Analyze complex mathematical models in which several parameters appear. In many cases, the first step in analyzing the model is to determine the conditions that will reduce the complex model to a simpler case. The Van der Waal equation of state is an extension of the ideal gas law for real gasses:

where P is pressure, V is volume, T is temperature, R is the universal gas constant, n is the number of moles, and a and b are constants. Rewrite the equation of state to see that it approaches the equation of the ideal gas law for large V.

For an ideal gas, .

Rearrange the Van der Waal equation to obtain the same ratio, and the result is

.

The terms on the right are close to 1 if V is sufficiently large.