Van der Waals Isotherms

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The Van der Waals equation of state for one mole of an imperfect fluid reads . The critical constants are predicted to be , , . The Van der Waals equation can be recast in the form of a universal reduced equation of state in terms of reduced variables , , . Isotherms where is constant can be plotted on the versus diagram using the slider for values of between 0.80 and 1.20. The critical isothermis shown in red.

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Below the critical temperature, for Van der Waals isotherms exhibit unphysical oscillatory behavior. Maxwell's construction corrects this by replacing the oscillating segment of the isotherm by a horizontal line, which is interpreted as belonging to a two-phase system, with liquid and vapor in equilibrium. The Maxwell construction is derived by arranging the two shaded regions produced by intersection with the Van der Waals isotherm to have equal areas. You can show the Maxwell construction by checking the box.

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Contributed by: S. M. Blinder (February 2008)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Snapshot 1: isotherm for

Snapshot 2: isotherm for , showing Maxwell construction

Snapshot 3: isotherm for , approaching the hyperbolic shape of an ideal-gas isotherm

The Van der Waals equation is discussed in all physical chemistry texts. See, for example:

P. W. Atkins and J. de Paula, Physical Chemistry, 8th ed., New York: Oxford University Press, 2006.

S. M. Blinder, Advanced Physical Chemistry: A Survey of Modern Theoretical Principles, New York: Macmillan, 1969.



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