When gas expands in a cylinder with radius r, the pressure at any given time is a

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When gas expands in a cylinder with radius r, the pressure at any given time is a function of the volume: P = P(V) . The force exerted by the gas on the piston (see the figure) is the product of the pressure and the area: F = πr2P. Show that the work done by the gas when the volume expands from volume V1 to volume V2 is

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