Finite-time thermodynamics and the gas-liquid phase transition

In this paper, we study the application of the concept of finite-time thermodynamics to first-order phase transitions. As an example, we investigate the transition from the gaseous to the liquid state by modeling the liquification of the gas in a finite time. In particular, we introduce, state, and solve an optimal control problem in which we aim at achieving the gas-liquid first-order phase transition through supersaturation within a fixed time in an optimal fashion, in the sense that the work required to supersaturate the gas, called excess work, is minimized by controlling the appropriate thermodynamic parameters. The resulting set of coupled nonlinear differential equations is then solved for three systems, nitrogen N-2, oxygen O-2, and water vapor H2O.