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DEGREES OF FREEDOM:- The number of directions in which a particle can move freely is defined as its degree of freedom. OR The number of independent coordinates required to specify completely the position and orientation of a particle in space, is defined as its degree of freedom Degrees of freedom are of three types: they are,
Degrees of freedom of translational motion f_t
Degrees of freedom of rotational motion f_r and
Degrees of freedom of vibrational motion f_v
Degrees of freedom of translational motion f_t:- These are due to translational motion of molecules. Maximum number of translational degrees of freedom is 3 irrespective of that the molecule may be monatomic or polyatomic, linear or Non linear. These are present at ordinary temperature.
Degrees of freedom of rotational motion f_r:
These are due to rotational motion of a molecule about an axis passing through the centre of mass of the molecule. Their number depends up on the structure of molecule.
These are also present at ordinary temperatures.
Degrees of freedom of vibrational motion f_v:
These are due to the vibrational motion of molecule about its equilibrium position.
Their number depends up on the structure of the molecules.
These are produced only at high temperatures.
Degrees of freedom for:-
Monoatomic gas:- A mono atomic gas molecule can move linearly in any direction along three co-ordinate axes. Hence its degrees of freedom is (f_t) = 3
Examples: molecules of noble gases like He (helium), Ne (neon), Ar (Argon) etc
Diatomic gas:- The center of mass of two atoms is free to move along three Co-ordinate axes. Hence its translational degrees of freedom is f_t = 3
The molecules if these gases can rotate about a perpendicular axis passing through their center of mass in two directions. Hence its degree of freedom of rotating motion is f_r=2 , Therefore, total degrees of freedom f = f_t+ f_r = 3 + 2= 5
For a tri atomic or polyatomic gas non linear :-
Degrees of freedom of translational motion, f_t = 3 and degrees of freedom of rotational motion, f_r = 3, Therefore, total degree of freedom, f =f_t+ f_r = 3 + 3 = 6
Note: In general, degrees of freedom can be determined as F = 3N -- B

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