An ideal monoatomic gas is contained in a cylinder with a movable piston so that the gas can do work on the outside world, and heat can be added or removed as necessary. The figure shows various paths that the gas might take in expanding from an initial state whose pressure, volume, and temperature are p0. V0, and T0 respectively. The gas expands to a state with final volume 4V0. For some answers, it will be convenient to generalize your results by using the variable Rv = Vfinal/Vinitial, which is the ratio of final to initial volumes (equal to 4 for the expansions shown in the figure.)
Calculate WA, the work done by the gas as it expands along path A from V0 to VA = RvV0.
Express WA in terms of p0, V0, and Rv.
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