Question

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

• A. $14RT$
• B. $13RT$
• C. $15RT$
• D. $11RT$

Answer 1

The correct option is D $11RT$

Given:
Number of moles of oxygen, $n_1=2$
Number of moles of argon, $n_2=4$
Temperature $=T$
To find:
Total internal energy of system, $U=?$

We know that, in an ideal gas internal energy is given by,
$U=\frac{f}{2}nRT$
where $f$ is degree of freedom.
So, total internal energy,
$U=U_1+U_2$
$\Rightarrow U=\frac{f_1}{2}{n}_{1}R{T}_1+\frac{f_2}{2}{n}_{2}R{T}_2$
$\Rightarrow U=\frac{5}{2}\times 2\times RT+\frac{3}{2}\times 4\times RT$
[ for $O_2$, $f=5$ and for $Ar,f=3$, also temperature is same for both gases ]
$\Rightarrow U=11RT$