An insulator container contains $4\, moles$ of an ideal diatomic gas at temperature $T.$ Heat $Q$ is supplied to this gas, due to which $2 \,moles$ of the gas are dissociated into atoms but temperature of the gas remains constant. Then
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(b) $Q = \Delta U$$ = {U_f} - {U_i}$ = [internal energy of $4$ moles of a monoatomic gas $+$ internal energy of $2$ moles of a diatomic gas] $-$ [internal energy of $4$ moles of a diatomic gas]
$ = \left( {4 \times \frac{3}{2}RT + 2 \times \frac{5}{2}RT} \right) - \left( {4 \times \frac{5}{2}RT} \right) = RT$
$Note : \,(a)\, 2$ moles of diatomic gas becomes $4$ moles of a monoatomic gas when gas dissociated into atoms.
$(b)$ Internal energy of $\mu $ moles of an ideal gas of degrees of freedom $F$ is given by $U = \frac{f}{2}\mu RT$
$F = 3$ for a monoatomic gas and $5$ for diatomic gas.
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