Blundell Thermal Physics · Problem 13.4

Heat engines and the second law

Physics — Statistical Mechanics · ideal-gas-cycle-efficiency

Problem

A possible ideal-gas cycle operates as follows: ((i)) from an initial state (p1,V1)(p_1, V_1) the gas is cooled at constant pressure to (p1,V2)(p_1, V_2); ((ii)) the gas is heated at constant volume to (p2,V2)(p_2, V_2); ((iii)) the gas expands adiabatically back to (p1,V1)(p_1, V_1). Assuming constant heat capacities, show that the thermal efficiency is 1−γ(V1/V2)−1(p2/p1)−1.(13.41)1 - \gamma \frac{(V_1/V_2) - 1}{(p_2/p_1) - 1}. \tag{13.41} (You may quote the fact that in an adiabatic change of an ideal gas, pVγpV^\gamma stays constant, where γ=cp/cV\gamma = c_p/c_V.)

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