Initial pressure and volume of a gas are P and V respectively. First it is expanded isothermally to

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11.Thermodynamics

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Initial pressure and volume of a gas are $P$ and $V$ respectively. First it is expanded isothermally to volume $4\ V$ and then compressed adiabatically to volume $V.$ The final pressure of gas will be (given $\gamma = 3/2)$

A

$1P$

B

$2P$

C

$4P$

D

$8P$

Solution

$1 \rightarrow 2: P V=P^{\prime} .4 V \Rightarrow 4 V \Rightarrow P^{\prime}=\frac{P}{4}$

$2 \rightarrow 3: P^{\prime}(4 V)^{\gamma}=P^{\prime}(V)^{\gamma} \Rightarrow P^{\prime}=P^{\prime}(4)^{\gamma}$

$P^{\prime}=\frac{P}{4}(4)^{\frac{3}{2}}=\frac{P}{4} \cdot 8=2 P$

Standard 11

Physics

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