Q. A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature $T$. Neglecting all vibrational moles, the total internal energy of the system is
A) $4\ RT$
B) $15\ RT$
C) $9\ RT$
D) $11\ RT$
Explanation
(d) Oxygen being a diatomic gas possesses 5 degrees of freedom, 3 translational and 2 rotational.
Argon being monoatomic has 3 translational degrees of freedom.
Total energy of the system
$= E_{oxygen} + E_{argon}$
$= n_{1}f_{1}\left( \frac{1}{2}RT \right) + n_{2}f_{2}(\frac{1}{2}RT)$
$= 2 \times 5 \times \frac{1}{2}RT + 4 \times 3 \times \frac{1}{2}RT$
$= 5RT + 6RT = 11RT$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.