VanderWaals’ equation

Thus the critical constants (qv) in terms of the constants in vanderWaals equation are ... 

The constants a b in vanderWaals equation can be eliminated by substituting for them expressions derived from the values of the critical constants, given by equations (14). This elimination can be so arranged that the new equation contains only the ratios of the pressure, volume and temperature to their critical values. These ratios are called the reduced values of the variables and may be written as ... 

In conclusion, it may be said that van der Waals equations can only provide reasonably accurate representation over limited ranges of variation of the pressure and temperature. For this reason many attempts were made to produce a more satisfactory equation by modifying vanderWaals equations. Such modifications were made by Berthelot (See item b ), Callendar (See item c-2), Clausius (See item C3), Dieterici (See item d2), Hirschfelder et al (See item 113), Keyes (See item ki), Lees (See item I3), and Macleod (See item mi) Accdg to Dunkle (Ref 17), for high temps and moderate pressures which give rise to large values of V so that P55>a/v2, van der Waals equation reduces to Abel s equation (See item ai)... 

C2) Callendar Equation of State. It is one of the modifications of vanderWaals equations, originally developed to represent the behavior of steam at moderate pressure. It was found to. >e applicable to other vapors and to gases ... 

Cj) Clausius Equation of State. It is a modification of vanderWaals equation, in which is introduced an expression l/T(V+c) to correct the pressure-correction term (a) for its variation with temperature. Clausius equation is given in Ref 8, p 161 in the form ... 

Compare with vanderWaals equation described in the "Introduction to the section on Equations of State... 

This equation is valid under the same conditions as the vanderWaals equation For gases at moderate densities equations (19) and (20) are given in Ref lb, p 59 Further in the paper there is a discussion of an attempt to find an equation of state of... 

Generalized vanderWaals Equation of State for Real Gases. The proposed generalized equation is ... 

Vj) VanderWaals Equation of State. It is listed in Vol 3 of Encycl, p C550-R, under "Covolume and fully described in the "Introduction to this section on Equations... 

VanderWaals equation - An equation of state for fluids which takes... 

The page http //www.hull.ac.uk/php/chsajb/genera1/vanderwaals.html, at Hull University s Website, includes an interactive page - the van der Waals calculator - to determine values for real and ideal gases, with the van der Waals equation. The site http //antoine.frostburg.edu/chem/senese/javascript/realgas.shtml includes a different calculator with more variables, but is not quite so easy to use. 

The principle, in the form originally stated by vanderWaals ca 1881 at the time of development of his equations of state (See under Introduction to Equations of State), is based on the reduction of the variables using the critical constants (qv). This formulation is the basis of the generalized charts for the compressibility and thermody-... 

W2) Wobl Equation of State. It is the 4th degree in the volume virial equation proposed in 1914 by Wohl and described in Addnl Ref Aj. it was used by Joffe (Ref 2a) far calcn of parameters of some gases in order to compare the results with those obtd by using the eq (5) of Joffe with equation of Beattie-Bridgeman and vanderWaals Joffe gives (Ref 2a, p 541) for Wohl equation ... 

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