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

The Correct Option is C

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:

\( 27RT. \)