N moles of an ideal diatomic gas is contained in a cylinder at temperature T. On supplying some heat to cylinder, N/3 moles of gas disassociated into atoms while temperature remains constant. Heat supplied to the gas is

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$\frac{N R T}{6}$

$\frac{N R T}{3}$

$\frac{8 N R T}{3}$

$\frac{5 N R T}{2}$

answer is D.

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Detailed Solution

$d Q = n C_{V} d T d Q = N \frac{5}{2} R I [\frac{211}{3} \frac{5}{2} R T + \frac{N}{3} \frac{3}{2} R T] = \frac{N 5 R T}{2} - [\frac{10 + 3}{6}] N R T = \frac{N R T}{6}$

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