Consider the gas-solid equilibrium under the extreme assumption that the entropy of the solid may be neglected over the temperature range of interest. Let 0

Consider the gas-solid equilibrium under the extreme assumption that the entropy of the solid may be neglected over the temperature range of interest. Let –ε0 be the cohesive energy of the solid, per atom. Treat the gas as ideal and monatomic. Make the approximation that the volume accessible to the gas is the volume V of the container, independent of the much smaller volume occupied by the solid.
(a) Show that the total Helmholtz free energy of the system is

F =Fs + Fθ = – Nsε0 + Ngτ[log(Ng/VnQ) – 1]’

Where the total number of atoms, N = Ns + Ng is constant.
(b) Find the minimum of the free energy with respect to Ng; show that in the equilibrium condition

Ng = nQVexp(–ε0/τ).

(c) Find the equilibrium vapor pressure.