1. Tardigrade
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  4. A perfect gas is found to obey the relation P V3 / 2= constant during an adiabatic process. If such a gas initially at a temperature T, is compressed to half of its initial volume, then its final temperature will be :

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Q. A perfect gas is found to obey the relation $P V^{3 / 2}=$ constant during an adiabatic process. If such a gas initially at a temperature $T$, is compressed to half of its initial volume, then its final temperature will be :

JIPMERJIPMER 2006Thermodynamics

Solution:

Gas obeys the equation
$P V^{3 / 2}=\text { constant }$
Comparing with $P V^{\gamma}=$ constant
$\gamma=\frac{3}{2}$
For arliabatic process
$T_{1} V_{1}^{\gamma-1} =T_{2} V_{2}^{\gamma-1}$
$T(V)^{3 / 2-1} =T_{2}\left(\frac{V}{2}\right)^{3 / 2-1}$
$T_{2} =T(2)^{3 / 2-1}$
$=(2)^{1 / 2} T$