A gas mixture consists of 2 moles of and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is [2017]

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Solution

Q.
A gas mixture consists of 2 moles of $O_{2}$ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is [2017]

1 15 RT

2 9 RT

3 11 RT

4 4 RT

Ans.
(3)

The internal energy of 2 moles of $O_{2}$ atom is

$U_{O_{2}} = \frac{n_{1} f_{1}}{2} R T = 2 \times \frac{5}{2} R T = 5 R T$

The internal energy of 4 moles of Ar atom is

$U_{A r} = \frac{n_{2} f_{2} R T}{2} = 4 \times \frac{3}{2} R T = 6 R T$

$∴$ The total internal energy of the system is

$U = U_{O_{2}} + U_{A r} = 5 R T + 6 R T = 11 R T$

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