A closed system consisting of 4 lb of a gas undergoes a

Chapter 1, Problem 1.28

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A closed system consisting of 4 lb of a gas undergoes a process during which the relation between pressure and volume is \(p V^{n}=\text { constant }\). The process begins with \(p_{1}=\) \(15 \mathrm{lbf} / \mathrm{in.}^{2}, \boldsymbol{v}_{1}=1.25 \mathrm{ft}^{3} / \mathrm{lb}\) and ends with \(p_{2}=53 \mathrm{lbf} / \mathrm{in} .^{2}\), \(v_{2}=0.5 \mathrm{ft}^{3} / \mathrm{lb}\). Determine (a) the volume, in \(\mathrm{ft}^{3}\) , occupied by the gas at states 1 and 2 and (b) the value of n. (c) Sketch Process 1–2 on pressure–volume coordinates.