solvent.

$(10$ marks$)$