Van der waal's equation


The Ideal Gas Law incorrectly assumes all gases are points in space with no volume, and their interaction with themselves is elastic, that molecules have no interaction with each other. The Ideal Gas Law is a simple, first order approximation of gas behaviour. At low gas density the Ideal Gas Law values are practically the same as real values. As density increases, gas behaviour deviates from the Ideal Gas Law model, and values become increasingly inaccurate. When working with dense atmopsheres, such as Venus or any gas giant, a different equation is required, one which is accurate for both high and low densities.

Van der waal's equation is a complex, second order approximation of gas behaviour. It incorporates density, with molecular size and interaction, and the individual characteristics of each gas constituent. Van der waal's equation is very accurate for both high and low densities. Terraformer uses Van Der Waal's equation for greater accuracy.

Calculations using Van der waal's equation are long and very complex. It's should be done by a computer program. I've calculated the atmosheric pressure of different planets, using both the Ideal Gas Law and Van der waal's equation. Following is a list showing the degree to which the Ideal Gas Law over/under-estimates the real value:

PlanetMolar density (mol/m3)Difference
Titan1824.8410.4317 % overestimate
Venus1491.7150.6468 % overestimate
Neptune166.5020.3258 % overestimate
Uranus157.7390.3259 % overestimate
Saturn89.5350.2463 % overestimate
Jupiter72.7580.1851 % overestimate
Earth42.3080.0152 % overestimate
Pluto0.7220.0001 % underestimate
Mars0.3510.0001 % overestimate
Io9.241 x 10-80.0000 % same

Note the difference between Titan and Venus, which is due to their significantly different atmospheric compositions. The difference between Neptune and Uranus is due to ethane in the atmosphere of Neptune. The underestimate of pluto, though minor, is due to the high concentration of methane.