Project ForgeThermodynamics
First Law of Thermodynamics
GATE 2014
Medium
In an air-standard Otto cycle, air is supplied at 0.1 MPa and 308 K. The ratio of the specific heats (γ) and the specific gas constant (R) of air are 1.4 and 288.8 J/kg·K, respectively. If the compression ratio is 8 and the maximum temperature in the cycle is 2660 K, the heat (in kJ/kg) supplied to the engine is __________.
1410 kJ/kg(± 10 accepted)
Explanation
T2=T1·r^(γ−1)=308×8^0.4=308×2.2974≈707.6 K (isentropic compression). cv=R/(γ−1)=288.8/0.4=722 J/kg·K=0.722 kJ/kg·K. Heat supplied (constant-volume combustion) = cv(T3−T2)=0.722×(2660−707.6)≈1409.7 kJ/kg.
Source: GATE ME 2014 (Session 1 / Set-1) (2014)
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