A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

Solution

Physics sir · 3 steps

Give each gas its own degrees of freedom, find each energy, and add them up.

1. 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.
2. Count freedoms. Argon is monatomic, so it has only 3 translational degrees of freedom. Oxygen is diatomic: 3 translational plus 2 rotational gives f = 5, because vibration is neglected.

   U = 8 × 3/2RT + 6 × 5/2RT = 12 RT + 15 RT

3. So. The total internal energy is U = 27 RT, which is option (b).

The idea to keep. For a mixture, internal energy just adds up gas by gas. Monatomic gets f = 3, diatomic without vibration gets f = 5, and each mole holds f/2RT.

Answer from the NTA final answer key. Solution by PrepWiser.