Serway & Jewett — Temperature: Problem 40

A vertical cylinder of cross-sectional area \(A\) is fitted with a tight-fitting, frictionless piston of mass \(m\) (Fig. P18.40). The piston is not restricted in its motion in any way and is supported by the gas at pressure \(P\) below it. Atmospheric pressure is \(P_0\). We wish to find the height \(h\) in Figure P18.40. (a) What analysis model is appropriate to describe the piston? (b) Write an appropriate force equation for the piston from this analysis model in terms of \(P, P_0, m, A,\) and \(g\). (c) Suppose \(n\) moles of an ideal gas are in the cylinder at a temperature of \(T\). Substitute for \(P\) in your answer to part (b) to find the height \(h\) of the piston above the bottom of the cylinder.