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

The efficicney of cycle is `eta =1 -T_(2)/T_(1)`
For adiabatic process `T I//y-1` = constant
For diatomic gas `gamma = 7/5`
`T_(1)V_(1)^(gamma-1) = T_(2)V_(2)^(gamma-1) rArr T_(1)=T_(2)(V_(2)/V_(1))^(gamma-1)`
`therefore eta = (1- 1/4) = 3/4 = 0.75`