 Pure substance
 Phase change processes
 Use of thermodynamic tables
 Diagrams T-v, P-v
 Ideal gas equation
2.1.- PURE SUBSTANCE:
Substance that has a fixed chemical composition
throughout is called a PURE SUBSTANCE.
Water, nitrogen, helium and carbon dioxide.
2.2.- PHASE OF A PURE SUBSTANCE:
At a room temperature and pressure, cooper is a
solid, mercury is a liquid, and nitrogen is a gas.
There are three principal phases:
Chapter 2
1
 SOLID
 LIQUID
 GAS
2.3.- CHANGE-PHASE PROCESSES OF PURE
SUBSTANCE:
There are many practical situations where two
phases
of
a
pure
substance
coexist
in
equilibrium. Water exits as a mixture of liquid and
vapor in the boiler and the condenser of a steam
power plant. The refrigerant turns from liquid to
vapor in a freezer o refrigerator.
COMPRESSED LIQUID AND SATURATED LIQUID
Liquid water at 20 ºC and 1 atm
pressure.
Under
theses
STATE 1
conditions, water exists in the
liquid phase, and it is called a
“COMPRESSED
LIQUID”
or
P = 1 atm
T = 20 ºC
subcooled liquid, meaning that
it is “Not about to vaporize”.
COMPRESSED LIQUID
Chapter 2
2
Heat is now added to the water
until its temperature rises to,
say 40ºC.
As more heat is transferred,
th e
temperature
will
STATE 2
keep
rising until it reaches 100ºC.
At this point, water is still a
P = 1 atm
T = 100 ºC
liquid, but any heat addition,
will cause some of the liquid
to vaporize. A liquid that is
SATURATED LIQUID
“about to vaporize” is called
“SATURATED LIQUID”.
SATURATED
VAPOR
VAPOR
AND
SUPERHEATED
Once boiling starts, the temperature will stop
rising until the liquid is completely vaporized
(100ºC and 1 atm). Any heat loss from this vapor,
will cause some of the vapor to condense (phase
change from vapor to liquid). A vapor that is
Chapter 2
3
“about to condense” is called a “SATURATED
VAPOR”
Therefore, state 4 is a saturated vapor state. A
substance at states between 2 and 4 is often
referred to as a “SATURATED LIQUID-VAPOR
MIXTURE”, since the “liquid and vapor phases
coexist in equilibrium” at these states.
STATE 3
P = 1 atm
T = 100 ºC
SATURATED LIQUID-VAPOR MIXTURE
STATE 4
P = 1 atm
T = 100 ºC
SATURATED VAPOR
As more heat is added will result in an increase in
both the temperature and the specific volume. At
4
the state 5, the temperature of the vapor is, let us
say, 300ºC; and if we transfer some heat from the
vapor, the temperature may drop somewhat but
no condensation will take place as long as the
temperature remains above 100ºC (for P= 1 atm).
A vapor that is “not about to condense” (i.e., not a
saturated vapor) is called a “SUPERHEATED
VAPOR”
STATE 5
P = 1 atm
T = 300 ºC
SUPERHEATED VAPOR
5
T, ºC
300
Superheated
100
Saturated
vapor
mixture
Compressed
liquid
20

SATURATION TEMPERATURE AND SATURATION
PRESSURE
“Water boils at 100ºC” is INCORRECT
“Water boils at 100ºC at 1atm pressure” is
CORRECT
100ºc
151.9ºC
1 Atm
(101.325 kPa)
(500 kPa)
6
“The temperature at which water starts boiling
depends on the pressure, therefore if the pressure
is fixed, so is the boiling temperature”
At a given pressure, the temperature at which a
pure substance starts boiling is called the
SATURATION TEMPERATURE ( TSat). Like wise, at
a given temperature, the pressure at which a pure
substance
starts
boiling
is
called
th e
SATURATION PRESSURE (PSat).
During a phase change process, pressure and
temperature are obviously dependent properties,
and there is a definite relation between them, that
is TSat = f(PSat).
Elevation
(m)
0
1000
2000
:
20000
Chapter 2
Atmospheric
Boiling
Pressure (kPa) Temperature (ºC)
101.33
100
89.55
96.3
79.50
93.2
:
:
5.53
34.5
7
2.4.- PROPERTY DIAGRAMS FOR PHASECHANGE PROCESSES
1.- The T-  Diagram
T, ºC
Critical point
374.1
4
SUPERHEATED
VAPOR
REGION
COMPRESSED
LIQUID
REGION
P2 =Constant >P1
SATURATED
LIQUID-VAPOR
REGION
Saturated
liquid line
0.00315
5
P1 =Constant
Saturated
vapor line

Critical point may be defined as “The point at
which the saturated liquid and saturated vapor
states are identical”
Chapter 2
8
2.- The P-  Diagram
P
Critical point
SUPERHEATED
VAPOR
REGION
COMPRESSED
LIQUID
REGION
SATURATED
LIQUID-VAPOR
REGION
T2 =Constant >T1
T1 =Constant
Saturated
liquid line
Saturated
vapor line

2.5.- PROPERTY TABLES
The properties are frequently presented in the
form of tables.
Chapter 2
9
ENTHALPY- A Combination Property
u1
P1,1
CONTROL
VOLUME
u2
P2 , 2
In the analysis of certain types of process,
particularly in power generation and refrigeration,
we frequently encounter the combination of
properties U+PV. For the sake of simplicity and
convenience, this combination is defined as a
new
property, “ENTHALPY”, and given the
symbol H:
H  U  PV (kJ)
h  u  P (kJ / kg)
Chapter 2
10
1- Saturated Liquid and Saturated Vapor States
The properties of saturated liquid and saturated
vapor for water are listed in table A-4
Sat.
Specific volume
m3/Kg
Sat.
Sat.
Liquid
Vapor
Temp.
ºC
Press
kPa
T
PSat
f
g
85
57.83
0.001033
2.828
90
70.14
0.001036
2.361
95
84.55
0.001040
1.982
Specific
temperature
Corresponding
saturation
pressure
Specific
volume of
saturated
liquid
Specific
volume of
saturated
vapor
f = specific volume of saturated liquid
 g = specific volume of saturated vapor
 f g = difference between  g and  f
 f g  g   f )
Chapter 2
(that is
11
The quantity
h fg is
called the “ENTHALPY OF
VAPORIZATION” (or latent heat of vaporization).
It represents the amount of energy needed to
vaporize a unit mass of saturated liquid at a given
+temperature o pressure. It decreases as the
temperature
or
pressure
increases,
and
it
becomes zero at the critical point.
SATURATED LIQUID-VAPOR MIXTURE.During a vaporization process, a substance exists
as part liquid and part vapor. That is, it is a
mixture of saturated liquid and saturated vapor.
To analyze this mixture properly, we need to know
the proportions of liquid and vapor phases in the
mixture. This done by defining a new property
called “QUALITY” “x” as the ratio of the mass of
vapor to the total mass of the mixture:
x
Chapter 2
m v apor
m total
12
Where: m total  mliquid  m v apor  m f  mg
P or T
Critical point
Saturated
liquid states
Saturated
vapor states
Sat. vapor
Sat. liquid

The
quality
of
a
system
that
consist
of
“SATURATED LIQUID” is 0 (or 0 percent), and the
quality of a system consisting of “SATURATED
VAPOR” is 1 (or 100 percent).
Consider a tank that contains a saturated liquidvapor mixture. The volume occupied by saturated
Chapter 2
13
Vf , and the volume occupied by
liquid is
saturated vapor is Vg . The total volume V is the
sum of these two:
vg
Saturated vapor
vg
v fg

Saturated liquidvapor mixture
Saturated liquid
V  Vf  Vg
V  mv  mt v av  mf v f  mgv g
mf  mt  mg  mt v av  (mt  mg )v f  mgv g
Dividing by
mt yields
v av  (1  x )v f  xv g
Chapter 2
14
Since x 
mg
m t . This relation can also be
expressed as
v av  v f  xv f g (m3/kg)
Where
v f g  v g  v f .Solving
for quality, we
obtain
v av  v f
x
vfg
This analysis given above can be repeated for
internal energy and enthalpy with the following
results:
uav  uf  xu f g (kJ/kg)
hav  hf  xh f g
Chapter 2
(kJ/kg)
15
2- Superheated Vapor
In the region to the right of the saturated vapor
line, a substance exists as superheated vapor.
Since the superheated region is a single phase
region (vapor phase only).
At
pressures
sufficiently
below
the
critical
pressure or temperatures sufficiently above the
critical temperature, a superheated vapor can be
approximated as an IDEAL GAS.
2- Compressed Liquid
The properties of compressed liquid are relatively
independent of pressure. Increasing the pressure
of a compressed liquid 100 times often causes
properties to change less than 1 percent. The
property most affected by pressure is enthalpy.
In the absence of compressed liquid data, a
general
approximation
is
TO
TREAT
COMPRESSED LIQUID AS SATURATED LIQUID
AT THE GIVEN TEMPERATURE. This is because
Chapter 2
16
the compressed liquid properties depend on
temperature more strongly that they do on
pressure. Thus
y  yf @T
2.6.- THE IDEAL-GAS EQUATION OF STATE
Any
equation
that
relates
th e
pressure,
temperature, and specific volume of a substance
is called an EQUATION OF STATE.
There are
several equation of state. The simplest and the
best known equation of state for substances in
the gas phase is THE IDEAL-GAS EQUATION OF
STATE.
In
1802,
J.
Charles
a nd
J.
Gay-Lussac,
experimentally determined that a low pressures
the volume of a gas is proportional to its
temperature. That is,
T
P  R 
 
Chapter 2
17
or
P  RT ………………..(2.4)
Where the constant of proportionality R is called
the “GAS CONSTANT”. Equation 2.4 is called the
IDEAL-GAS EQUATION OF STATE, or simply the
IDEAS-GAS RELATION, and a gas that obeys this
relation is called an IDEAL GAS.
In this equation, P is the absolute pressure, T is
the absolute temperature, and

is the specific
volume.
The gas constant R is different for each gas (table
2-3) and is determined from
R
Where
Ru
M
R u is
kJ / kg.K or kPa.m / kg.K 
3
the UNIVERSAL GAS CONSTANT
and M is the molar mass (also called molecular
Chapter 2
18
weight) of the gas. The constant
Ru
is the same
for all substances, and its value is
8.314 kJ/(kmol.K)
8.314 kPa.m3/(kmol.K)
0.08314 bar.m3/(kmol.K)
Ru
1.986Btu/(lbmol.R)
10.73 psia.ft3/(lbmol.R)
1545 ft.lbf/(lbmol.R)
The MOLAR MASS (M) can simply be defined as
the “mass of one mole” (also called a gram-mole,
abbreviated “gmol”) of a substance in grams, or
the mass of one kmol (also called a “kilogrammole”, abbreviated kgmol) in kilograms.
In English units, it is the mass of 1 lbmol (1
pound-mole = 0.4536 kmol) in lbm (1 pound-mass
= 0.4536 kg).
Chapter 2
19
Notice that the molar mass of a substance has the
way it is defined. When we say the molar mass of
nitrogen is 28, it simply means the mass of 1 kmol
of nitrogen is 28 kg, or the mass of 1 lbmol of
nitrogen is 28 lbm. That is,
M = 28 kg/kmol = 28 lbm/lbmol
The mass of a system is equal to the product of
its molar mass M and the mole number N:
m = MN
The values of R and M for several substances are
given in Table A-1.
The ideal-gas equation of state can be written in
several different forms:
V  m  PV  mRT
mR  MNR  NRu  PV  NRuT
V  N  P  RuT
Chapter 2
20
Where  is the molar specific volume, i.e., the
volume per unit mole (in m3/kmol or ft3/lbmol)
P1V1 P2 V2

T1
T2
An ideal gas is an IMAGINARY substance that
obeys the relation:
P  RT
IS A WATER VAPOR AN IDEAL GAS?
The error involved in treating water vapor as an
ideal gas is calculated and plotted in Fig. 2.37. It is
clear from this figure that at pressures below 10
kPa, water vapor can be treated as an ideal gas,
regardless of its temperature, with negligible error
(less than 0.1 percent). But at higher pressures,
the ideal-gas assumption yields unacceptable
errors, particularly in the vicinity of the critical
point and saturated vapor line.
Chapter 2
21
Fig. 2.37
Chapter 2
22
2.7.- COMPRESSIBILITY FACTOR- A MEASURE
OF DEVIATION FROM IDEAL-GAS BEHAVIOR
The deviation from ideal-gas behavior at a given
temperature and pressure can accurately be
accounted by introduction of a correction factor
called “COMPRESSIBILITY FACTOR” Z. It is
defined as:
Z
P
or P  ZRT
RT
It can also be expressed as
actual
Z
ideal
Where:
Chapter 2
ideal
RT

P
23
Obviously,
z  1 for ideal gases, and for real
 1
Z
gases
 1
Gases behave differently at a given temperature
and pressure, but they behave very much the
same at temperatures and pressures normalized
with respect to their critical temperatures and
pressures. The normalization is done as:
P
PR 
Pcr
and
T
TR 
Tcr
“GENERALIZED COMPRESSIBILITY CHART” is
given in the Appendix in Fig. A-13
Chapter 2
24
2.8.- OTHER EQUATIONS OF STATE.
Van der Waals Equation of State
a 

 P  2   b   RT
 

Beattie-Bridgeman Equation of State
RuT 
c 
A
  B   2
P
1 
3 
 
T 

Benedict-Webb-Rutin Equation of State
RuT 
C0  1
bRuT  a
P
  B0RuT  A 0  2  2 
3

T




a
c 
   2
 6  3 2  1  2 e

T 
 
Virial Equation of State
RT a(T ) b(T ) c(T ) d(T )
P
 2  3  4  5  ...





Chapter 2
25