Question

A gas mixture consist of $3\text{moles}$ of oxygen and $5\text{moles}$ of argon at temperature $T$. Considering only translational and rotational modes, the total internal energy of the system is:

• A. $15RT$
• B. $12RT$
• C. $4RT$
• D. $20RT$

Answer 1

The correct option is A $15RT$

The total internal energy of the mixture is given by,

$U=\frac{f_1}{2}{n}_{1}RT+\frac{f_2}{2}{n}_{2}RT$

Considering translational and rotational modes,

degrees of freedom of oxygen (diatomic gas)
$f_1=5$

degrees of freedom of argon (monoatomic gas)
$f_2=3$

$\text{Given that,}{n}_1=3,n_2=5$

$\therefore U=\frac{5}{2}\left(3RT\right)+\frac{3}{2}\times 5RT$

$\Rightarrow U=15RT$

Hence, option $\left(A\right)$ is correct.