# barcode generator vb.net code Volumetric Properties of Pure Fluids in Software Generate QR-Code in Software Volumetric Properties of Pure Fluids

CHAPTER 3 Volumetric Properties of Pure Fluids
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For pressures above the range of applicability of Eq (337) but below the critical pressure, the virial equation truncated to three terms often provides excellent results In this case Eq (312), the expansion in 1/ V , is far superior to Eq (311) Thus when the virial equation is truncated to three terms, the appropriate form is:
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This equation can be solved directly for pressure, but is cubic in volume Solution for V is easily done by an iterative scheme with a calculator
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Figure 31 1 Density-series virial coefficients B and C for nitrogen
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Values of C , like those of B , depend on the gas and on temperature However, much less is known about third virial coefficients than about second virial coefficients, though data for a number of gases are found in the literature Since virial coefficients beyond the third are rarely known and since the virial expansion with more than three terms becomes unwieldy, its use is uncommon Figure 311 illustrates the effect of temperature on the virial coefficients B and C for nitrogen; although numerical values are different for other gases, the trends are similar The curve of Fig 311 suggests that B increases monotonically with T ; however, at temperatures much higher than shown B reaches a maximum and then slowly decreases The temperature dependence of C is more difficult to establish experimentally, but its main features are clear: C is negative at low temperatures, passes through a maximum at a temperature near the critical, and thereafter decreases slowly with increasing T A class of equations inspired by Eq (312), known as extended virial equations, is illustrated by the BenedictIWebbRubin equation
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G B Webb, L C Rubin, J Chern Phys, vol 8, pp 334-345, 1940; vol 10, pp 747-758,1942
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34 Application of the Virial Equations
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RT BORT - AO- C O / T ~ bRT - a aa c Y -Y P=- - + V V V3 + - + - V 3~ 2+ ~ ) e x p ~ V6 ( T where Ao, Bo, Co,a , b, c, a , and y are all constant for a given fluid This equation and its modifications, despite their complexity, are used in the petroleum and natural-gas industries for light hydrocarbons and a few other commonly encountered gases
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CHAPTER 3 Volumetric Properties of Pure Fluids
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35 CUBIC EQUATIONS OF STATE
If an equation of state is to represent the P V T behavior of both liquids and vapors, it must encompass a wide range of temperatures and pressures Yet it must not be so complex as to present excessive numerical or analytical difficulties in application Polynomial equations that are cubic in molar volume offer a compromise between generality and simplicity that is suitable to many purposes Cubic equations are in fact the simplest equations capable of representing both liquid and vapor behavior
The van der Waals Equation of State
The first practical cubic equation of state was proposed by J D van der waals6 in 1873:
Here, a and b are positive constants; when they are zero, the ideal-gas equation is recovered Given values of a and b for a particular fluid, one can calculate P as a function of V for various values of T Figure 312 is a schematic P V diagram showing three such isotherms Superimposed is the "dome" representing states of saturated liquid and saturated vapor For the isotherm TI > T,, pressure is a monotonically decreasing function with increasing molar volume The critical isotherm (labeled T,) contains the horizontal inflection at C characteristic of the critical point For the isotherm T2 < T,, the pressure decreases rapidly in the subcooledliquid region with increasing V; after crossing the saturated-liquid line, it goes through a minimum, rises to a maximum, and then decreases, crossing the saturated-vapor line and continuing downward into the superheated-vapor region Experimental isotherms do not exhibit this smooth transition from saturated liquid to saturated vapor; rather, they contain a horizontal segment within the two-phase region where saturated liquid and saturated vapor coexist in varying proportions at the saturation or vapor
6~ohannes Diderik van der Waals (1837-1923), Dutch physicist who won the 1910 Nobel Prize for physics