Question

A gas mixture consists of $2$ moles of oxygen and $4$ moles of Argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

• A. $4\, RT$
• B. $9\, RT$
• C. $11\, RT$
• D. $15\, RT$

Answer 1

The Correct Option is C

To determine the total internal energy of the gas mixture, we need to understand the internal energies of individual gas molecules and how they contribute to the total energy in a mixture.

We have a mixture of oxygen (O₂) and Argon (Ar). Let's examine each gas separately:

• Oxygen (O₂): Oxygen is a diatomic molecule, and for diatomic gases, the internal energy per mole is given by \frac{5}{2} RT because of the translational and rotational degrees of freedom (we neglect vibrational modes as specified).
• Argon (Ar): Argon is a monoatomic gas, and for monoatomic gases, the internal energy per mole is \frac{3}{2} RT due to translational degrees of freedom.

Now, calculate the internal energies contributed by each component:

1. Internal Energy of Oxygen:
   • Moles of Oxygen = 2
   • Internal energy of Oxygen = 2 \times \frac{5}{2} RT = 5RT
2. Internal Energy of Argon:
   • Moles of Argon = 4
   • Internal energy of Argon = 4 \times \frac{3}{2} RT = 6RT

The total internal energy of the gas mixture is the sum of the internal energies of oxygen and argon:

• Total internal energy = 5RT + 6RT = 11RT

Thus, the correct answer is 11\, RT.