1. Tardigrade
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  3. Physics
  4. One mole of an ideal gas undergoes a process P=(P0/1+(V0 / V)2) . Here P0 and V0 are constants. The change in temperature of the gas when volume is changed from V=V0 to V=2 V0 is (x P0 V0/10 R) . Find x. (Here R= Universal gas constant)

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Q. One mole of an ideal gas undergoes a process $P=\frac{P_{0}}{1+\left(V_{0} / V\right)^{2}} .$ Here $P_{0}$ and $V_{0}$ are constants. The change in temperature of the gas when volume is changed from $V=V_{0}$ to $V=2 V_{0}$ is $\frac{x P_{0} V_{0}}{10 R} .$ Find $x$.
(Here $R=$ Universal gas constant)

Kinetic Theory

Solution:

$P V=n R T$
At $V=V_{0}: R T_{1}=\left(\frac{P_{0}}{2}\right)\left(V_{0}\right)$
At $V=2 V_{0}: R T_{2}=\left(\frac{4 P_{0}}{5}\right)\left(2 V_{0}\right)$
$\Rightarrow T_{2}-T_{1}=\frac{11 P_{0}\, V_{0}}{10 R}$