Question

If a gaseous mixture consists of 3 moles of oxygen and 4 moles of argon at an absolute temperature \( T \), then the total internal energy of the mixture is
(Neglect vibrational modes and \( R \) is the universal gas constant)

• A. \( 11RT \)
• B. \( 12.5RT \)
• C. \( 13.5RT \)
• D. \( 15.5RT \)

Hint:

Always apply \( U = \frac{f}{2}nRT \) for each gas component using the appropriate degrees of freedom—3 for monoatomic, 5 for diatomic (neglecting vibrations).

Answer 1

The Correct Option is C

Step 1: Use the formula for internal energy: \[ U = \frac{f}{2} nRT \] where \( f \) is the degrees of freedom. Step 2: Oxygen is diatomic \( f = 5 \), and argon is monoatomic \( f = 3 \) Step 3: Compute internal energy contribution from each gas: \[ U_{\text{oxygen}} = \frac{5}{2} . 3RT = \frac{15}{2}RT = 7.5RT \] \[ U_{\text{argon}} = \frac{3}{2} . 4RT = \frac{12}{2}RT = 6RT \] Step 4: Total internal energy: \[ U_{\text{total}} = 7.5RT + 6RT = \boxed{13.5RT} \]