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.