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Tuesday, 14 March 2017

Kinetic theory of gases - IV


Law of equipartion of energy: For any thermodynamical system in thermal
equilibrium, the energy of the system is equally divided amongst its various degree
of freedom and energy associated with each degree of freedom corresponding to


each molecule is 1/2KBT where KB is the Boltzmann’s constant and T is absolute temperature.
The law of equipartition of energy holds good for all degrees of freedom whether translational , rotational or vibrational.
A monoatomic gas molecule has only translational kinetic energy

So a monoatomic gas molecule has only three (translational) degrees of
freedom.
In addition to translational kinetic energy, a diatomic molecule has two
rotational Kinetic energies

Here the line joining the two atoms has been taken as x-axis about which there is
no rotation. So, the degree of freedom of a diatomic molecule is 5, it does not
vibrate.

At very high temperature, vibration is also activated due to which two extra degree
of freedom emerge from vibrational energy. Hence at very high temperature
degree of freedom of diatomic molecule is seven.

*(Each translational and rotational degree of freedom corresponds to one mole of
absorption of energy and has energy 1/2kBT).

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