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

<p>The internal energy (U) of a gas depends on its degrees of freedom (f). <br/><br/>For a monatomic gas like neon, the degrees of freedom are f = 3 (translational). For a diatomic gas like oxygen, the degrees of freedom are f = 5 (3 translational + 2 rotational).</p> <p>The internal energy for each component of the gas mixture can be calculated using the formula:</p> <p>$U = \frac{f}{2}nRT$</p> <p>where n is the number of moles, R is the universal gas constant, and T is the temperature.</p> <p>For the 4 moles of neon (monatomic):</p> <p>$U_{Ne} = \frac{3}{2} \cdot 4RT = 6RT$</p> <p>For the 2 moles of oxygen (diatomic):</p> <p>$U_{O_2} = \frac{5}{2} \cdot 2RT = 5RT$</p> <p>Now, to find the total internal energy, we sum the internal energies of the individual components:</p> <p>$U_{total} = U_{Ne} + U_{O_2} = 6RT + 5RT = 11RT$</p> <p>Thus, the total internal energy of the system is 11RT.</p>