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.

Dear Lokanna,

In order to answer your question, one should almost explain whole kinetic theory of gases, whilst the expression you are discussing about is the simplest form of internal energy equation which shows internal energy dependency to temperature and mole fraction of a gas. This equation is simplified from rigorous hypothesis and complex equations of kinetic theory of gases. I do recommend study classic thermodynamic text books and look for kinetic theory of gases explanations. Also some short and simplified texts of statistical thermodynamics would be useful.

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.

Go through this.this relation is very much clear by this link

http://en.wikipedia.org/wiki/Degrees_of_freedom_(physics_and_chemistry)

Equipartition Theory