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

To determine the total internal energy of a gas mixture comprising argon and oxygen at temperature \(T\), we must ascertain the degrees of freedom for each molecular species.

Step 1: Identify gases and their degrees of freedom

• Argon (Ar) is a monatomic gas with 3 degrees of freedom (\(f=3\)). Its internal energy per mole is:

\[\text{Internal energy per mole} = \frac{3}{2} RT\]

• Oxygen (O₂) is a diatomic gas, possessing 5 degrees of freedom at ambient temperatures (vibrational modes disregarded). Its internal energy per mole is:

\[\text{Internal energy per mole} = \frac{5}{2} RT\]

Step 2: Compute individual gas internal energies

• For 8 moles of argon: \(U_{\text{argon}} = 8 \times \frac{3}{2} RT = 12RT\)
• For 6 moles of oxygen: \(U_{\text{oxygen}} = 6 \times \frac{5}{2} RT = 15RT\)

Step 3: Calculate total internal energy of the mixture

• Total internal energy: \(U_{\text{total}} = U_{\text{argon}} + U_{\text{oxygen}} = 12RT + 15RT = 27RT\)

The computed total internal energy of the system is \(27 RT\), aligning with the provided options. Thus, the correct answer is 27 RT.