A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is :

Solution

Physics sir · 3 steps

Give each gas its own degrees of freedom, find each energy, then just add the two.

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 degrees. Argon is monatomic, so it has only 3 translational degrees of freedom. Oxygen with a rigid bond has 3 translational and 2 rotational, so f = 5. A rigid bond means no vibration.

   U = 3 × 5/2RT + 5 × 3/2RT = 7.5 RT + 7.5 RT

3. So. The total internal energy is 15 RT, which is option (c).

The idea to keep. In a mixture, energies add gas by gas. Monatomic gives 3/2RT per mole, rigid diatomic gives 5/2RT per mole. Never use one f for the whole mixture.

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