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PROBLEM STATEMENT: I have a 1 liter cylinder with a massless, frictionless piston. There is some liquid water in the cylinder, with air above it. The temperature is initially 298 K, and the system pressure matches the outside pressure of 1 bar. I increase the external pressure to 10 bars (a) suddenly or (b) gradually/reversibly. The system is adiabatic. The increase in temperature from adiabatic compression of the gas phase causes some of the water to evaporate. In the final equilibrium state of the system, determine the final temperature, volume, and mass of liquid water for scenarios (a) and (b). First consider the case where there is exactly enough liquid water initially, such that, at final equilibrium, all of the water has just barely evaporated. Then consider cases where there is initially twice this amount of liquid water and half this amount for each of the two scenarios.

Allowable assumptions are that

1. The gas phase can be treated as an ideal gas mixture

2. Negligible air dissolves in the water