EGR 2500 - Thermodynamic Properties I
In the previous chapter we studied the principle of conservation of energy and
introduced the concept of internal energy. In order to apply an energy balance to a
system, we need to know the properties of the system and how these properties
are related to each other.
1. Simple and Pure Substance and the State Postulate: (Section 4.1)
 A simple compressible substance is one in which the effects of motion, gravity,
surface tension, viscosity and electrical or magnetic fields are absent. These
effects are due to external force fields and are negligible for most of the
problems that we will be considering in this class.
 A pure substance is one that has a uniform and invariable chemical composition
throughout and may exist in more than one phase.
Examples:
 Water; CO2, Oxygen, Copper
 Mixture if liquid and vapor water
 Air (as long as it’s in gas form)
Oil
Water
 State Postulate: To characterize the state of a simple compressible pure
substance, we need to know two independent properties. If gravitational effects
are to be considered, for example, then a third property – in this case height, z –
needs to be specified. Two properties are independent if one property can be
varied while the other is held constant. Temperature and specific volume are
always independent properties. Temperature and pressure, however, are
independent for single phase systems, but are dependent properties for
multiphase systems.
2. Phases and Phase Change Processes of Pure Substances: (Section 4.2-4.4)
We all know that substances can exist in different phases: solid, liquid and vapor,
or in a mixture of two or more of these phases. Each phase is characterized by a
distinct molecular structure, and if present with another phase, can easily be
discerned from the other phase by a phase boundary surface.
For real substances, such as water, refrigerant-134a, or ammonia which cannot be
treated as ideal gases, the equation of state which relates P, v, and T can be very
complicated and the thermodynamic properties are generally given in tabular form.
The equation of state for such substances can be shown in graphical form, as seen
in the P-v-T surfaces shown below.
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EGR 2500 - Thermodynamic Properties I
P-v-T surface of a substance that contracts on freezing (From “Thermodynamics: an Engineering
Approach,” 4th ed. by Cengel and Boles)
P-v-T surface of a substance that expands on freezing (From “Thermodynamics: an Engineering
Approach,” 4th ed. by Cengel and Boles)
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EGR 2500 - Thermodynamic Properties I
In order to gain insight into what happens during phase change processes, let’s
consider the results of heating liquid water from 20 oC, 1 atm while keeping
pressure constant. We’ll assume that the water is heated in a quasi-equilibrium
fashion. We will focus on phase change from liquid to vapor.
P = Const = 1 atm
T1 = 20oC
P1 = 1 atm = 101.325 kPa
Compressed liquid
T2 = 100oC
T3 =
Saturated liquid
T4 =
Saturated vapor
Saturated liquid-vapor mixture
T5 = 300oC
Superheated vapor
 At state 1, the water is in the liquid phase and it is called a compressed liquid or
a subcooled liquid, meaning that it is not about to vaporize.
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EGR 2500 - Thermodynamic Properties I
Not drawn to scale
 At state 2, the water has reached 100 oC and is still liquid form. However, any
heat addition, no matter how small, will cause some of the liquid to vaporize.
That is, a phase-change process from liquid to vapor is about to take place. A
liquid which is about to vaporize is called a saturated liquid. Properties of the
saturated liquid state are designated using a subscript f:
vf,
uf,
hf,
sf
 At a given pressure, the temperature at which a pure substance starts to boil (or
condense) is called the saturation temperature, Tsat.
For example:
 Water at 1 atm,
 Water at 1 MPa=1000 kPa
 Refrigerant R-22 at 1 bar,
Tsat = 100 oC
Tsat = 179.9 oC
Tsat = -41.09 oC
Note: Tsat is a function of
pressure and of the type of
substance
 Similarly, at a given temperature, the pressure at which a pure substance starts
to boil (or condense) is called the saturation pressure, Psat.
For example:
 Water at 100 oC,
 Water at 179.9 oC,
LAILA GUESSOUS | OAKLAND UNIVERSITY
Psat = 101.3 kPa = 1 atm
Psat = 10 bar = 1 MPa
Note: Psat is a function of
temperature and of the
type of substance
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EGR 2500 - Thermodynamic Properties I
 At state 4, the water is still at 100 oC, but it is now all vapor. However, any heat
loss, no matter how small, will cause some of the vapor to condense. That is, a
phase-change process from vapor to liquid is about to take place. A vapor
which is about to condense is called a saturated vapor. Properties of the
saturated vapor state are designated using a subscript g:
vg,
ug,
hg,
sg
 Thermodynamic properties at the saturated liquid and saturated vapor states are
tabulated either as a function of temperature (Table A-4 and Table A-4E for
water) or as a function of pressure (Table A-5 and A-5E for water). Note: “E”
in the Table # indicates English units.
u fg  u g  u f
h fg  h g  h f
s fg  s g  s f
 At state 3 (or any state between states 2 and 4), the water consists of a mixture
of liquid and vapor and is referred to as a saturated liquid-vapor mixture.
 If the constant-pressure heating continues beyond state 4, say state 5, the water
remains in vapor form and the temperature begins to increase beyond the
saturation temperature. The water is then said to be in the superheated vapor
phase, meaning that it is not about to condense.
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EGR 2500 - Thermodynamic Properties I
If we were to repeat the entire process in the reverse direction, i.e., start at state 5
and cool the water at a constant pressure of 1 atm, the process will retrace the same
path, i.e., the line connecting points 1-2-3-4-5 represents the equilibrium states of
water at 1 atm, in the range of temperatures studied.
 Mixture Quality:
Consider points 3 and 3’ on the previous diagram:
 Both are at a temperature of 100 oC and a pressure of 1 atm
 Both are in the saturated liquid-vapor mixture phase
However, are they at the same state?
Why? They have different volumes
(and specific volumes, v = /m) and the proportions of liquid and vapor in the
mixture are different.
In order to discern between two different saturated liquid-vapor mixture states at a
given pressure or temperature, we define a property called quality, x.
What can we say about the amount of vapor in state 3’ compared to the amount of
vapor in state 3?
The quality of a mixture is then defined as:
Where
m = mass of mixture
mvapor = mass of vapor in mixture
The concept of quality only has significance for saturated liquid-vapor mixtures
(including saturated liquid and saturated vapor points). It has no meaning in the
compressed liquid or superheated vapor regions.
For a saturated liquid:
For a saturated vapor:
For a mixture of liquid and vapor:
If you get x < 0 or x > 1, then you’ve either made a calculation mistake or the
phase is not a mixture.
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EGR 2500 - Thermodynamic Properties I
 Saturation Temperature and Saturation Pressure:
Saturation temperature and saturation pressure are dependent properties for a
given pure substance. There exists a definite relation Tsat = f(Psat) or conversely, Psat
= f(Tsat) for each substance. The temperature at which a substance starts to boil
depends on the pressure; therefore, if the pressure is fixed, so is the boiling
temperature and vice versa. A plot of Psat vs. Tsat is called a liquid-vapor saturation
curve. Note: Psat values listed as a function of T in Tables A-4 and A-4E (for water)
and Tsat values listed as a function of P in Tables A-5 and A-5E (for water)
Values shown
for water
Elevation, m
Patm, kPa
Tboil H2O, oC
0
101.33
100.0
1000
89.55
96.5
2000
79.5
93.3
5000
54.05
83.3
10000
26.5
66.3
20000
5.53
34.7
Now, suppose that we repeat the exact same piston-cylinder experiment, but this
time at a higher pressure, say 1 MPa:
Not drawn to scale.
Values for water.
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EGR 2500 - Thermodynamic Properties I
At a pressure Pcr = 22.06 MPa (for water), the saturation line will become a point
and the temperature is Tcr = 373.95 oC. This point is called the critical point and is
defined as the point at which the saturated liquid and saturated vapor states are
identical.
At pressures above the critical point, there will be no distinct phase-change
process. Instead, v will continue to increase, and all times there will be only one
phase present. Eventually it will resemble a vapor, but one can not tell when the
change occurred. Beyond the critical point, liquid and vapor phases cannot co-exist
in equilibrium.
Note: Tables A-1 and A-1E list the critical temperature and critical pressure values
for different substances.
 T-v Diagram:
The saturated liquid states in the previous figure can be connected by a line called
the saturated liquid line and the saturated vapor states in the same figure can be
connected by another line called the saturated vapor line. These two lines meet at
the critical point and form what is known as the vapor dome.
Not drawn to scale
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EGR 2500 - Thermodynamic Properties I
While the T-v diagram was developed using a constant pressure process, it is
actually a unique representation of the phase/state of a pure substance.
Let’s introduce a new property, specific enthalpy: h = u + pv
T-u, T-h, or T-s diagrams are very similar to T-v diagrams.
 P-v Diagram:
The general shape of a P-v (or P-u, P-h, P-s) diagram of a pure substance is very
similar to that of a T-v diagram. The one difference lies in the T = constant
(isotherm) lines, which show a decreasing trend.
Not drawn to scale
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EGR 2500 - Thermodynamic Properties I
 Some Phase Rules:
Refer to the T-v and P-v diagrams. Determine the phase of a substance in the
following cases:
a) Given T or P and v (or u, h, s): v f  v  v g
This also applies if u f  u  u g or h f  h  h g
b) Given T or P and v (or u, h, s):
v  vg
c) Given T or P and v (or u, h, s):
v  vf
d) v  v f
e) v  v g
 Extending the P-v diagrams to include the solid phase
The liquid-vapor phase diagrams that were discussed so far can be extended to
include the solid phase as well as the solid-liquid and solid-vapor saturation
regions.
Substance that contracts on freezing
Substance that expands on freezing
Most substances contract on freezing. However, some substances such as water,
silicon, gallium, antimony, and bismuth expand on freezing
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EGR 2500 - Thermodynamic Properties I
 P-T Diagram:
The next figure shows the P-T diagram, which is also known as the phase diagram,
for substances that expand or contract upon freezing.
At the triple point, all three phases, liquid, vapor and
solid, exist in equilibrium. For water this occurs at a temperature of 0.01 oC and a
pressure of 0.6117 kPa. Table 4-3 lists the Triple point temperatures and pressures
of various substances.
Notes:
 Points that fall on a line are in a mixture involving the two
phases that the line separates.
 P and T are independent in a single phase region.
 P and T are dependent in a two-phase region (If you set
Psat, Tsat is fixed and vice versa).
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EGR 2500 - Thermodynamic Properties I
 Some More Phase Rules:
Given T, you can look up Psat@T in the saturated temperature table (e.g., Table A-4
for water)
Given P, you can look up Tsat@P in the saturated pressure table (e.g., Table A-5 for
water)
a) Given T and P: P < Psat@T
b) Given T and P: P > Psat@T
If it’s not water, it could also be a
c) Given T and P: T < Tsat@P
It could also be
is T is low enough
d) Given T and P: T > Tsat@P
e) Given T and P: T = Tsat@P or P = Psat@T
This includes the saturated liquid and saturated vapor points. If this is the case,
then P and T are not independent, so one needs to know another property such as x,
u, v, h or s to define the state.
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