A sample of gas with gamma=1.5 is taken through an adiabatic process in which volume is compressed f

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11.Thermodynamics

hard

A sample of gas with $\gamma=1.5$ is taken through an adiabatic process in which the volume is compressed from $1200\, {cm}^{3}$ to $300\, {cm}^{3}$. If the initial pressure is $200\, {kPa}$. The absolute value of the workdone by the gas in the process $= \,..... J.$

A

$0.5$

B

$240$

C

$48$

D

$480$

(JEE MAIN-2021)

Solution

$\gamma=1.5$

$p_{1} v_{1}^{\gamma}=p_{2} v_{2}^{\gamma}$

$(200)(1200)^{1.5}=P^{2}(300)^{1.5}$

$P_{2}=200[4]^{3 / 2}=1600 {kPa}$

$\mid$ W.D. $\mid=\frac{{p}_{2} {v}_{2}-{p}_{1} {v}_{1}}{v-1}=\left(\frac{480-240}{0.5}\right)=480 {J}$

Standard 11

Physics

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