. The isothermal compressibility κ of a gas is defined as:
Calculate κ for a van der Waals gas using the method of implicit differentiation
(with respect to P). Show that in the limit of infinite volume,
it yields 1/P (the same result as the ideal gas law).
Based on the lecture notes, the van der Waals equation can be written
Implicit differentiation with respect to P at constant T gives (i.e., side
by side):