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Question

Two moles of an ideal monoatomic gas occupies a volume V at 27C. The gas expands adiabatically to a volume 2V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.


Your Answer
A
 189 K, 2.7 kJ
Your Answer
B
 195 K, 2.7 kJ
Correct Answer
C
 189 K, 2.7 kJ
Your Answer
D
 195 K, 2.7 kJ

Solution

The correct option is A  189 K, 2.7 kJ
For adiabatic process relation of temperature and volume is,
T2Vγ12=T1Vγ11T2(2V)2/3=300(V)2/3[γ=53 for monoatomic gases ]T2=30022/3189K
Also, in adiabatic process,
ΔQ=0,ΔU=ΔW
or ΔU=nR(ΔT)γ1=2×32×253(300189)
2.7kJT2189K,ΔU2.7kJ

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