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Why is the average energy corresponding to a vibrational degree of freedom double that of a translational degree of freedom

Why is the average energy corresponding to a vibrational degree of freedom double that of a translational degree of freedom

Grade:12

1 Answers

Eshan
askIITians Faculty 2095 Points
4 years ago
According to the law of equipartition of energy, every degree of freedom has average enerrgy of\dfrac{1}{2}kTper molecule.

There are 3 degrees of freedom corresponding to translational motion, 3 corresponding to vibrational motion.

So the average energy corresponding to transational motion only is3\times\dfrac{1}{2}kT =\dfrac{3}{2}kT

When we also consider the vibrational motion of the molecule, the body has both transalational as well as vibrational motion, and each type of motion contributes 3 degrees of freedom.

Hence average energy per molecule when vibration is considered(in addiition to translation) is(3+3)\times\dfrac{1}{2}kT =3kT

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