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Question

# A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy of O2 molecules to that of N2 molecules per degree of freedom is

A
1:1
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B
1:2
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C
2:1
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D
Depends on moment of inertia.
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Solution

## The correct option is A 1:1According to law of equipartition of energy, Energy associated with each molecule for each degree of freedom E=12KT Both N2 and O2 are diatomic gas ∴Rotational degree of freedom (fr)=2 for both N2 and O2 ∴ Average rotational kinetic energy per molecule, fr=12KT (Average rotational kinetic energy per molecule depends upon degree of freedom and temperature. It does not depends on mole.) ∴ Average rotational kinetic energy associated of O2 molecule per degree of freedom = Average rotational kinetic energy associated of N2 molecule per degree of freedom

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