Data and Equation for KRD
2
Internal DATA AND EQUATION Ideal Gas constant: K mol cal R R mol lb Btu R R mol lb atm ft R o o 987 . 1 987 . 1 73 . 0 3 K kmol atm m R K mol atm dm R K mol dm kPa R 3 3 3 082 . 0 082 . 0 314 . 8 Volume change with conversion: 0 0 0 1 P T V V X P T 0 0 0 1 P T v v X P T Arrhenius equation: Numerical Integration of Integrals 1. Trapezoid rules 0 1 1 0 2 1 0 X X h where X f X f h dX X f X X 2. Simpson’s one-third rule (three point) 2 4 3 0 2 2 1 0 2 0 X X h where X f X f X f h dX X f X X 3. Simpson’s three-eighths rule(four point) 3 3 3 8 3 0 3 3 2 1 0 3 0 X X h where X f X f X f X f h dX X f X X () E RT A k T Ae
description
Data and Equation for KRD
Transcript of Data and Equation for KRD
Internal
DATA AND EQUATION
Ideal Gas constant:
Kmol
calR
Rmollb
BtuR
Rmollb
atmftR
o
o
987.1
987.1
73.03
Kkmol
atmmR
Kmol
atmdmR
Kmol
dmkPaR
3
3
3
082.0
082.0
314.8
Volume change with conversion:
00
0
1P T
V V XP T
00
0
1P T
v v XP T
Arrhenius equation:
Numerical Integration of Integrals
1. Trapezoid rules
01102
1
0
XXhwhereXfXfh
dXXf
X
X
2. Simpson’s one-third rule (three point)
2
43
02210
2
0
XXhwhereXfXfXf
hdXXf
X
X
3. Simpson’s three-eighths rule(four point)
3
338
3 033210
3
0
XXhwhereXfXfXfXfhdXXf
X
X
( )E
RTAk T Ae
Internal
4. Five point quadrature formula
3
4243
0343210
3
0
XXhwhereXfXfXfXfXf
hdXXf
X
X
Useful integrals in reactor design
X
X
X
X
X
X
X
MXM
XM
MXMX
dX
X
XXXdX
X
X
XX
XdX
X
X
XX
dXX
X
XX
dX
X
X
X
dX
XX
dX
0
2
2
0 2
2
0 2
0
0
0 2
0
11
ln1
1
1
1
11ln12
1
1
1
1ln
1
1
1
1
1
1ln1
1
1
1ln1
1
11
1
1ln
1
