# In a certain themodynamical process,

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:

$(50)$

$P=k v^{3}$

$p v^{-3}=k$

$x=-3$

$w=\frac{n R\left(T_{1}-T_{2}\right)}{x-1}$

$=\frac{n R(100-300)}{-3-1}$

$=\frac{n R(-200)}{-4}$

$=50 n R$