Two ideal van der Waals fluids are contained in a cylinder, separated by an internal moveable piston. There is one mole of each fluid, and the two fluids have the same values of the van der Waals constants b and c; the respective values of the van der Waals constant “a” are α1 and α2. The entire system is in contact with a thermal reservoir of temperature T. Calculate the Helmholtz potential of the composite system as a function of T and of the total volume V. If the total volume is doubled (while allowing the internal piston to adjust), what is the work done by the system?
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