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

Answer

B

Explanation

`TV^(gamma-1) = constant`
`T_(1)V^((7)/(5)-1) = T_(2) (32V)^((7)/(5)-1) , (T_(2))/(T_(1)) = (1)/((32)^(2//5)) = (1)/(4)`
`eta = 1 - (T_(2))/(T_(1)) = 1- (1)/(4) = (3)/(4)`