2.4 Real Gases

Real gases don't have accurate simple algebraic equations of state. The reason is that real gases turn into liquids and solids under the proper conditions and it is not possible to have a simple accurate algebraic equation mimic that behavior. As an example look at the schematic isotherm in the diagram below. All points on the isotherm are at the same temperature

Figure 2.1: Isotherm on a p-V diagram

Start at the right and move left. The rightmost part of the curve is the p-V curve for the gas. At point B the gas starts to condense to a liquid and all along the line segment from B to A two phases coexist, one liquid, one gaseous. As long as both phases exist together, the pressure is constant. Thus the line in the graph is flat. At point A all the gas has condensed and all that is left is the sharply rising p-V curve for the liquid.^2.7

The thing to notice is that while the isotherm is continuous, its derivative with respect to volume is not continuous! Since all simple algebraic equations have continuous derivatives, there is no hope that any such equation can be found for this isotherm.

But what about an equation just for the gas phase? The problem remains. As one gets close to point B on the diagram, the simple algebraic curve will have to deviate from reality.

In fact, a number of different approximate equations of state have been suggested for real gases. All of them start having difficulty as the condensation point is approached.