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

Options

A. 0.25
B. 0.5
C. 0.75
D. 0.99

Answer

C

Explanation

For an adiabatic process `TV^(gamma-1)` = constant
`therefore` During the adiabatic expansion part `V_(1)=VandV_(2)=32V` and for a diatomic gas `gamma=7/5`
`thereforeT_(1)V_(1)^(gamma-1)=T_(2)V_(2)^(gamma-1)`
`thereforeT_(1)/T_(2)=(V_(2)/V_(1))^(gamma-1)=(32/1)^(7/5-1)=(32)^(2/5)`
`thereforeT_(1)/T_(2)=(2^(5))^(2/5)=2^(2)=4`
`thereforeeta=1-T_(2)/T_(1)=1-1/4=3/4=0.75`