Thermodynamics: An Engineering Approach, 6th Edition
Yunus A. Cengel,
g , Michael A. Boles
McGraw-Hill, 2008
Chapter 3
PROPERTIES OF PURE
SUBSTANCES
Mehmet Kanoglu
Modified by
Dr. Mostafa H. Sharqawy (ME203, KFUPM, Fall 2012)
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Objectives
• Concept of a pure substance
• Ideal gas equation of state
• Real
R l gas and
d th
the compressibility
ibilit ffactor
t
• Physics of phase-change processes.
• Ill
Illustrate
t t the
th P-v,
P T-v,
T and
d P-T
P T property
t diagrams
di
and
d P-v-T
P T
surfaces of pure substances.
g thermodynamic
y
properties
p p
of p
pure substances
• Determining
from tables of property data.
2
PURE SUBSTANCE
• Pure substance: A substance that has a fixed chemical
composition throughout and can exist in different phases.
Example
Not pure substance
H2O
Oil
(O2 + N2)
Water
A mixture of various chemical elements or compounds is a pure substance
as long as the mixture is homogeneous (e.g. Air).
A mixture of oil and water is NOT a pure substance because it forms two
chemically dissimilar regions.
A mixture
mi t re of two
t o or more phases of a pure
p re substance
s bstance is still a p
pure
re
substance as long as the chemical composition of all phases is the same.
3
THE IDEAL-GAS EQUATION OF STATE
•
•
Equation of state: Any equation that relates the pressure, temperature, and
specific volume of a substance.
The simplest and best-known equation of state for substances in the gas phase
is the ideal-gas equation of state.
Ideal gas equation of state
Absolute temperature [K]
Gas constant [kJ/kg-K]
Specific volume [m3/kg]
Ab l t pressure [kP
Absolute
[kPa]]
Use Table A1 to find R or M for different gases
M: molar
M
l mass (k
(kg/kmol)
/k l)
Ru: universal gas constant =
8.314 [kJ/kmol-K]
4
Problem
The pressure in an automobile tire depends on the temperature of the air in the
tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. If the
volume of the tire is 0.025 m3, determine the pressure rise in the tire when the air
temperature in the tire rises to 50
50°C
C. Also,
Also determine the amount of air that must
be bled off to restore pressure to its original value at this temperature. Assume the
atmospheric pressure is 100 kPa.
5
Problem
A 1-m3 tank containing air at 25°C and 500 kPa is connected through a valve to
another tank containing 5 kg of air at 35°C and 200 kPa. Now the valve is opened,
and the entire system is allowed to reach thermal equilibrium with the
surroundings which are at 20
surroundings,
20°C
C. Determine the volume of the second tank and
the final equilibrium pressure of air.
6
REAL GAS
Compressibility factor Z A factor that accounts for the deviation of real gases from
ideal-gas behavior at a given temperature and pressure.
Pcritical and Tcritical are given
in Table A-1 for gases.
Z
Z is a function of reduced
pressure (Pr = P / Pcritical)
and reduced temperature
(Tr = T / Tcritical).
Z is found from Figure A-15
(G
(Generalized
li d
compressibility chart)
g
At low Pr ((< 0.1)) or at high
Reduced pressure Pr
Tr (> 2), Z ≈ 1 and the gas
can be approximated as an Z can also be determined from a knowledge of PR and vR.
ideal gas.
7
REAL GAS
Question: What is the criteria for low pressure
and high temperature?
Answer: The p
pressure or temperature
p
of a g
gas
is high or low relative to its critical temperature
or pressure.
At very low pressures, all gases
approach ideal-gas behavior
(regardless of their temperature)
because the molecular forces are very
low.
8
Is Water Vapor an Ideal Gas?
•
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).
•
At higher pressures, however, the
ideal gas assumption yields
unacceptable
t bl errors, particularly
ti l l iin
the vicinity of the critical point and
the saturated vapor line.
•
In air
air-conditioning
conditioning applications, the
water vapor in the air can be
treated as an ideal gas. Because
the pressure of the water-vapor in
the air is very low (≈
( 5 kPa).
•
In steam power plant applications
the pressures involved are usually
very high; therefore, ideal-gas
relations
l ti
should
h ld nott b
be used.
d
9
Problem
Carbon
C
b dioxide
di id gas enters
t
a pipe
i att 3 MPa
MP and
d 500 K att a rate
t off 2 kg/s.
k / CO2 is
i
cooled at constant pressure as it flows in the pipe and the temperature CO2
drops to 450 K at the exit. Determine the volume flow rate and the density of
carbon dioxide at the inlet and the volume flow rate at the exit of the p
pipe
p using
g
(a) the ideal-gas equation and (b) the generalized compressibility chart. Also,
determine (c) the error involved when the ideal-gas model is used.
10
PHASES OF A PURE SUBSTANCE
The molecules in a solid are kept at
their positions by the large spring-like
inter-molecular
inter
molecular forces.
The arrangement of atoms in different phases: (a) molecules are at relatively fixed
positions in a solid, (b) groups of molecules move about each other in the liquid
phase, and (c) molecules move about at random in the gas phase.
11
PHASE-CHANGE OF PURE SUBSTANCE
12
PHASE-CHANGE OF PURE SUBSTANCE
•
•
•
•
•
Compressed liquid
(subcooled liquid): A
substance that it is not about to
vaporize.
i
Saturation temperature Tsat:
The temperature at which a
pure substance
b t
changes
h
phase
h
at a given pressure.
Saturation pressure Psat: The
pressure att which
hi h a pure
substance changes phase at a
given temperature.
Saturated liquid: A liquid that is about to vaporize (all saturated liquid
properties take a subscript f, i.e. vf, uf, hf, sf and the quality, x = 0).
Quality
y x: The ratio of the vapor
p mass to the total mass in the saturated
liquid-vapor mixture.
13
PHASE-CHANGE OF PURE SUBSTANCE
•
•
•
Saturated vapor: A vapor
that is about to condense (all
saturated vapor
p p
properties
p
take a subscript g, i.e. vg, ug,
hg, sg and the quality, x = 1).
Saturated liquid–vapor
mixture:
i t
Th state
The
t t att which
hi h
the liquid and vapor phases
coexist in equilibrium.
Superheated vapor: A vapor
that is not about to condense
(i.e., not a saturated vapor).
•
Latent heat: The amount of energy absorbed or released during a
phase-change process.
•
gy absorbed during
g
Latent heat of vaporization: The amount of energy
vaporization and it is equivalent to the energy released during
condensation.
14
f
g
If the entire
process between
b t
state 1 and 5 is
reversed by
cooling the water
while maintaining
the pressure at
the same value,
the water will go
back to state 1on
the same path,
and the amount of
heat released will
exactly match the
amount of heat
added during the
heating process.
15
PHASE-CHANGE AT DIFFERENT PRESSURES
At higher pressure, the saturation temperature is higher and (vg – vf) is less.
At the critical point, this difference is zero.
f
g
T v diagram of constantT-v
constant
pressure phase-change
processes of a pure
substance at various
pressures (numerical
(
i l
values are for water).
16
•
saturated liquid line
•
saturated vapor line
•
compressed liquid region
•
superheated vapor region
•
saturated liquid–vapor mixture region (wet region)
Critical point: The point
at which the saturated
liquid and saturated vapor
states are identical.
17
PROPERTY TABLES
•
•
•
•
Thermodynamic properties of substances are frequently presented in tables.
Some thermodynamic properties can be measured easily, but others cannot and
are calculated by using the relations between them and measurable properties.
For pure substances, two independent properties are required to get other
properties.
ti
There is a table for each region. compressed liquid table, superheated vapor
table and saturation table.
18
Saturated Liquid and Saturated Vapor States
T bl A–4:
Table
A 4 Saturation
S t ti properties
ti off water
t under
d ttemperature
t
Table A–5: Saturation properties of water under pressure.
19
Problem
A cooking pan whose inner diameter is
20 cm is filled with water and covered
with a 4-kg lid. If the local atmospheric
pressure is 101 kPa,
kPa determine the
temperature at which the water starts
boiling when it is heated.
20
Saturated Liquid–Vapor Mixture
Quality,
y, x : The ratio of the mass of vapor
p to the total mass of the mixture.
Quality is between 0 and 1
0: sat. liquid, 1: sat. vapor.
The properties of the saturated liquid are the same whether it exists alone or in
a mixture with saturated vapor.
21
Problem
A 1.8-m3 rigid tank contains steam at 220
°C. One third of the volume is in the liquid
phase and the rest is in the vapor form.
Determine:
(a) The pressure of the steam
(b) The mass of liquid
(c) The mass of vapor
(d) The quality of the saturated mixture
(e) The density of the mixture.
((f)) The
e internal
te a e
energy
e gy o
of tthe
e mixture
tu e (U)
(g) The enthalpy of the mixture (H)
V
Vapor
Liquid
22
In the region to the right of the
saturated vapor line and at
temperatures above the critical
point temperature, a substance
exists as superheated vapor.
In this region,
region temperature and
pressure are independent
properties.
Superheated Vapor
Compared
C
d tto saturated
t t d vapor,
superheated vapor is characterized by
At a specified
P superheated
P,
h t d
vapor exists at
a higher h than
the saturated
vapor.
A partial
listing of
Table A–6.
23
Compressed Liquid
Compressed
p
liquid
q
is characterized by
y
The compressed liquid properties
depend on temperature much more
strongly
t
l th
than th
they d
do on pressure.
y  v, u, or h
A compressed liquid
may be approximated
as a saturated liquid at
the given temperature
temperature.
At a given P
and T,
T a pure
substance will
exist as a
compressed
liquid if
24
Problem
C
Complete
l t the
th following
f ll i ttable
bl ffor water
t
p [kPa]
T [oC]
300
1600
h [kJ/kg]
x
Phase
0
600
300
5000
v [m3/kg]
0.4
200
25
P-v diagram of a pure substance.
The pressure in a piston–cylinder
piston cylinder device can be
reduced by reducing the weight of the piston.
26
Extending the
Diagrams to Include
the Solid Phase
For water,
Ttp = 0.01°C
Ptp = 0.6117 kPa
At triple-point pressure
and temperature
temperature, a
substance exists in three
phases in equilibrium.
P-v diagram of a substance that
contracts on freezing.
P-v diagram of a substance that
expands on freezing (such as water).
27
Sublimation: Passing from
the solid phase directly into
the vapor phase.
Phase Diagram
At low pressures (below
the triple-point value),
P-T diagram of pure substances.
solids evaporate without
melting first (sublimation).
(sublimation)
28
Reference State and Reference Values
• The values of u,, h,, and s cannot be measured directly.
y Theyy are
calculated from measurable properties using the relations
between properties.
give the changes
g in p
properties,
p
not the
• However, those relations g
values of properties at specified states.
• Therefore, a reference state is chosen and a value of zero for a
convenient property is assigned at that reference state.
• The reference state for water is 0.01°C and for R-134a is -40°C in
tables.
• Some properties may have negative values as a result of the
reference state chosen.
• Sometimes different tables list different values for some
properties at the same state as a result of using a different
reference
f
state.
t t
• However, In thermodynamics we are concerned with the changes
in properties, and the reference state chosen is of no
consequence in calculations
calculations.
29
Problem
A rigid tank with a volume of 2.5 m3 contains 15 kg of saturated liquid–
vapor mixture of water at 75°C. Now the water is slowly heated.
Determine the temperature at which the liquid in the tank is completely
vaporized. Also, show the process on a T-v diagram with respect to
saturation lines.
Vapor
Liquid
30
Problem
A piston–cylinder device initially contains 50 L of
liquid water at 40°C and 200 kPa. Heat is
transferred to the water at constant pressure
until the entire liquid is vaporized.
(a) What is the mass of the water?
(b) What is the final temperature?
(c) Determine the total enthalpy change.
((d)) Show the p
process on a T-v diagram
g
with
respect to saturation lines.
31
Problem
A tank whose volume is unknown is divided into two parts by a partition.
One side of the tank contains 0.01 m3 of refrigerant-134a that is a
saturated liquid at 0.8 MPa, while the other side is evacuated. The
partition is now removed, and the refrigerant fills the entire tank. If the
final state of the refrigerant is 20°C and 400 kPa, determine the
volume of the tank.
32
Summary
•
•
Pure substance
P
b t
The ideal gas equation of state
 Is water vapor an ideal gas?
•
•
•
Compressibility factor and real gases
Phases of a pure substance
Phase-change
Phase
change processes of pure substances
 Compressed liquid, saturated liquid, saturated vapor, superheated
vapor
 Saturation temperature and saturation pressure
•
Property diagrams for phase change processes
 The T-v diagram, The P-v diagram
•
Property
p y tables
 Saturation table, superheated vapor table, compressed liquid table
 Reference state and reference values
33