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 increases from V to 32V , the efficiency of the engine is :-

Question

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 increases from V to 32V , the efficiency of the engine is :- (A) 0.25 (B) 0.5 (C) 0.75 (D) 0.99

Tardigrade Admin · Accepted Answer

T1V1&gamma; - 1=T2V2&gamma; - 1⇒ (T2/ T1)=(1/4) So, η=1-(T2/ T1)=0.75

Q. 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 increases from $V$ to $32 V$ , the efficiency of the engine is :-

$0.25$

$0.5$

$0.75$

$0.99$

$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1} \Rightarrow \frac{T _{2}}{T _{1}} = \frac{1}{4}$
So, $η = 1 - \frac{T _{2}}{T _{1}} = 0.75$

Q. 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 increases from V to 32V , the efficiency of the engine is :-

0.25

0.5

0.75

0.99