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  4. 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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Q. $N$ 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 ?

JEE MainJEE Main 2017Kinetic Theory

Solution:

$u_{1}=N \frac{5}{2} RT$
$u_{f} =2n \frac{3}{2}RT+\left(N-n\right) \frac{5}{2}RT$
$=\frac{1}{2}\, n\,RT+\frac{5}{2} nRT$
$\Delta u=Q=\frac{1}{2}\,n\,RT$