Transcript Chapter 3

Properties of Pure
Substances
Chapter 3
Why do we need physical
properties?
 As we analyze thermodynamic
systems we describe them using
physical properties
 Those properties become the input to
the equations we’ll use to solve
thermodynamic problems
Pure Substance
In Chemistry you defined a pure
substance as an element or a
compound
Something that can not be separated
In Thermodynamics we’ll define it as
something that has a fixed chemical
composition throughout
Examples
Ice in equilibrium
with pure water
Air
Air in equilibrium
with liquid air is
not a pure
substance – Why?
Phases of Pure Substances
We all have a pretty good idea of what
the three phases of matter are, but a
quick review will help us understand
the phase change process
Solid
 Long range order
 Three dimensional
pattern
 Large attractive
forces between
atoms or molecules
 The atoms or
molecules are in
constant motion –
they vibrate in place
 The higher the
temperature – the
more vibration
Platinum Atoms
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Liquid
 When a solid reaches a
high enough temperature
the vibrations are strong
enough that chunks of the
solid break of and move
past each other
 Short range order
 Inside the chunks the
atoms or molecules look
a lot like a solid
 Ex. You only break 5%
to 15% of the water
hydrogen bonds to go
from solid to liquid
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Gas
Molecules are far apart
No long or short range
order
High kinetic energy
In order to liquefy, lots
of that kinetic energy
must be released
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Solid to Liquid to Gas
On a molecular level, the difference
between the phases is really a matter
of degree
We identify melting points and
vaporization points based on changes
in properties
 Ex – big change in specific volume
Consider what happens when we heat
water at constant pressure
Piston cylinder
device –
maintains
constant
pressure
5
T
2
3
Liquid to
Gas Phase
Change
4
1
v
Liquid to Gas Phase Change
Liquid to Gas Phase Change
Superheated
Gas
Compressed
Liquid
Two Phase
Region
Critical Point
Critical Point
Above the critical point there is no
sharp difference between liquid and
gas!!
Pressure-volume
diagram
Property Diagrams
So far we have sketched
 T – v diagram
 P – v diagram
 What about the P – T diagram?
Property Diagrams
Combine all three
You can put all three properties
P
T
V
On the same diagram
Expands on Freezing
Contracts on Freezing
3 Dimensional Phase Diagrams
State Postulate
The state of a simple
compressible system is
completely specified by
two independent,
intensive properties
State Postulate
Remember that during a phase
change, Temperature and Pressure are
not independent
Property Tables
P - pressure
T - temperature
v – specific volume
u – specific internal energy
h – specific enthalpy
h = u + Pv
s – specific entropy -define in Chapter 7
A word about enthalpy
 Enthalpy is a combination property
h=u+Pv
H=U+PV
 It is useful because it makes some
equations easier to solve
 You could do all of thermodynamics
without it – but its more convenient
to use it.
Saturated Liquid and Saturated
Vapor States
Saturation Properties
Saturation Pressure is the pressure at
which the liquid and vapor phases are in
equilibrium at a given temperature.
Saturation Temperature is the
temperature at which the liquid and
vapor phases are in equilibrium at a
given pressure.
Table A-4 and A-5
A-4
pg 890
 Saturated water temperature table
A-5
pg 892
 Saturated water pressure table
Transitions from liquid to gas
g stands for gas
f stands for fluid
fg stands for the
difference
between gas and
fluid
u fg  ug  u f
h fg  hg  h f
s fg  sg  s f
Quality
x
masssaturated vapor
masstotal

mg
m f  mg
Fraction of the material that is gas
x = 0 the material is all saturated liquid
x = 1 the material is all saturated gas
x is not meaningful when you are out of
the saturation region
Quality
X=0
X=1
Average Properties
y  y f  x( yg  y f )
01
fg
 y f  x y = yg
When x = 0 we have all liquid, and y
When x = 1 we have all gas, and y
= yf
= yf + yfg = yg
Superheated Properties
Table A-6,
pg 894
Compressed Liquid
y  y f @T
h  h f @T  v f ( P  Psat )
We only need to adjust h if there is a big
difference in pressure
Linear Interpolation
A
B
100
5
130
X
200
10
130  100 x  5

200  100 10  5
Equations of State
Equations vs Tables
The behavior of many gases (like
steam) is not easy to predict with an
equation
That’s why we have tables like A-4, A5 and A-6
Other gases (like air) follow the ideal
gas law – we can calculate their
properties
Ideal Gas Law
PV=nRT
PV=nRuT
 Used in your Chemistry class
 From now on we will refer to the gas
constant , R, as the universal gas
constant, Ru , and redefine R=Ru/MW
PV=mRT
 R is different for every gas
 Tabulated in the back of the book
Ideal Gas Law
v = V/m
Pv = RT
 This is the form we will use the most
Relates 3 properties
P, v and T
When does the ideal gas law
apply?
 The ideal gas equation of state can be derived
from basic principles if one assumes:
1. Intermolecular forces are small
2. Volume occupied by the particles is small
These assumptions are true when the molecules are far
apart – ie when the gas is not dense
Criteria
The ideal gas law applies when the
pressure is low, and the temperature
is high - compared to the critical
values
The critical values are tabulated in the
Appendix
Is Steam an Ideal Gas?
Compressibility Factor
You can adjust the ideal gas law with
a fudge factor, called the
compressibility factor
Pv = z RT
z is just a value you put in to make it
work out
z = 1 for ideal gases
Principle of Corresponding
States
The Z factor is approximately the
same for all gases at the same
reduced temperature and reduced
pressure
T
TR 
Tcr
and
P
PR 
Pcr
Comparison of z factors
What do you do when P or T is
unknown?
vactual
vR 
R Tcr
Pcr
Check out Appendix A-15 pg 908
Other Equations of State
Van der Waals
a
( P  2 )(v  b)  R T
v
2
2
cr
27 R T
a
64 Pcr
and
RTcr
b
8 Pcr
Beattie-Bridgeman
F
I
G
J
H K
Ru T
c
a
P  2 1  3 (v  B)  2
v
vT
v
aI
F
A A G
1  J and
H vK
o
bI
F
B B G
1 J
H vK
o
Benedict-Webb-Rubin
F
G
H
IJ
K
Ru T
Co 1 bRu T  a
P
 Bo Ru T  Ao  2 2 
3
v
T v
v
F
I
G
J
H K
a
c
  / v 2
 6  3 2 1 2 e
v
v T
v
Percentage
Error for
Nitrogen
Summary
In this Chapter we learned
 How the state of a substance changes
with Temperature and Pressure
 How to read and use property tables
 When we can use the ideal gas law
 Alternative equations of state