
Internal Energy
The energy of a thermodynamic system that
is NOT either the kinetic energy or gravitational potential energy of the system
as a whole is known as Internal Energy.
The internal energy is associated
with the internal degrees of freedom of the system. For an Ideal
Gas, the internal energy is only a function of the gas temperature and is a
measure of the mean translational kinetic energy of the gas atoms. These atoms
have three translational degrees of freedom, each of which has a mean translational
kinetic energy of ˝kT, where k is Boltzman's constant = 1.381 x
10^{ 23} J/ K. For a mole of gas, there are N atoms (Avogardro's
number = 6.022 x 10^{ 23} /mole) and so the internal energy
per mole of gas, u, is: u = 3NkT/2 = (3/2) RT , where R is the Gas
Constant = 8.314 J/mole.K
For real molecular gases additional degrees
of freedom must be considered. Each of the independent translational, rotational
and vibrational modes of the system has a mean energy of ˝kT in the classical
limit. 
