To state the law of energy conservation we need to be more specific than we have been previously about the concept of internal energy which we shall denote by the symbol U. The internal energy of matter in thermal equilibrium is what we call a state function of the thermodynamic variables of the system. U depends only on the values of these parameters, not on greater detail about internal motion nor on the history of how the system reached that specific state of thermal equilibrium. The thermodynamic variables of relevance at this stage are P, T, and V. But the equation of state does not permit us to independently specify all these variables; if we know two then we can calculate the third. Thus we have that U is a function of any set of two of these three variables: P and T, or P and V, or T and V.
There is an important analogy here to the potential energy that we introduced in mechanics. That function also was a configurational energy dependent only on the present state of the system and not on how that state was obtained.
An ideal gas is particularly simple. It is a non-interacting system of
particles so the internal energy in thermal equilibrium
at a specific temperature, T, is independent of the volume available to the
gas. This result which can be verified experimentally,
essentially states that 
which has units of energy
is proportional to the average kinetic energy of molecules in an ideal
gas. The internal energy U is simply the sum of this kinetic energy
and depends therefore only on T, not on the volume available to the
molecules.
Having defined the internal energy we can discuss where this energy comes from or goes to in different types of thermodynamic processes. There are two ways by which U can change.