Q. 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) $Q = 4RT$
Explanation
(b) $Q = \mathrm{\Delta}U = U_{f} - U_{i} =$ [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
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.