A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be [2023]

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Solution

Q.
A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be [2023]

1 8 RT

2 16 RT

3 4 RT

4 11 RT

Ans.
(4)

${(C_{v})}_{\max} = \frac{n_{1} C v_{1} + n_{2} C v_{2}}{n_{1} + n_{2}}$

${(C_{v})}_{\max} = \frac{2 \times \frac{5}{2} R + 4 \times \frac{3}{2} R}{2 + 4} = \frac{11 R}{6}$

$Δ U = n {(C_{v})}_{mix} Δ T$ $= 6 \times \frac{11 R}{6} \times Δ T = 11 R T$

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