In class, we derived the Wilson$-$Frenkel law for interface$-$limited growth,

$v=[nvexp(-\frac{G_A}{k_{B}T})]\frac{G}{k_{B}T}$

In other words, the growth rate $v$ is directly proportional to driving force, $G,$ which reflects the free energy difference between the two phases. Here, we will adapt the same expression to describe the velocity of a solid$-$vapor interface. Assume constant temperature, an ideal vapor phase, and that the volume of the vapor phase is much greater than that of the solid phase. From this information, show that $G=kT\frac{P}{P}$ and hence the growth rate is given by vprop$\frac{P}{P}.$