# Internal energy

Internal energy at a specific state can't be calculated, but using kinetic theory of gases and the law of equipartition of energy, average kinetic energy is directly proportional to temperature. For an ideal gas, internal energy is due to kinetic energy, as we neglect potential energy. This means internal energy is a function of temperature only. This gives for a monatomic gas, the equation: $$<E>=\frac{3}{2}RT,$$

from $U=\frac{f}{2}RT$ from law of equipartition theorem, where f is number of degrees of freedom.

So why can't we find internal energy of a particular state?

• We can, in the case you mentioned it is function of temperature and number of particles only. However, in general, internal energy is not a function of those two variables only, but may depend on density and possibly other variables. – Ján Lalinský Aug 26 '17 at 22:51
• but here we are discussing about ideal gas. for an ideal gas it depends only on temperature – Leela Prathap Aug 4 '18 at 16:01

As internal energy is a state function so its change is defined. To find its value in a given state we have to consider a reference state of the system in which it is taken zero arbitrarily. In your result of kinetic theory zero kelvin is the reference temp or state.

• But in kinetic theory we took absolute terms like temperature, pressure we did not take any reference state – Leela Prathap Aug 28 '17 at 1:53

You seem to be taking an almost universal rule and understanding it as absolutely universal.

The limitation on knowing internal energies is (a) if we only know the macrostate and (b) applies to almost, but not quite, all systems.

The 'almost' is important here because for a few—generally very simple—models and a few physical systems that are very well represented by those models we can compute the internal energy knowing only the macroscopic variables.

And the ideal gas is the premier example of such a system.

So, the short answer to your question us that the ideal gas is one of a small number of exception to the general rule.