Q 11-12-157JEE MainJEE Main 2017 (9 Apr)Medium
$N$ moles of diatomic gas in a cylinder is at a temperature $T$. Heat is supplied to the cylinder such that the temperature remains constant but $n$ moles of the diatomic gas get converted into monoatomic gas. The change in the total kinetic energy of the gas is:
Answer: (D) $\dfrac12nRT$
Initial kinetic energy: $\dfrac52NRT$.
$n$ moles of diatomic molecules give $2n$ moles of atoms. Finally:
$$K = \frac52(N - n)RT + \frac32(2n)RT = \frac52NRT + \frac12nRT$$
Change in kinetic energy $= \dfrac12nRT$.
Solution by Sreeraj P, M.Sc Physics