The Ratio of Specific Heats

The ratio of specific heats:

is an important parameter in the study of high-speed flows. This is a measure of the relative internal complexity of the molecules of the gas. It has been determined from kinetic theory of gases that the ratio of specific heats can be related to the number of degrees of freedom, n, of the gas molecules by the relation:

At normal temperatures, there are six degrees of freedom, namely three translational and three rotational, for diatomic gas molecules. For nitrogen, which is a diatomic gas, n = 5 since one of the rotational
degrees of freedom is negligibly small in comparison with the other two. Therefore:

Y = 7/5 = 1.4.

Monatomic gases, such as helium, have 3 translational degrees of freedom only, and therefore:

Y = 5/3 = 1.67.

This value of 1.67 is the upper limit of the values which the ratio of specific heats y can take. In general Y varies from 1 to 1.67, that is:

The specific heats of a gas are related to the gas constant R. For a perfect gas this relation is: