Determine efficiency of carnot cycle if in adiabatic expansion volume $3$ times of initial value and $\gamma =1.5$
AIIMS 2019, Medium
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Consider the following expression.
$T _{1} V _{1}^{ \gamma -1}= T _{2} V _{2}^{ \gamma -1}$
$\frac{ T _{2}}{ T _{1}}=\left(\frac{ V _{1}}{ V _{2}}\right)^{ \gamma -1}$
Substitute the values.
$\frac{ T _{2}}{ T _{1}}=\left(\frac{1}{3}\right)^{1.5-1}$
$=\frac{1}{\sqrt{3}}$
The efficiency is given as,
$\eta=1-\frac{ T _{2}}{ T _{1}}$
$=1-\frac{1}{\sqrt{3}}$
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