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barcode generator vb.net code Residual Properties in Software
62 Residual Properties Create QRCode In None Using Barcode generation for Software Control to generate, create QR Code image in Software applications. QR Code ISO/IEC18004 Recognizer In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. Since V = Z R T I P , the residual volume and the compressibility factor are related: QR Code Generation In Visual C#.NET Using Barcode creator for .NET Control to generate, create QR Code image in .NET applications. QRCode Generation In Visual Studio .NET Using Barcode encoder for ASP.NET Control to generate, create QR Code image in ASP.NET applications. The definition for the generic residual property is: Drawing Denso QR Bar Code In VS .NET Using Barcode drawer for Visual Studio .NET Control to generate, create QR Code ISO/IEC18004 image in .NET applications. Make QRCode In VB.NET Using Barcode creation for .NET framework Control to generate, create Denso QR Bar Code image in .NET framework applications. where M is the molar value of any extensive thermodynamic property, eg, V, U , H , S, or G Note that M and Mig, the actual and idealgas properties, are at the same temperature and pressure Equation (637), written for the special case of an ideal gas, becomes: EAN13 Creation In None Using Barcode maker for Software Control to generate, create UPC  13 image in Software applications. UPCA Generation In None Using Barcode creator for Software Control to generate, create UPCA Supplement 5 image in Software applications. Subtracting this equation from Eq (637) itself gives: Data Matrix Creation In None Using Barcode drawer for Software Control to generate, create Data Matrix image in Software applications. Barcode Maker In None Using Barcode printer for Software Control to generate, create bar code image in Software applications. This fundamental property relation for residual properties applies to fluids of constant composition Useful restricted forms are: GTIN  128 Creator In None Using Barcode creator for Software Control to generate, create EAN128 image in Software applications. Code 128A Printer In None Using Barcode creation for Software Control to generate, create Code128 image in Software applications. and In addition, the defining equation for the Gibbs energy, G = H  T S , may also be written for ~ ; the special case of an ideal gas, Gig = Hig  T S ~by difference, Creating C 2 Of 5 In None Using Barcode generator for Software Control to generate, create 2/5 Industrial image in Software applications. Code 3/9 Decoder In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. GR= f f R The residual entropy is therefore: Draw Barcode In Java Using Barcode generation for Android Control to generate, create bar code image in Android applications. Drawing GS1 DataBar Stacked In Java Using Barcode creation for Java Control to generate, create GS1 DataBar Truncated image in Java applications. ~,'j'~
Recognizing Bar Code In .NET Framework Using Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications. ANSI/AIM Code 128 Generation In Java Using Barcode encoder for Java Control to generate, create Code 128 image in Java applications. Thus the residual Gibbs energy serves as a generating function for the other residual properties, and here a direct link with experiment does exist It is provided by Eq (643), written: (const T) Integration from zero pressure to arbitrary pressure P yields: Code39 Decoder In Visual C# Using Barcode recognizer for .NET Control to read, scan read, scan image in VS .NET applications. Recognize Bar Code In Java Using Barcode Control SDK for BIRT reports Control to generate, create, read, scan barcode image in BIRT applications. CHAPTER 6 Thermodynamic Properties of Fluids
where at the lower limit G ~ / R is equal to zero because the zeropressure state is an idealgas T state In view of Eq (640): Differentiation of Eq (646) with respect to temperature in accord with Eq (644) gives: I%=T~
(E),P
d~ (const T ) The residual entropy is found by combination of Eqs (645) through (647): The compressibility factor is defined as Z = P V / R T ;values of Z and of (a Z/a T ) p therefore come from experimental P V T data, and the two integrals in Eqs (646) through (648) are evaluated by numerical or graphical methods Alternatively, the two integrals are evaluated analytically when Z is expressed as a function of T and P by a volumeexplicit equation of state Thus, given P V T data or an appropriate equation of state, we can evaluate H R and sR and hence all other residual properties It is this direct connection with experiment that makes residual properties essential to the practical application of thermodynamics Applied to the enthalpy and entropy, Eq (641) is written: H = fyig +ffR
s = s i p + sR
Thus, H and S follow from the corresponding idealgas and residual properties by simple addition General expressions for Hig and s i g are found by integration of Eqs (623) and (624) from an idealgas state at reference conditions To and Po to the idealgas state at T and P : ~ H i p = H$ C$ d~
sip= S +
lo c" dT T
P R ln Po
Substitution into the preceding equations gives: 3~hermodynamic properties for organic compounds in the idealgas state are given by M Frenkel, G J Kabo, K N Marsh, G N Roganov, and R C Wilhoit, Thermodynamics of Organic Compounds in the Gas State, Thermodynamics Research Center, Texas A & M Univ System, College Station, Texas, 1994 62 Residual Properties
Recall (Secs 41 and 55) that for purposes of computation the integrals in Eqs (649) and (650) are represented by: and Equations (649) and (650) may be expressed alternatively to include the mean heat capacities introduced in Secs 41 and 55: where H~ and S R are given by Eqs (647) and (648) Again, for computational purposes, the mean heat capacities are represented by: Since the equations of thermodynamics which derive from the first and second laws do not permit calculation of absolute values for enthalpy and entropy, and since in practice only relative values are needed, the referencestate conditions To and Po are selected for convenience, and values are assigned to H and S: arbitrarily The only data needed for application of Eqs (651) and (652) are idealgas heat capacities and P V T data Once V , H, and S are known at given conditions of T and P , the other thermodynamic properties follow from defining equations The true worth of the equations for ideal gases is now evident They are important because they provide a convenient base for the calculation of realgas properties Residual properties have validity for both gases and liquids However, the advantage of Eqs (649) and (650) in application to gases is that H~ and S R , the terms which contain all the complex calculations, are residuals that generally are quite small They have the nature of corrections to the major terms, Hig and S'g For liquids, this advantage is largely lost, because H~ and sR must include the large enthalpy and entropy changes of vaporization Property changes of liquids are usually calculated by integrated forms of Eqs (628) and (629), as illustrated in Ex 61

