Question

Define the degree of freedom of a gas and find them for
(a) Monoatomic gas
(b) Diatomic gas

Answer 1

A degree of freedom of a physical system is an independent parameter that is necessary to characterize the state of a physical system. In general, a degree of freedom may be any useful property that is not dependent on other variables.

In three-dimensional space, three degrees of freedom are associated with the movement of a particle. A diatomic gas molecule has 5 degrees of freedom. This set may be decomposed in terms of translations, rotations, and vibrations of the molecule. The center of mass motion of the entire molecule accounts for 3 degrees of freedom. In addition, the molecule has two rotational degrees of motion and one vibrational mode. The rotations occur around the two axes perpendicular to the line between the two atoms. The rotation around the atom–atom bond is not a physical rotation. This yields, for a diatomic molecule, a decomposition of:

N = 6 = 3 + 2 +1

As defined above one can also count degrees of freedom using the minimum number of coordinates required to specify a position. This is done as follows:

1. For a single particle we need 2 coordinates in a 2-D plane to specify its position and 3 coordinates in 3-D space. Thus its degree of freedom in a 3-D space is 3.
2. For a body consisting of 2 particles (ex. a diatomic molecule) in a 3-D space with constant distance between them (let's say d) we can show (below) its degrees of freedom to be 5.