First slide

Law of equipartition of energy

Question

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

Moderate

A

15 RT
B

9 RT
C

11 RT
D

4 RT

Solution

$The internal energy of 2 moles of O_{2} atom is$
$U_{O_{2}} = \frac{n_{1} f_{1}}{2} R T = 2 \times \frac{5}{2} \times R T = 5 RT$
The internal energy of 4 moles of Ar atom is
$U_{Ar} = \frac{n_{2} f_{2} R T}{2} = 4 \times \frac{3}{2} \times R T = 6 RT$
$∴ The total internal energy of the system is$
$U = U_{O_{2}} + U_{Ar} = 5 R T + 6 R T = 11 R T$

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