?When gas expands in a cylinder with radius \(r\), the pressure at any given time is a
Chapter 5, Problem 29(choose chapter or problem)
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: \(F=\pi r^{2} P\). Show that the work done by the gas when the volume expands from volume \(V_{1}\) to volume \(V_{2}\) is
\(W=\int_{V_{1}}^{V_{2}} P d V\)
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