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Laws of Thermodynamics
GATE 2009
Hard
An ideal gas with molar heat capacity Cp=(5/2)R (R=8.314 J/mol.K) is compressed adiabatically from 1 bar and 300K to pressure P2 in a closed system. The isentropic (ideal, reversible) final temperature after compression is 600K, and the mechanical efficiency of compression is 50%. The (actual) work required for compression (in kJ/mol) is
- A3.74
- B6.24
- 7.48
- D12.48
Explanation
Cv=Cp−R=(3/2)R. Ideal (isentropic) work=Cv×ΔT=1.5×8.314×(600−300)=3741.3 J/mol=3.741 kJ/mol. Actual work (accounting for 50% mechanical efficiency)=ideal work/efficiency=3.741/0.5≈7.48 kJ/mol.
Source: GATE CH 2009 (2009)
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