CHE3161 Chemistry & Chemical Thermodynamics
CHE4162 Particle Technology
Lecture
11
:
Lecture 4: Volumetric Properties of Pure Fluids – Part 2
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
CHE4162 Particle Technology
Two Forms of the Virial Equations
ØFor convenience, define a dimensionless ratio called the
compressibility factor, Z, by
ØThen with a = RT, we get two forms of the virial expansions
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Lecture
11
:
PV
Z≡
= 1+ B' P + C' P 2 + D' P 3 + ......
RT
Dilute Phase
PV
B C
D
Z≡
= 1+ + 2 +Pneumatic
3 + ......
RT
V V
V
transport
8
B, C,Rhodes:
D, B’, C’Chapter
, D’ are virial
coefficients
B
B' =
RT
C − B2
C' =
(RT) 2
D − 3BC + 2B 3
D' =
(RT) 3
CHE4162 Particle Technology
Ideal Gas VS Real Gas
ØVirial EOS are firmly based on
statistical mechanics, providing physical
significance (molecular interactions) to
virial coefficients.
Lecture 11 :
ØIn the absence of molecular
Dilute Phase
interactions, the virial expansion would
reduce to Z = 1 or PV = RT Pneumatic
transport
ØFor real
gases,Chapter
as P è 0,
Rhodes:
8 Z è 1 or PV
è RT
CHE4162 Particle Technology
Ideal Gas VS Real Gas
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
CHE4162 Particle Technology
Ideal Gas
Lecture 11 :
Dilute Phase
Pneumatic
This equation does not imply that Cp and CV are themselves
transport
constant
for an
ideal gas,
Rhodes:
Chapter
8 but only they vary with temperature in
such a way that their difference is equal to R
CHE4162 Particle Technology
Ideal Gas VS Real Gas
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
CHE4162 Particle Technology
Process Calculations For Ideal Gases
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
CHE4162 Particle Technology
Process Calculations For Ideal Gases
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
CHE4162 Particle Technology
Process Calculations For Ideal Gases
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
CHE4162 Particle Technology
Three Formats for dW and dQ
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
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Isothermal Process
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
CHE4162 Particle Technology
Isothermal Process
Lecture 11 :
Dilute Phase
Pneumatic
V2
P2
Q = −W =transport
RT ln = −RT ln
Rhodes: Chapter 8
V
P
1
€
1
CHE4162 Particle Technology
Isobaric Processes
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
CHE4162 Particle Technology
Isobaric Processes
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
Q = ΔH =
∫ C dT
p
CHE4162 Particle Technology
Isochoric Processes
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
CHE4162 Particle Technology
Isochoric Processes
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
Q = ΔU =
∫C
V
dT
Adiabatic Processes
(with constant heat capacity)
CHE4162 Particle Technology
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
Adiabatic Processes
(with constant heat capacity)
CHE4162 Particle Technology
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
CHE4162 Particle Technology
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
CHE4162 Particle Technology
Lecture 11 :
Dilute Phase
Pneumatic
Note: The three equations
are restricted to ideal gases with
transport
Rhodes:heat
Chapter
8
constant
capacities
undergoing mechanically reversible
adiabatic expansion or compression
Example 3.3
CHE4162 Particle Technology
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
Solution
CHE4162 Particle Technology
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
Solution
CHE4162 Particle Technology
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
Polytropic Processes
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Particle
Technology
Polytropic means “turning many ways”, and “polytropic process”
suggests a model of some versatility.
Lecture 11 :
Dilute Phase
Pneumatic
transport
Rhodes: Chapter 8
Irreversible Process
CHE4162
Particle
Technology
ØAll equations developed in this section have been derived from
mechanical reversible, closed system for ideal gases.
ØHowever, the equations giving property changes – dU, dH, ΔU and
ΔH – are valid for ideal gases regardless of the process in both closed
Lecture 11 :
and open systems (State Functions).
DiluteforPhase
ØOn the other hand, an equation
Q or W, unless it is equal to
property change, is subject to the restrictions of derivation (Path
Pneumatic
Functions)
transport
ØTo Rhodes:
calculate Chapter
the work 8of an irreversible process, a two-step
procedure may be used: calculate the work for a mechanically
reversible process and then multiply (work produced) or divide
(work required) by a an efficiency to give actual work.