Transcript MEGR 324 – Heat Transfer

ChemE 260
Equations of State
Dr. William Baratuci
Senior Lecturer
Chemical Engineering Department
University of Washington
TCD 2: E & F
CB 2: 6 – 8, Supplement
April 4, 2005
•
Equations of State
Relationship between P, V and T : P  fxn  V,T
• Ideal Gas EOS:
PV  RT
• Universal Gas Constant: R
– R = 8.314 J/mol-K = 0.082054 L-atm/mol-K = 1.987 Btu/lbmole-oR
• When does the IG EOS apply ?
– When molecules interact very little with each other
– At high T and low P
RT
– Generally:
V
 20 L / mole
– Diatomic gases are
Baratuci
ChemE 260
April 4, 2005
P
especially unlikely to interact Vdiatomic
RT

 5 L / mole
P
Advanced Equations of State
• Compressibility Factor EOS (graphical)
• Virial EOS
• Van der Waals EOS
• Redlich-Kwong EOS
• Soave-Redlich-Kwong EOS
Baratuci
ChemE 260
April 4, 2005
Compressibility Factor EOS
• Compressibility Factor:
PV
V
V
Z


R T R T / P VIG
• Principle of Corresponding States
• Reduced Properties:
T
TR 
TC
P
PR 
PC
• Compressibility Charts
– Z vs PR
– Curves of constant TR
– Curves of constant VRideal
Baratuci
ChemE 260
April 4, 2005
ideal
R
V
V
V
 ideal 
R TC / PC
VC
Virial EOS
• Uses a power series expansion to describe
deviations of Z from 1, the IG value
PV
B C
D
E
Z
 1   2  3  4  ...
RT
V V
V
V
• B, C, D, etc are the Virial “constants”
– functions of T, only
– Determined experimentally
• Truncated Virial EOS:
– Estimating B:
Baratuci
ChemE 260
April 4, 2005
0.422
B 0  0.083  1.6
TR
PV
B
Z
 1
RT
V
R TC
B
B 0   B1 

PC
0.172
B1  0.139  4.2
TR
Van der Waals EOS
RT
a
P
 2
Vb V
• First cubic EOS
• Constants have physical interpretation
27 R 2 TC2
a
64 PC
Baratuci
ChemE 260
April 4, 2005
1 R TC
b
8 PC
RK & SRK EOS’s
RT
a
P

V  b V V  b T1 / 2
• Redlich-Kwong

R 2 TC5 / 2
a  0.42748
PC
R TC
b  0.08664
PC
• Soave-Redlich-Kwong
R 2 TC2
a  0.42748
PC


  1  m 1  TR 


Baratuci
ChemE 260
April 4, 2005

RT
a
P

Vb V Vb

R TC
b  0.08664
PC
2
m  0.48508  1.55171   0.1561 2

Applications of EOS’s
• Given any 2 of the 3 variables, P, Vand T,
determine the value of the unknown
• Cubic EOS’s and other even more sophisticated
EOS’s can be used to…
– predict properties of liquids
– Estimate molar internal energies, enthalpies and
entropies of gases and liquids
– In this way, sophisticated EOS’s are used to generate
the Thermodynamic “Data” Tables that we use
Baratuci
ChemE 260
April 4, 2005
Next Class
• Problem Session !
• After that…
– Chapter 3 – Heat Effects
• Internal Energy and Enthalpy
• Using the NIST Webbook
Baratuci
ChemE 260
April 4, 2005
Example #1
• An Application of Equations of State
– Estimate the pressure
of
ammonia
at
a
o
temperature
of 22 C and a specific volume of
3
0.600 m /kg.
•
•
•
•
•
•
Baratuci
ChemE 260
April 4, 2005
The Ideal Gas EOS
The Virial EOS
The van der Waal EOS
The Soave-Redlich-Kwong EOS
The Compressibility Factor EOS
The Steam Tables
Example #1 – Answers
•
•
•
•
•
Ideal Gas:
Virial:
van der Waal:
SRK:
Z-Factor:
Ans.:
Ans.:
Ans.:
Ans.:
Ans.:
• Steam Tables:
Ans.:
Baratuci
ChemE 260
April 4, 2005
P = 288.2 kPa
P = 280.6 kPa
P = 283.6 kPa
P = 281.5 kPa
P = 282.0 kPa
P = 281.0 kPa
P = 281.7 kPa