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:
|Planet||Molar density (mol/m3)||Difference|
|Titan||1824.841||0.4317 % overestimate|
|Venus||1491.715||0.6468 % overestimate|
|Neptune||166.502||0.3258 % overestimate|
|Uranus||157.739||0.3259 % overestimate|
|Saturn||89.535||0.2463 % overestimate|
|Jupiter||72.758||0.1851 % overestimate|
|Earth||42.308||0.0152 % overestimate|
|Pluto||0.722||0.0001 % underestimate|
|Mars||0.351||0.0001 % overestimate|
|Io||9.241 x 10||0.0000 % 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.