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Suppose I have a cylinder with a movable partition inside, separating it into two subsystems. The partition is movable, but will not transmit heat or matter. The same type of gas is contained in each subsystem, but the pressures and temperatures are different. The same amount of mass (M) is in each subsystem. The question is, how to find the equilibrium situation, given P1, T1, V1, P2, T2, V2, the initial pressures, temperatures, and volumes of the two subsystems, assuming the motion of the partition is quasistatically slow.
I have solved it by invoking conservation of total mass, energy, volume and entropy (no entropy production for a quasistatic process, i.e. reversible), and requiring the pressures on either side to be equal.
I would like to solve it by finding the minimum or maximum of something, but I don't know what that something is. It can't be total energy U, that's constant. It can't be total enthalpy (H) because, for an ideal gas H=(5/3)U and U is conserved. It can't be total entropy, that's constant. That leaves Helmholtz free energy, or Gibbs free energy or something else? If so, why?
Thanks
I have solved it by invoking conservation of total mass, energy, volume and entropy (no entropy production for a quasistatic process, i.e. reversible), and requiring the pressures on either side to be equal.
I would like to solve it by finding the minimum or maximum of something, but I don't know what that something is. It can't be total energy U, that's constant. It can't be total enthalpy (H) because, for an ideal gas H=(5/3)U and U is conserved. It can't be total entropy, that's constant. That leaves Helmholtz free energy, or Gibbs free energy or something else? If so, why?
Thanks