Thermodynamic process is shown below on a $P-V$ diagram for one mole of an ideal gas. If $V _{2}=2 V _{1}$ then the ratio of temperature $T _{2} / T _{1}$ is ...... .
JEE MAIN 2021, Diffcult
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$PV ^{1 / 2}= c$
$\frac{ nRT }{ V } V ^{1 / 2}= c$
$T = c ^{1} V ^{1 / 2}$
$\frac{ T _{2}}{ T _{1}}=\left(\frac{ V _{2}}{ V _{1}}\right)^{1 / 2}=\left(\frac{2 V _{1}}{ V _{1}}\right)^{1 / 2}$
$\frac{ T _{2}}{ T _{1}}=\sqrt{2}$
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