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. $4RT$
• B. $5RT$
• C. $15RT$
• D. $11RT$

Answer 1

Answer: (D)

$11RT$

For an ideal gas, the internal energy is given by,

$U=\frac{f}{2}nRT$.

For a monoatomic gas, there are only 3 translational degrees of freedom and for a diatomic gas there are 3 translational + 2 rotational degrees of freedom.

So,
$U=2\times \frac{5}{2}\times RT+4\times \frac{3}{2}RT=11RT$