Q 11-11-120JEE MainJEE Main 2021 (25 Feb, Shift 1)Medium
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 °C to 300 °C will be $xnR$ where $n$ denotes number of moles of a gas. Find $x$.
Numerical value type. Enter your answer.
Answer: 50
$$W = \int P\,dV = \int kV^3\,dV = \frac{k(V_2^4 - V_1^4)}{4} = \frac{P_2V_2 - P_1V_1}{4} = \frac{nR(T_2 - T_1)}{4}$$
$$W = \frac{nR\times200}{4} = 50\,nR \Rightarrow x = 50$$
Solution by Sreeraj P, M.Sc Physics