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Thermodynamics
First Law of Thermodynamics
GATE 2022
Hard

An engine running on an air standard Otto cycle has a displacement volume 250 cm³ and a clearance volume 35.7 cm³. 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).

4810 kPa(± 15 accepted)

Explanation

r=(250+35.7)/35.7≈8. Isentropic compression: T2=300×8^0.4≈689.2K, P2=100×8^1.4≈1837.9kPa. Constant-volume heat addition: T3=T2+q/cv=689.2+800/0.718≈1803.4K. Since V is constant from 2→3, P3=P2×(T3/T2)≈1837.9×2.617≈4810kPa — this is the maximum pressure in the cycle (state 3).

Source: GATE ME 2022 Session 1 (ME-1) (2022)

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