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

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

NTA AbhyasNTA Abhyas 2020

Solution:

Oxygen being a diatomic gas possesses 5 degrees of freedom, 3 translational and 2 rotational.
Argon being monoatomic has 3 translational degrees of freedom.
Total energy of the system
$=E_{o x y g e n}+E_{a r g o n}$
$=n_{1}f_{1}\left(\frac{1}{2} R T\right)+n_{2}f_{2}\left(\right.\frac{1}{2}RT\left.\right)$
$=2\times 5\times \frac{1}{2}RT+4\times 3\times \frac{1}{2}RT$
$=5RT+6RT=11RT$