Although frequently treated as a constant, the latent heat of vaporization is actually a function of temperature. Subtracting eqs.(7) and (8) gives the following expression for
which holds when the vapour is saturated and at equilibrium with a plane liquid water surface. Now consider the change in as one proceeds from temperature to along phase transition boundary in the plane i.e.
But
and
so that eq.(13) becomes:
where is the specific heat of water vapour at constant pressure.
Using the Clausius-Clapeyron equation eq.(12) and the fact that gives:
which may be further simplified using the perfect gas equation to give:
Finally, assuming and to be constant and integrating eq.(14) gives:
where is the latent heat of vaporization at .
Bolton (1980) showed that an approximate solution to eq.(12) is:
where is given in and is in degrees Celsius.