GATE 2022 ME (ME1) – Question 34
A polytropic process is carried out from an initial pressure of 110 kPa and volume of 5 m$^3$ to a final volume of 2.5 m$^3$. The polytropic index is given by $n = 1.2$. The absolute value of the work done during the process is _______ kJ (round off to 2 decimal places).
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Correct answer: 406.88 to 410.96
Explanation
For $PV^n$ = constant, $P_2 = P_1\left(\frac{V_1}{V_2}\right)^n = 110 \times 2^{1.2} = 252.7$ kPa. The work is $W = \frac{P_2V_2 - P_1V_1}{n - 1} = \frac{252.7 \times 2.5 - 110 \times 5}{0.2} = \frac{631.8 - 550}{0.2} = 408.9$ kJ (done on the gas, as it is compressed).