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van der Waals' equation of state

Graph of the van der Waals equation for a real gas (red)
Graph of the van der Waal's equation for a real gas (red). If a quantity of gas is compressed at constant temperature under normal conditions, the red curve is not followed all the way: at a certain critical pressure a change of state occurs – there is a sudden reduction in volume and the gas liquefies (broken blue line). A whole family of related van der Waals curves exist for different temperatures in three dimensions these give rise to a pressure-volume-temperature surface. For a certain critical temperature, there is no well in the curve, only a point of inflection. At and above this temperature, there is no definable phase transition between the gaseous and liquid states.
An equation, formulated by Johannes van der Waals, which represents the behavior of ordinary gases more accurately than does the ideal gas law. Van der Waals' equation of state is:

(P + a/V 2)(V - b) = RT

for a gram-molecule of a substance in the gaseous and liquid phases, where P = pressure, V = volume, T = temperature, and R = the gas constant. The term a/V 2 is a correction for the mutual attraction of the molecules, and b is a correction for the actual volume of the molecules themselves. (The values of the constants a and b depend on the particular gas in question.) The attractive forces between molecules are known as van der Waal's forces.

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