5. Gas-solid equilibrium. Consider the gas-solid equilibrium under the ex- treme assumption that the entropy of the solid may be neglected over the tem- perature range of interest. Let 80 be the cohesive energy ofthe 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. ta) Show that the total Helmholtz free energy oflhe system is F = F. + F, = N,so + N,r[log{N,/Vnol t] . as; where the total number of atoms. N = N' + N, is constant. [b] Find the mini- mum of the free energy with respect to N,; show that in the equilibrium condition N, = nQVeitpl-t:0/t}. {79] (c) Find the equilibrium vapor pressure