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Question

# 10 litres of a mono atomic ideal gas at 0oC and 10 atm pressure is suddenly released to 1 atm pressure and the gas expands adiabatically against this constant pressure. The final temperature and volume of the gas respectively are:

A
T=174.9K, V=64.0 liters
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B
T=153K, V=57 liters
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C
T=165.4K, V=78.8 liters
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D
T=161.2K, V=68.3 liters
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Solution

## The correct option is A T=174.9K, V=64.0 litersGiven that monoatomic gasT1=00C=273K, V1=10L, P1=10atmP2=1atm, V2=VFor an adiabatic processwork, w=(P2V2−P1V1)γ−1where γ=5/3 for monoatomic gasAlso, for expansion against constant P, w=−Pext(V2−V1)thus, −Pext(V2−V1)=(P2V2−P1V1)γ−1−1(V−10)=(1.V−10.10)5/3−110−V=3×(V−100)25V=320V=64LApplying ideal gas law:P1.V1=nRT110.10=n×0.0821×273n=4.47Also, P2.V2−P1.V1−=nR(T2−T1)1×64−10×10=4.47×0.0821×(T2−273)−36=0.367(T2−273)T2=174.9KThus final volume is 64L and temperature is 174.9K.

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