GATE 2022 ME (ME1) – Question 62
An engine running on an air standard Otto cycle has a displacement volume 250 cm$^3$ and a clearance volume 35.7 cm$^3$. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).
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Correct answer: 4809
Explanation
The compression ratio is $r = \frac{250 + 35.7}{35.7} = 8.0$. After compression, $T_2 = 300 \times 8^{0.4} = 689.2$ K and $P_2 = 100 \times 8^{1.4} = 1837.9$ kPa. The heat addition raises the temperature by $\frac{800}{0.718} = 1114.2$ K, so $T_3 = 1803.4$ K. At constant volume $P_3 = P_2\frac{T_3}{T_2} = 1837.9 \times \frac{1803.4}{689.2} = 4809$ kPa.