Molecular Energy

Recall from kinetic theory that p = Nm<c2>/3V. Rearranging, we get pV = Nm<c2>/3

Compare with the ideal gas law: pV = nRT.

Comparing the right hand side of the two equations above, we get Nm<c2>/3 = nRT, where n is the number of moles, and R the gas constant.

Rearranging, m<c2>/2 = 3kT/2, where k is the Boltzmann constant. (k = R/NA, where is the Avogadro constant. Note that N = nNA.)

The left hand side of m<c2>/2 = 3kT/2 is the average kinetic energy. The right hand side is proportional to T. This shows that the kinetic energy of a molecule is proportional to the temperature.




Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 2 October 2010.