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)

$\eta=1-\frac{T_{2}}{T_{1}}$
$0.8=1-\frac{T_{2}}{T_{1}}$
$\frac{T_{2}}{T_{1}}=0.2$
$T_{2}V_{2}^{\gamma - 1}=T_{1}V_{1}^{\gamma - 1}$
$\left(\frac{V_{2}}{V_{1}}\right)^{\gamma - 1}=\frac{T_{1}}{T_{2}}=5$
$\frac{V_{1}}{V_{2}}=\left(\frac{1}{5}\right)^{\frac{5}{2}}$