Question:
In a certain themodynamical process, the pressure of gas depends on its volume as $\mathrm{kV}^{3}$. The work done when the temperature changes from $100^{\circ} \mathrm{C}$ to $300^{\circ} \mathrm{C}$ will be______ $\mathrm{nR}$, where $\mathrm{n}$ denotes number of moles of a gas.
Solution:
$(50)$
$P=k v^{3}$
$p v^{-3}=k$
$x=-3$
$w=\frac{n R\left(T_{1}-T_{2}\right)}{x-1}$
$=\frac{n R(100-300)}{-3-1}$
$=\frac{n R(-200)}{-4}$
$=50 n R$
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