Representative Computer Programs in Software

Drawing Quick Response Code in Software Representative Computer Programs

from which,

D + I ) + -2 t~ ,

B y Eq (517),

L: :

* (T - To)

By Eqs (678) and (679),

By Eq (1165),

HRB:=(TR,PR,omega)- >PR*(BO(TR)-TR*DBO(TR)+omega*(Bl (TR) -TR*DB1 (TR))): SRB:=(TR,PR,omega)- >-PR*(DBO(TR)+omega*DBl (TR)): PHIB:=(TR,PR,omega)- >exp((PR/TR)*(BO(TR)+omega*Bl(TR))):

D 2 SOLUTION OF EXAMPLE PROBLEMS BY MATHCAD@ Example 38 -Molar volumes by the RedlichIKwong equation

(a) Saturated vapor: Given:

q:=66048

j3:=0026214

Initial guess: Z:=1 Solve block:

qj3 z-j3 Z(Z + B )

The problem formulation is the same for parts ( a ) through (d):

Antoine vapor-pressure equations:

A1 :=1659158 B1:=364331 C1:=-33424

A2:=1425326 B2:=266554 C2:=-53424

Expressions for activity coefficients:

(a) BUBL P Calculation: Given:

T:=31815

x1 :=025

x2:=1-XI xl yl(T,xl) P1(T)

P:=xlyI (T,xl)PI(T) + X ~ Y ~ ( T , X I ) P ~ ( T ) yl :=

Calculated results:

P=735

(b) DEW P Calculation: Given:

Initial guesses: Solve block:

yl P XI = y l (T,xl) P I(T)

(c) BUBL T Calculation: Given:

Initial guesses: Solve block:

P I (T)=

T:=300

yl:=07

~ 2y2(T,~l)

(d) DEW T Calculation:

Given:

P:=10133 T:=300 yl:=040

XI :=05

Initial guesses: Solve block:

T= yl P ~l P I(T) (T,xl)

A1+ln(P1(T))

Example 1313 - Solution of two reaction-equilibrium equations Given: Initial guesses: Solve block:

Definition: Initialguesses:

n:=1 yH2 :=096

ycH4:=001

Solve block:

yCO2 :=001

The LeeIKesler tables are adapted and published by permission from "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States," by Byung Ik Lee and Michael G Kesler, AIChE J, 21, 510-527 (1975) The numbers printed in italic type are liquid-phase properties

Tables E l - E4 Correlation for the compressibility factor Tables E5 - E8 Correlation for the residual enthalpy Tables E9 - E12 Correlation for the residual entropy Table E13 - E16 Correlation for the fugacity coefficient

646 650 654 658

Table E2 Values of Z'

Table E5 Values of ( H ~ ) ' / R T ,

Table E6 Values of ( H ~ ) ' / R T ,

00500 01000 02000 04000 06000

Table E7 Values of ( H ~ ) O / R T ,

Table E8 Values of ( H ~ ) ' / R T ,

P, =

P,= T,

65 8

Table E14 Values of 4'

15000 20000

50000 70000 10000

When a value is required from a table at conditions which lie between listed values, interpolation is necessary If M, the quantity sought, is a function of a single independent variable X and if linear interpolation is appropriate, as in the tables for saturated steam, then a direct proportionality exists between corresponding differences in M and in X When M, the value at X, is intermediate between two given values, M I at X I and M2 at XZ, then:

For example, the enthalpy of saturated vapor steam at 41395 K (1408"C) is intermediate between the following values taken from Table F 1:

Substitution of values into Eq (F1) with M = H and X = T yields:

When M is a function of two independent variables X and Y and if linear interpolation is appropriate, as in the tables for superheated steam, then double linear interpolation is required Data for quantity M at values of the independent variables X and Y adjacent to the given values are represented as follows:

Double linear interpolation between the given values of M is represented by:

Table F1 Properties of Saturated Steam, SI Units Table F2 Properties of Superheated Steam, SI Units

All tables are generated by computer from programs' based on "The 1976 International Formulation Committee Formulation for Industrial Use: A Formulation of the Thermodynamic Properties of Ordinary Water Substance," as published in the ASME Steam Tables, 4th ed, App I, pp 11-29, The Am Soc Mech Engrs, New York, 1979 These tables served as a worldwide standard for 30 years, and are entirely adequate for instructional purposes However, they have been replaced by the "International Association for the Properties of Water and Steam Formulation 1997 for the Thermodynamic Properties of Water and Steam for Industrial Use" These and other newer tables are discussed by A H Harvey and W T Pany, "Keep Your Steam Tables up to Date," Chemical Engineering Progress, vol 95, no 11, p 45, Nov, 1999

' w e gratefully acknowledge the contributions of Professor Charles Muckenfuss, of Debra L Sauke, and of Eugene N Dorsi, whose efforts produced the cornputer programs from which these tables derive