In the pressure-squared formulation, we assume that the product is constant. We have already seen that this approximation is valid for . With this simplification, Equation 5.37 becomes:
Now, we can use the identity:
Substituting Equation 5.40b into Equation 5.39 results in:
This is the diffusivity equation for real gases in terms pressure-squared, . Again, the product represents a non-linear term which we evaluate at either the initial pressure, , or the average pressure, .