(All Steps) Consider a volume V of gas in a cylinder fitted with a piston at one end, where the pressure p of the gas is a function p(V) of its volume (Fig.
Question: Consider a volume \(V\) of gas in a cylinder fitted with a piston at one end, where the pressure \(p\) of the gas is a function \(p(V)\) of its volume (Fig. 6.5.17). Let \(A\) be the area of the face of the piston. Then the force exerted on the piston by gas in the cylinder is \(F=p A\). Assume that the gas expands from volume \(V_{1}\) to volume \(V_{2}\). Show that the work done by the force \(F\) is then given by
\[W=\int_{V_{1}}^{V_{2}} p(V) d V\]
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