Project ForgeThermodynamics
First Law of Thermodynamics
GATE 2018
Hard
A vehicle powered by a spark ignition engine follows an air standard Otto cycle (γ=1.4). The engine generates 70 kW while consuming 10.3 kg/hr of fuel. The calorific value of fuel is 44,000 kJ/kg. The compression ratio is __________ (correct to two decimal places).
7.6(± 0.3 accepted)
Explanation
Heat input rate = (10.3/3600)×44,000 ≈ 125.89 kW. Thermal efficiency η = Wnet/Qin = 70/125.89 ≈ 0.5560. For an Otto cycle, η = 1 − r^(1−γ) → r^(−0.4) = 1−0.5560 = 0.4440 → r^0.4 = 1/0.4440 = 2.2523 → r = 2.2523^(1/0.4) = 2.2523^2.5 ≈ 7.61.
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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