Question

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

• A. 29 RT
• B. 20 RT
• C. 27 RT
• D. 21 RT

Answer 1

Answer: (C)

27 RT

Answer 2

The total internal energy U of a gas mixture is given by:

$U = nC_{V}T.$

For argon (a monatomic gas), $C_{V, Ar} = \frac{3R}{2}$. For oxygen (a diatomic gas), $C_{V, O_2} = \frac{5R}{2}$.

Therefore, the internal energy of the mixture is:

$U = n_1C_{V, Ar}T + n_2C_{V, O_2}T.$

Substitute $n_1 = 8$, $n_2 = 6$:

$U = 8 \times \frac{3R}{2} \times T + 6 \times \frac{5R}{2} \times T = 27RT.$

Thus, the answer is:

$27RT.$