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Degrees of Freedom & Internal Energy question from NEET 2017

Q35NEET 2017Medium

Degrees of Freedom & Internal Energy

A gas mixture consists of 2 moles of O2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

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Answer: (c)

$U = \sum n\frac{f}{2}RT$ ; $\text{O}_2$ (no vibration) $f = 5$ , Ar $f = 3$ .
$U = 2 \times \frac{5}{2}RT + 4 \times \frac{3}{2}RT = 5RT + 6RT$
So the answer is (c) $11RT$ .

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