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  4. In a certain thermodynamical process, the pressure of a gas depends on its volume as kv3 . The work done when the temperature changes from 100° C to 300° C will be nR , where n denotes number of moles of a gas.

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Q. In a certain thermodynamical process, the pressure of a gas depends on its volume as $kv^{3}$ . The work done when the temperature changes from $100^\circ C$ to $300^\circ C$ will be $nR$ , where $n$ denotes number of moles of a gas.

NTA AbhyasNTA Abhyas 2022

Solution:

$P=kv^{3}$
$pv^{- 3}=k$
$x=-3$
$w=\frac{n R \left(T_{1} - T_{2}\right)}{x - 1}$
$=\frac{n R \left(\right. 100 - 300 \left.\right)}{- 3 - 1}$
$=\frac{n R \left(\right. - 200 \left.\right)}{- 4}$
$=50nR$