Question

A diatomic ideal gas is used in a Car engine as the working substance. lf during the adiabatic expansion part of the cycle, volume of the gas increases from $V$ to $32$ $V$ the efficiency of the engine is

• A. $0.5$
• B. $0.75$
• C. $0.99$
• D. $0.25$

Answer 1

The correct option is B $0.75$

The efficiency of cycle is
$\eta =1-\frac{T_2}{T_1}$
For adiabatic process
$T{V}^{\gamma -1}=$ constant
For diatomic gas $\gamma =\frac{7}{5}$
$T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$

$T_1=T_2(\frac{V_2}{V_1}{)}^{\gamma -1}$

$T_1=T_2(32{)}^{\frac{7}{5}-1}$

$=T_2(2^5{)}^{2/5}$
$=T_2\times 4$

$T_1=4T_2$.
$\eta =(1-\frac{1}{4})=\frac{3}{4}=0.75$