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Laws of Thermodynamics
GATE 2016
Hard
An ideal gas (Cv=30 J/mol·K, R=8.314, γ=1.277) is adiabatically, irreversibly compressed from 3bar/300K to 6bar in a closed system. Irreversible work=1.5× reversible work. The final temperature (K) in the irreversible case, rounded to 1 decimal place, is
373.1 K(± 2 accepted)
Explanation
T2s=300×2^((γ-1)/γ)=300×2^0.217=348.7K. Wrev=Cv(T2s−T1)=30×48.7=1461 J/mol. Wirrev=1.5×1461=2191.5 J/mol=Cv(T2−300) ⟹ T2=300+73.05=373.1K.
Source: GATE CH 2016 (2016)
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