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

Question

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 (A) 4 RT (B) 15 RT (C) 9 RT (D) 11 RT

Tardigrade Admin · Accepted Answer

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} (\frac{1}{2} RT) + n_{2} f_{2} (\frac{1}{2} RT)

= 2 \times 5 \times \frac{1}{2} RT + 4 \times 3 \times \frac{1}{2} RT

= 5 RT + 6 RT = 11 RT

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

$4 RT$

$15 RT$

$9 RT$

$11 RT$

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

4RT

15RT

9RT

11RT

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 =Eoxygen​+Eargon​ =n1​f1​(21​RT)+n2​f2​(21​RT) =2×5×21​RT+4×3×21​RT =5RT+6RT=11RT

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

$4 RT$

$15 RT$

$9 RT$

$11 RT$