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$^\circ$C to 300$^\circ$C will be ___________ nR, where n denotes number of moles of a gas.

<p>In this thermodynamical process, the pressure $ P $ of a gas is related to its volume $ V $ by the equation $ P = kV^3 $. Thus, we have:</p> <p>$ PV^{-3} = k $</p> <p>This implies that the value of $ x $ is $-3$ in the relationship. To find the work done ($ W $) when the temperature changes from 100°C to 300°C, we can use the formula:</p> <p>$ W = \frac{nR(T_1 - T_2)}{x - 1} $</p> <p>Substitute the given temperatures and the value of $ x $:</p> <p>$ W = \frac{nR(100 - 300)}{-3 - 1} $</p> <p>Calculate the expression:</p> <p>$ W = \frac{nR(-200)}{-4} $</p> <p>Which simplifies to:</p> <p>$ W = 50 \, nR $</p>