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

Solution

1. The internal energy of a gas is given by $U=\frac{f}{2}nRT$, where $f$ is the number of degrees of freedom.
2. For oxygen (diatomic, $f=5$) with $n=2$ moles, the internal energy is $$\begin{array}{rl}{U}_{O_2}& =\frac{5}{2}\times 2\times RT\\ & =5RT\end{array}$$.
3. For argon (monatomic, $f=3$) with $n=4$ moles, the internal energy is $$\begin{array}{rl}{U}_{Ar}& =\frac{3}{2}\times 4\times RT\\ & =6RT\end{array}$$.
4. The total internal energy is the sum $$\begin{array}{rl}{U}_{total}& =5RT+6RT\\ & =11RT\end{array}$$.
5. Hence the answer is (A).