Now adapt the ideas of the energy and entropy of mixing to gasses in different cylinder. The temperature is fixed (there is a thermal reservoir so that all changes are done isothermally). A system starts with n(He)=10 moles of helium in a cylinder with a piston on top (on the left) where the pressure is 2 Atm; and there is cylinder of Ar n(Ar)=2 moles on the right at pressure of 3 Atm. Assume that both gasses behave as ideal non-interacting gasses. The original state of the system is the one just described. Now the two independent cylinders are connected by a tube with a membrane that will allow He to easily transit but Ar cannot and the system now comes to equilibrium. Q2a) From what we have learned about Energy of mixing and the chemical potential, what new principle is there (which gives us a new relation) expressed in terms of the chemical potential that can be applied at equilibrium for this type of system? Hint: It is a bit more than just u(alpha)=u(beta) and involves the pressure. Q2b) After the system comes to equilibrium, determine how many moles of each gas are in each cylinder. Q2c) How much work was done by moving the gas around to come to equilibrium? Q2d) How much electrical work could have been done had there been a generator to capture the mass flow of the He? Q2e) What is the entropy change, and what is the enthalpy change for this reaction? Q2f) Is the process spontaneous as written?