Consider the following statement: during a 1st order phase transition, the temperature of the system stays constant and any extra heat goes into turning a larger portion of the system into the new phase. In particular this implies that a system can exist as a certain admixture of two phases at the critical temperature.
Consider a highly idealised scenario. Imagine pure water filling a box of fixed size V with periodic boundary conditions. Therefore, there are no surface effects, no impurities, and I will also ignore gravity.
Suppose nonetheless that I have a mechanism for cooling/heating the system as slowly and adiabatically as you like.
Is there still a 1st order 'boiling' phase transition at some critical temperature $T_c$?
If yes, what would coexistence look like?
For 2), after reaching $T_c$ I presume some extra heat will lead to nucleation of bubbles of vapour. There seem to me to then be 2 + 1 possibilities:
a) These bubbles have stable configurations for certain special radii. Then I guess the system will be a mixture of water and bubbles floating around (modulo bubble mergers and splitting).
b) Bubbles are never stable but always either expand or collapse. Indefinite expansion seems wrong because then it would seem to imply that nucleating a single bubble is enough to percolate the whole system, which seems to contradict the possibility of coexistence altogether. The only way I can see this working is if bubbles continuously nucleate, maybe expand a bit, maybe collide with others, but somehow always re-collapse, in such a way that on average the ratio of gas to liquid is fixed.
c) The system eventually relaxes to some other non-bubble like configuration of the vapour region that is stable, and that takes into account my periodic boundary conditions. (e.g. a slab sitting at particular x,y coords and filling the whole periodic z axis). This would defeat my attempt to make the global structure of the space irrelevant.
