Question

A gas mixture of $2$ moles of $O_2$ and $4$ moles of $Ar$ are at temperature $T$. Neglecting all the vibrational modes, the total internal energy of the system is

• A. $4RT$
• B. $15RT$
• C. $9RT$
• D. $11RT$

Answer 1

The correct option is D $11RT$

We know that, Internal energy $\left(U\right)$
$U=\frac{nfRT}{2}$
For $O_2$, [$n=2$ and $f=5$ (diatomic)]
$U_1=\frac{2\times 5\times RT}{2}$
$=5RT$ ... (1)
For $Ar$, [$n=4$ and $f=3$ (monoatomic)]
$U_2=\frac{4\times 3\times RT}{2}$
$=6RT$ ... (2)
On adding (1) and (2),
Total internal energy $=11RT$
So, total internal energy of gas mixture is $11RT$