Project ForgeProcess Calculations
Laws of Thermodynamics
GATE 2015
Hard
An ideal gas at 0.1MPa, 2m³ is reversibly adiabatically compressed to 1MPa, then cooled at constant pressure to 0.2m³. Cp=2.5R, R=8.314 J/mol·K. The total work done (kJ) ON the gas, rounded to 1 decimal place, is
756 kJ(± 15 accepted)
Explanation
γ=Cp/Cv=2.5/1.5=5/3. Adiabatic: V2=2×(0.1/1)^0.6=0.502m³. W1=(P2V2−P1V1)/(γ−1)=(502.4−200)/0.6667=453.6kJ. Isobaric: W2=−P2ΔV=−1000×(0.2−0.502)=302.4kJ. Total=453.6+302.4=756.0kJ.
Source: GATE CH 2015 (2015)
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