Phase Boundary between mono and diatomic gases

[samjohnny]

Homework Statement

Consider a gas (note: treat as ideal) that has phase coexistence between diatomic and monatomic forms at $T_0$ and $P_0$. Compute the equation for the P,T phase boundary between monatomic and diatomic gases.

Homework Equations

$u_v (V,T) = \frac{5}{2} RT - \frac{a}{v} - u_b$

$u_i (V,T) = \frac{5}{2} RT - u_b$

Where $u_b$ is the energy holding atoms together in a diatomic gas.
And $u_i$ and $u_v$ are the molar energies of ideal and van der waals diatomic gases respectively.

The Attempt at a Solution

I'm assuming that the equation for the phase boundary has something to do with computing $\frac{dP}{dT}$. So the first thing that springs to mind is the Clausius Clapeyron, however, how to relate that to the equations given for the internal energies I'm not sure.

 

[_coyote_]

I'm also not sure how to incorporate the fact that the boundary is between two different phase states. Any help is appreciated!