A diatomic ideal gas is used in Carnot's engine as working substance. Duting aidabatic expansion of the cycle , if the volume of the gas increases from V t0 32 V, then the efficiency of the engine is

Options

A. 0.25
B. 0.5
C. 0.67
D. 0.75

Answer

D

Explanation

Given, volume at C=V and volume at D= 32 V For adiabatic expansion CD,
`T_(c)V_(c)^(gamma-1)=T_(D)V_(D)^(gamma-1) rArr (T_C)/(T_D)= ((V_D)/(V_C))^(gamma-1)`
`= ((32V)/(V))^(gamma-1) = 32^(7/2-1)`
`rArr (T_C)/(T_D)=(32)^(2/5)=4`
Now, efficiency of Carnot.s cycle.
`eta =1 - (T_D)/(T_C)=1-1/4= 3/4=0.75`