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Question:

A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32V, the efficiency of the engine is?

0.75

0.99

0.25

0.5

Solution:

The efficiency of cycle is η=1−T2/T1
For adiabatic process TVγ−1=constant
For diatomic gas γ=7/5
T1Vγ−11=T2Vγ−12
T1=T2(V2/V1)γ−1
T1=T2(32)7/5−1=T2(25)2/5=T2×4
T1=4T2.
η=(1−1/4)=3/4=0.75