Van der Waals equation is also known as Van der Waals equation of state for real gases which do not follow ideal gas law. According to ideal gas law, PV = nRT where P is the pressure, V is the volume, n is the number of moles, T is the temperature and R is the universal gas constant. The Van der Waals Equation derivation is explained below.
Derivation of Van der Waals equation
For a real gas, using Van der Waals equation, the volume of a real gas is given as (Vm – b), where b is the volume occupied by per mole.
Therefore, ideal gas law when substituted with V = Vm – b is given as:
Because of intermolecular attraction P was modified as below
Where,
Vm: molar volume of the gas
R: universal gas constant
T: temperature
P: pressure
V: volume
Thus, Van der Waals equation can be reduced to ideal gas law as PVm = RT.\
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Van der Waals Equation Derivation for one mole of gas
Following is the derivation of Van der Waals equation for one mole of gas that is composed of non-interacting point particles which satisfies ideal gas law:
Van der Waals equation applied to compressible fluids
Compressible fluids like polymers have varying specific volume which can be written as follows:
Where,
p: pressure
V: specific volume
T: temperature
A,B,C: parameters
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