(I am self-studying as can be verified from my post history and, additionally, I believe this question has more general applicability.)
Callen asks us to consider the following in his famous textbook:
Question: Discuss the equilibrium that eventually results if a solid is placed in an initially evacuated closed container and is maintained at a given temperature. Explain why the solid-gas coexistence curve is said to define the " vapor pressure of the solid" at the given temperature.
Essentially, the goal of the problem seems to be to define vapor pressure.
I have answered as follows:
When the solid is initially placed in the evacuated chamber (we suppose it is maintained at a temperature $T$ throughout), it will experience zero pressure. In general, the solid phase is not the minimum $G$ phase at zero pressure, so the solid will begin to sublimate (i.e off-gas) to form the gas phase (which is generally the minimum $G$ phase at zero pressure). As $N_g$ (the moles of gas phase) increases, we will begin to observe a pressure increase. This process will tend to continue until we reach the point $(T,P)$ at which the solid and vapor can coexist. At this point, any "parcel" of one mole of substance has equal $g$, whether it's in the gas or solid phase. It's therefore no more likely to be in one or the other and, unless there is some further driving force, the system will now stay where it is (with solid in equilibrium with said amount of gas). This amount of gas will have a certain pressure -- the vapor pressure!
But I have two questions here:
- I wrote that "unless there is some further driving force, the system will now stay where it is", but why should this be? Surely fluctuations will occur?
- Given 1), if there are fluctuations, then some fluctuations will be such as to produce more gas phase. But, if this is so, then how can the vapor pressure be well-defined given that (presumably) more $N_g$ means higher pressure?
Edit: I think some of my problem may be in not appreciating that, from a kinetic theory perspective, solids can also exert pressure, but I am not sure.