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A diatomic ideal gas is used in a Carnot...

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

A

`0.5`

B

`0.75`

C

`0.99`

D

`0.25`

Text Solution

Verified by Experts

The correct Answer is:
B
The efficiency of cycle is `eta=1-(T_2)/(T_1)`
For adiabatic process `TV^(gamma-1)`= constant
For a diatomic gas, `gamma=7"/"5`
`T_1V_(1)^(gamma-1)= T_2V_(2)^(gamma-1)`
`implies T_1=T_2((V_2)/(V_1))^(gamma-1) implies T_1=T_2(32)^((7)/(5)-1)`
`= T_2(2^5)^(2/5)= T_2xx4`
`implies T_1=4t_2" ":. eta= (1-(1)/(4))= (3)/(4)=0.75`.
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