Thermodynamically efficient or not?

A linear diatomic ideal gas (with adiabatic exponent, γ = 1.4 \gamma = 1.4 ) was initially at T = 26 0 C T = 260^{\circ} C , P = 700 Pa P = 700 \ \text{Pa} and occupied a volume, V = 28 L V = 28 \ \text{L} . The gas is now taken through three thermodynamic processes as follows:

  • First: Gas is expanded isobarically to a volume of 84 L 84 \ \text{L} (Process AB) .

  • Second: It is taken through a polytropic process having equation P V n = constant PV^n = \text{constant} with n = 1.5 n = 1.5 (Process BC) .

  • Third: After the polytropic process is carried out, the gas comes back to its initial temperature and an isothermal process is carried out in the third step and the gas returns back to its initial state (Process CA) .

Find the percentage efficiency η \eta of the above cycle.


The answer is 38.63.

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