For a one component system consider a liquid droplet forming spontaneously from the vapor at constant temperature (as shown below). Let the initial and final phases be enclosed by a frictionless piston/cylinder assembly consisting of an impermeable adiabatic wall, which allows work to be exchanged with the surroundings. Assume that the external pressure remains constant at value Po. The number of monomers in the vapor phase before droplet formation is No.Nv is the number of monomers in the vapor phase after droplet formation and Nd is the number in the droplet(No=Nv+Nd). The volume of the vapor phase before droplet formation is Vo; it is Vv after droplet formation and the volume of the droplet is Vd. (Note that V=Vv+Vd=Vo ). Prove that the work required to form a liquid droplet containing n monomers is Wn=n[d(Po,T)v(Po,T)]+A=n+A where d is the chemical potential of the droplet and v is the chemical potential of the vapor phase, both measured at pressure P0