= Solution
The relation describes the slope of the <phase coexistence curve> of a pure substance in the pressure-temperature plane:
$$
\boxed{\frac{dp}{dT}=\frac{L}{T\Delta V}.}
$$
Here $p(T)$ is the common equilibrium <pressure> of the two phases, $T$ is their common absolute <temperature> in kelvins, and the <derivative> is taken along their coexistence curve. Choose a direction of transformation from phase 1 to phase 2. Then $L$ is the reversible <latent heat> for that transformation and $\Delta V=V_2-V_1$ is the corresponding <volume> change, using the same <amount of substance> for both quantities.
In the molar convention used below, $L=h_{m,2}-h_{m,1}$ has units $\mathrm{J\,mol^{-1}}$ and $\Delta V=v_{m,2}-v_{m,1}$ has units $\mathrm{m^3\,mol^{-1}}$, so the right-hand side has units $\mathrm{Pa\,K^{-1}}$. For vaporization, both $L$ and $\Delta V$ are positive. The displayed general relation is also called the <Clapeyron equation>; the ideal-vapor approximation used in (c) gives its usual Clausius form.
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