Air expands adiabatically in a pistoncylinder assembly

Chapter 2, Problem 2.70

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Air expands adiabatically in a piston–cylinder assembly from an initial state where \(p_{1}=100 \mathrm{lbf} / \mathrm{in} .^{2}, v_{1}=3.704 \mathrm{ft}^{3} / \mathrm{lb}\), and \(T_{1}=1000^{\circ} \mathrm{R}\), to a final state where \(p_{2}=50 \mathrm{lbf} / \mathrm{in.}^{2}\) The process is polytropic with n = 1.4. The change in specific internal energy, in Btu/lb, can be expressed in terms of temperature change as \(\Delta u=(0.171)\left(T_{2}-T_{1}\right)\). Determine the final temperature, in \({ }^{\circ} \mathrm{R}\). Kinetic and potential energy effects can be neglected.

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