N moles of a diatomic gas in a cylinder are at a temperature T. Heat… | JEE Main 2017 (9 Apr, Shift 1)

Q36JEE Main 2017 · 9 APR · SHIFT 1Difficult

Degrees of Freedom & Internal Energy

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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Answer: (a)

Temperature is constant. Each mole of diatomic gas splits into 2 moles of monoatomic gas.
Before: KE of these $n$ moles $= n\cdot\frac{5}{2}RT$ .
After: $2n$ moles monoatomic, KE $= 2n\cdot\frac{3}{2}RT = 3nRT$ .
$\Delta KE = 3nRT - \frac{5}{2}nRT = \frac{1}{2}nRT$
So the answer is (a) $\frac{1}{2}nRT$ .

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