Van der Waals Isotherms for Real and Ideal Gases

The van der Waals equation of state, , represents the behavior of real gases in response to pressure, molar volume, and temperature at finite concentrations. The constant stands for the reduction in pressure due to the attractive forces of the molecules and the constant stands for their volume. Ideal gases have smooth isotherms whereas real gases exhibit curious undulations below a certain temperature called the critical temperature.

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Reference
[1] J. H. Noggle, Physical Chemistry, 3rd ed., New York: HarperCollins, 1996.
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