# how to calculate degree of freedom of any molecule or atom

Godfrey Classic Prince
633 Points
11 years ago

Dear krishna veni,

The number of independent parameters required to specify the configuration of a system. This concept is applied in the kinetic theory to specify the number of independent ways in which an atom or molecule can take up energy. There are however various sets of parameters that may be chosen, and the details of the consequent theory vary with the choice.

In a diatomic gas the two atoms require six coordinates between them, giving six degrees of freedom. Commonly these are interpreted as six independent ways of storing energy: on this basis the molecule has three degrees of freedom for different directions of translational motion, and in addition there are two degrees of freedom for rotation of the molecular axis and one vibrational degree of freedom along the bond between the atoms. The rotational degrees of freedom each contribute their share, kT/2, to the total energy; similarly the vibrational degree of freedom has an equal share of kinetic energy and must on average have as much potential energy. The total energy per molecule for a diatomic gas is therefore 3kT/2 (for translational energy of the whole molecule) plus 2kT/2 (for rotational energy) plus 2kT/2 (for vibrational energy), i.e. a total of 7kT/2. 2. The least number of independent variables required to define the state of a system in the phase rule. In this sense a gas has two degrees of freedom (e.g. temperature and pressure).
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