JEE Main 2023 · 10 April · evening · Single correct · +4 / −1
A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,
- (a) 4RT
- (b) 16RT
- (c) 8RT
- (d) 11RT
Answer and solution
Answer (d) 11RT
Solution
Physics sir · 3 steps
Give each gas its own degrees of freedom, find each energy, then add the two.
- Equipartition. Each degree of freedom carries 1/2RT per mole. So n moles of a gas with f degrees of freedom have U = f/2nRT.
- Count degrees. Oxygen is diatomic. With vibration neglected it has 3 translational and 2 rotational degrees, so f = 5. Neon is monatomic and has only the 3 translational degrees, so f = 3.
U = 5/2(2)RT + 3/2(4)RT = 5RT + 6RT
- So. The total internal energy is 11RT, which is option (d).
The idea to keep. For a mixture, never average the degrees of freedom first. Find f/2nRT for each gas separately and add: monatomic f = 3, rigid diatomic f = 5.
Answer from the NTA final answer key. Solution by PrepWiser.