Question

A diatomic gas is used in carnot heat engine having efficiency $80$ %. Find the ratio of initial volume to final volume of gas during adiabatic expansion.

• A. ${\left(\frac{1}{5}\right)}^{\frac{3}{2}}$
• B. ${\left(\frac{1}{3}\right)}^{\frac{5}{2}}$
• C. ${\left(\frac{1}{5}\right)}^{\frac{5}{2}}$
• D. ${\left(\frac{1}{5}\right)}^{\frac{2}{5}}$

Answer 1

Answer: (C)

$\eta =1-\frac{T_2}{T_1}$
$0.8=1-\frac{T_2}{T_1}$
$\frac{T_2}{T_1}=0.2$
$T_2{V}_2^{\gamma -1}=T_1{V}_1^{\gamma -1}$
${\left(\frac{V_2}{V_1}\right)}^{\gamma -1}=\frac{T_1}{T_2}=5$
$\frac{V_1}{V_2}={\left(\frac{1}{5}\right)}^{\frac{5}{2}}$