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A gas mixture consists of 2 moles of O₂ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

1. 15 RT
2. 9 RT
3. 11 RT
4. 4 RT

Correct answer: 9 RT

Solution

O₂ is a diatomic gas with 5 degrees of freedom (3 translational + 2 rotational), so its internal energy is (5/2) nRT = (5/2)(2)RT = 5RT. Ar is a monoatomic gas with 3 degrees of freedom (only translational), so its internal energy is (3/2) nRT = (3/2)(4)RT = 6RT. Total internal energy = 5RT + 6RT = 11RT.

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