The ideal-gas equation of state is very simple, but its range of applicability is limited. It is desirable to have equations of state that represent the P-v-T behavior of substances accurately over a larger region with no limitations. Such equations are naturally more complicated. Several equations have been proposed for this purpose (Fig. 3–57), but we shall discuss only three: the van der Waals equation because it is one of the earliest, the Beattie-Bridgeman equation of state because it is one of the best known and is reasonably accurate, and the Benedict-Webb-Rubin equation because it is one of the more recent and is very accurate.