A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Considering only translational and rotational modes, the total internal energy of the system is

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4RT

20RT

12RT

15RT

answer is A.

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Detailed Solution

We know that
$\begin{aligned} U_{1} = \frac{f_{1}}{2} n_{1} R T = \frac{5}{2} (3 R T) \\ U_{2} = \frac{f_{2}}{2} n_{2} R T = \frac{3}{2} 5 R T \end{aligned}$
Therefore, total energy,
$\begin{aligned} U = U_{1} + & U_{2} \end{aligned}$
$= \frac{15}{2} R T + \frac{15}{2} R T$
$= 2 \times \frac{15}{2} R T \Rightarrow U = 15 R T$

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