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

`T_(B) = T_(1) , T_(C) = T_(2) , gamma= 1.4 V_(B) = V ,V_(C) = 32V`
`T_(B)V_(B)^(gamma-1)= T_(C)V_(C)^(gamma-1)`
`(T_(C))/(T_(B)) = (T_(2))/(T_(1)) = ((V_(B))/(V_(C)))^(gamma-1)= ((1)/(32))^(gamma-1) = (1)/(4)`
`eta=1- (T_(2))/(T_(1)) = 1- (1)/(4) =(3)/(4)= 0.75`