We embark now on a rather ambitious journey. Given a fluid, we would like to develop mathematical relationships for predicting its behavior under any imaginable condition of pressure, temperature and volume (P-V-T). In other words, we want to describe the P-V-T behavior of fluids in general.
As we stated earlier, this is a very challenging problem. The way science approaches these sorts of problems is to introduce simplifications of the physical reality. In other words, we formulate a set of assumptions and come up with a base model that we might call ideal. From that point on, once the base model has been established, we look at a real case by estimating how close (or far) it performs, with respect to the base (ideal) case, and introducing the corresponding corrections. Such corrections will take into account all the considerations that our original assumptions left out.
Let us discuss our base case for fluids (the simplest fluid we may deal with): the ideal or perfect gas.