N moles of a diatomic gas in a cylinder are 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. What is the change in the total kinetic energy of the gas?

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$\frac{1}{2} nRT$

$\frac{5}{2} nRT$

$\frac{3}{2} nRT$

answer is C.

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Detailed Solution

Initial kinetic energy of the system

$K_{i} = \frac{5}{2} RTN$

Final kinetic energy of the system
$\begin{array}{l} K_{f} = \frac{5}{2} RT (N - n) + \frac{3}{2} RT (2 n) \\ ΔK = K_{f} - K_{l} = nRT [3 - \frac{5}{2}] = \frac{1}{2} nRT \end{array}$

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