What are degrees of freedom?

Answer

The degrees of freedom of a system are defined as the total number of co-ordinates or independent quantities required to descirbe the configuration of the system completely. In a system consisting of `N` particles, if the particles posses `k` independent relations between them, then the number of degree of freedom of the system is given by
`f = 3 N-K ..............(i)`
Let us calculate the degrees of freedom in the following cases:
(a) Monoatomic gas molecule. In such a case. `N=1` and obvously `k = 0`.
`:. f = 3 xx1 - 0 = 1........(ii)`
Thus, a monoatomic gas molecule possesses `3` degree of freedom
(b) Diatomic gas molecule. In a diatomic gas molecule, the two atoms are held at a fixed distance by the molecules bond. Thus, `N = 2` and `k =1`.
`:. f = 3 xx2 - 1 = 5 .............(iii)`.
Thus, a diatomic gas molecule possesses `5` degree of freedom.
(c) Triatomic gas molecule. In a triatomic gas molecule, the three atoms are held at fixed distances relative to one another by the three molecules bonds. Thus, `N = 3` and `k = 3`
`:. f = 3 xx3 - 3 = 6 ........(iv)`
Thus, a triatomic gas molecule possesses `6` degree of freedom.