Question

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

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

Answer 1

The correct option is D $11RT$

Let ${}^{\prime }{\mu }^{\prime }$ be the number of moles of a gas.
By neglecting vibrational degrees of freedom,
Number of degrees of freedom of $Ar$ $f_1=3$
Number of degrees of freedom of $O_2$ $f_2=5$
Internal energy of 2 moles of oxygen
$U_{O_2}=\mu \left(\frac{f_2}{2}RT\right)=2\times \frac{5}{2}RT=5RT$
Internal energy of 4 moles of Argon
$U_{Ar}=\mu \left(\frac{f_1}{2}RT\right)=4\times \frac{3}{2}RT=6RT$
$\therefore$ Total internal energy of the mixture of two gases is
$U=U_{o_2}+U_{Ar}=11RT$
Thus, option (d) is the correct answer.