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 = mr*P. Show that the work done by the gas when the volume expands from volume V, to volume Vz is w = (* PdV Jv. V piston head

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 = mrP. Show that the work done by the gas when the volume expands from volume V, to volume Vz is w = ( PdV Jv. V piston head