Two subsystems are contained within a cylinder and are separated by an internal piston. Each subsystem is a mixture of one mole of helium gas and mole of neon gas (each to be considered as a monatomic ideal gas). The piston in the center of the cylinder, each subsystem occupying a volume of 10 liters. The walls of the cylinder are diathermal, and the system is in contact with a thermal reservoir at a temperature of 100°C. The piston is permeable to helium but impermeable to neon. one Recalling (from Problem 5.3-10) that the Helmholtz potential of a mixture of simple ideal gases is the sum of the individual Helmholtz potentials (eadh expressed as a function of temperature and volume), show that in the present case V No 0 0 1 vaNo where TO, Io, and Mo are attributes of a standard state (recall Problem 53-1) N is the total mole number, N is the mole number of n subsystem 1, and V) and Va tively eon (component 2) in are the volumes of subsystems 1 and 2, respe- How much work is required to push the piston to such a position that the volumes of the subsystems are 5 liters and 15 liters? Carry out the calculation both by calculating the change in F and by a direct integration (as in Problem 6.2-1)