Question

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

• A. Q=2RT
• B. Q=RT
• C. Q=3RT
• D. Q=4RT

Answer 1

The correct option is B Q=RT

$Q=△U=U_f-U_i$= [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]
$=(4\times \frac{3}{2}RT+2\times \frac{5}{2}RT)-(4\times \frac{5}{2}RT)=RT$
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.