The number of independent directions in which a system (or gas molecule) can have motion, are known as the number of degrees of freedom of that molecule or object. The number of degree of freedom is needed to express the position, motion and energy of a body. If a molecule in motion is confined to a straight line it has only one transnational degree of freedom, while if the similar molecule is confined to move in a plane, it will have two translational degrees of freedom. If the particle is free to move in plane, it will have three dimensional degrees of freedom.
A gas particle can have following kinds of energies:
(a) Translational kinetic energy
(b) Rotational kinetic energy
(c) Vibrational kinetic energy
Degree of freedom of monatomic gas: If instead of molecule, we suppose a molecular of a monatomic gas, which consists of a one atom, the translational motion can take place in any direction in space. Thus it can be solved along three co-ordinate axes and can have three independent motions and hence three degrees of freedom. A mono atomic particle can also rotate but due to its small moment of inertia rotational kinetic energy is not significant. Therefore it does not check rotational degrees of freedom.
Degree of freedom f = 3 (all translational)
(ii) Degree of freedom of diatomic gas: The molecules of diatomic and linear polyatomic gases are made up of two atoms joined rigidly to one another through a bond. Such a particle cannot only move as a whole but can also rotate about one of the three co-ordinate dimensions. However its moment of inertia about the axis joining the two atoms is negligible compared to that about the other two dimensions. Hence it has only 2 rotational motions. Thus, a simple particle has 5 degrees of freedom. At sufficiently great temperatures it has vibration energy in addition to its two degrees of freedom, Thus at high temperatures a diatomic particle has 7 degrees of freedom, 3 translational, 2 rotational and 2 vibration.
Degree of freedom, f = 5 (3 translational +2 rotational) at room temperature
f = 7 (3 translational+2 rotational+2 vibration) at high temperature
(iii) Degree of freedom of nonlinear polyatomic gas: A polyatomic (non-linear) molecule (such as NH3) can rotate about any of three co-ordinate dimension. Hence it has 6 degrees of freedom, 3 rotational and 3 translational. At normal temperature a polyatomic gas molecule has vibration energy greater than that of a perfect gas. The atoms within the particle may also vibrate with respect to each other at high temperature. In that case, the particle will have an additional degree of freedom, with reference to vibration motion.
Degree of freedom, f = 6 (3 translational +3 rotational) at room temperature
f = 8 (3 translational+3 rotational+2 vibration) at high temperature
(iv) Degree of freedom of solids: An atom in a solid state has no degrees of freedom for transnational and rotational speed. At great temperatures due to vibration along 3 axes it has 3 ´ 2(directions) = 6 degrees of freedom.
F = 6 due to vibration at high temperature
(v) Degree of freedom of diatomic, monatomic liner and non-linear polyatomic gas:
|
Nature of motion
|
Degree of Freedom
|
|
Translator
|
Rotational
|
Vibration
|
Total
|
|
Monatomic
|
3
|
0
|
0
|
3
|
|
Diatomic
|
3
|
2
|
0
|
5
|
|
Linear
|
3
|
2
|
0
|
5
|
|
Non-linear
|
3
|
3
|
0
|
6
|
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