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Definitions and Basic Principles of Thermodynamics
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DOI: 10.1007/978-3-319-29835-1_1
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Chapter 1
Definitions and Basic Principles
of Thermodynamics
Any subject that deals with energy, or heat in general, requires an understanding of
at least the basic principles of thermodynamics and, as in any science we encounter
in our life, thermodynamics has its own unique language and vocabulary associated
with it. Understanding of such language and vocabulary as well as abbreviations or
acronyms and an accurate definition of basic concepts forms a sound foundation for
the development of the science of thermodynamics, where it will lead us to have a
better understanding of heat, energy, etc. and allow us to have a better grasp of
fields and sciences that at least encounter the lateral parameters. In the case of a
thermodynamic system, this science can be simply defined as a quantity of matter or
a region in a space of consideration for study, and anything external to this system is
called the system’s surroundings and what separates this region from the rest of the
space is defined as the boundary of the system. So, in this chapter we will talk about
the basic principles that make up the science of thermodynamics [1–6].
1.1
Thermodynamics and Energy
Thermodynamics can be defined as the study of energy, energy transformations,
and its relation to matter. Matter may be described at a molecular (or microscopic)
level using the techniques of statistical mechanics and kinetic theory. For engineering purposes, however, we want “averaged” information, i.e., a macroscopic (i.e.,
bulk energy flow), not a microscopic, description. The reasons behind acquiring
such averaged information in a macroscopic form are twofold:
1. Microscopic description of an engineering device may produce too much information to manage.
2. More importantly, microscopic positions and velocities for example are generally not useful and lack enough information to determine how macroscopic
systems will act or react unless, for instance, their total effect is integrated.
© Springer International Publishing Switzerland 2017
B. Zohuri, Compact Heat Exchangers, DOI 10.1007/978-3-319-29835-1_1
1
2
1 Definitions and Basic Principles of Thermodynamics
Fig. 1.1 Piston (boundary)
and Gas (system)
Gas, Fluid
System
Boundary
The observation driven macroscopic point of view deals with bulk energy flow
which we encounter in Classical Thermodynamics; whereas, the theory driven
microscopic point of view is about molecular interactions which we encounter in
statistical physics/mechanics or kinetic theory.
We therefore neglect the fact that real substances are composed of discrete
molecules and model matter from the start as a smoothed-out continuum. The
information we have about a continuum represents the microscopic information
averaged over a volume. Classical thermodynamics is concerned only with
continua.
A thermodynamic system is a quantity of matter of fixed identity, around which
we can draw a boundary (see Fig. 1.1 for an example). The boundaries may be fixed
or moveable. Work or heat can be transferred across the system boundary. Everything outside the boundary is the Surroundings.
However, restricting ourselves by surroundings requires definition of a boundary
that separates the system from the rest of the space of consideration (see Fig. 1.2),
which results in defining a control volume.
When working with devices such as engines it is often useful to define the system
to be an identifiable volume with flow in and out. This is termed a control volume.
An example is shown in Fig. 1.3.
Another definition that we need to know is the concept of a “state” in thermodynamic. The thermodynamic state of a system is defined by specifying values of a
set of measurable properties sufficient to determine all other properties. For fluid
systems, typical properties are pressure, volume, and temperature. More complex
systems may require the specification of more unusual properties. As an example,
the state of an electric battery requires the specification of the amount of electric
charge it contains.
Properties may be extensive or intensive. Extensive properties are additive.
Thus, if the system is divided into a number of sub-systems, the value of the
property for the whole system is equal to the sum of the values for the parts.
Volume is an extensive property. Intensive properties do not depend on the quantity
of matter present. Temperature and pressure are intensive properties.
Specific properties are extensive properties per unit mass and are denoted by
lower case letters:
1.1 Thermodynamics and Energy
3
Fig. 1.2 Boundary around
electric motor (system)
System boundary
Electrical energy
(work)
System boundary
.
m, p , T
1
1
complex
process
.
m, p , T
2
2
Fig. 1.3 Sample of control volume
Specific Volume ¼
V
¼υ
m
Specific properties are intensive because they do not depend on the mass of the
system.
The properties of a simple system are uniform throughout. In general, however,
the properties of a system can vary from point to point. We can usually analyze a
general system by sub-dividing it (either conceptually or in practice) into a number
of simple systems in each of which the properties are assumed to be uniform.
It is important to note that properties describe states only when the system is in
equilibrium.
In summary, the science of thermodynamics, through its two most important
laws, drives the analysis of thermal systems which is achieved through the application of the governing conservation equations, namely Conservation of Mass,
Conservation of Energy (first law of thermodynamics), the second law of thermodynamics, and the property relations. While the Energy part can be viewed as the
ability to cause changes, as we have learned from our early physics in college,
energy is conserved and it transforms from one form into another. For example, a
car moving along a straight line on a level road skids to a stop. Its energy was
initially kinetic energy (the energy due to motion). What is taking place in this case
can be described as:
4
1 Definitions and Basic Principles of Thermodynamics
• The transfer of energy across boundaries, where
Heat + Gas in piston-cylinder assembly Work Move piston
• The storage of energy in molecules
Bulk motion Work and Heat Internal energy
The fundamental thing to understand is that a PWR converts nuclear energy to
electrical energy and it does this by converting the nuclear energy first to thermal
energy and then converting the thermal energy to mechanical energy, which is
finally converted to electrical energy. The science of thermodynamics deals with
each of these conversion processes. To quantify how each of these processes takes
place we must understand and apply the laws of thermodynamics.
1.2
Scope of Thermodynamics
Thermodynamics is the science that deals with energy production, storage, transfer,
and conversion. It is a very broad subject that affects most fields of science
including biology and microelectronics. The primary forms of energy considered
in this text will be nuclear, thermal, chemical, mechanical, and electrical. Each of
these can be converted to a different form with widely varying efficiencies. Predominantly thermodynamics is most interested in the conversion of energy from
one form to another via thermal means. However, before addressing the details of
thermal energy conversion, consider a more familiar example. Newtonian mechanics defines work as force acting through a distance on an object. Performing work is
a way of generating mechanical energy. Work itself is not a form of energy, but a
way of transferring energy to a mass. So when one mass gains energy, another mass,
or field, must lose that energy.
Consider a simple example. A 65-kg woman decides to go over Niagara Falls in
a 25-kg wooden barrel. (The first person to go over the fall in a barrel was a woman,
Annie Taylor.) Niagara Falls has a vertical drop of 50 m and has the highest flow
rate of any waterfall in the world. The force acting on the woman and barrel is the
force of gravity, which at the surface of the earth produces a force of 9.8 N for every
kilogram of matter that it acts on. So we have
W ¼ F D F ¼ ð65 þ 25Þ 9:8 ¼ 882:0 N D ¼ 50 m
W ¼ 882:0 50:0 ¼ 44, 100 N-m ¼ 44:1 kJ
A Newton meter is a Joule and 1000 J is a kilo-Joule. Therefore, when the woman
and barrel went over the falls, by the time they had reached the bottom, the force of
gravity had performed 44.1 kJ of work on them. The gravitational field had 44.1 kJ
of potential energy stored in it, when the woman and the barrel were at the top of the
falls. This potential energy was converted to kinetic energy by the time the barrel
reached the bottom of the falls. Kinetic energy is also measured in Joules, as with all
other forms of energy. However, we are usually most interested in velocities when
1.2 Scope of Thermodynamics
5
we talk about kinetic energies, so let us extract the velocity with which she hit the
waters of the inlet to Lake Ontario.
ΔKE ¼ ΔPE ¼ 44:1 kJ ¼ 1=2 mV2 ¼ ð90=2Þkg V 2
V 2 ¼ 44:1 kJ=ð90=2Þ kg
Now it is a matter of converting units. A Joule is a Newton-meter. 1 N is defined as
1 kg accelerated at the rate of 1 m/s/s. So
44:1 kJ ¼ 44, 100 N-m
¼ 44, 100 kg m=s=s m
¼ 44, 100 kgðm=sÞ2
V2
V
¼ 44, 100 kgðm=sÞ2 =ð90=2Þkg
¼ 490=ð1=2Þ ¼ 980ðm=sÞ2
¼ 31:3 m=s ð 70 mphÞ
Needless to say she recommended that no one ever try that again. Of course, others
have, some have made it, and some have drowned.
Before leaving this example, it is worth pointing out that when we went to
calculate the velocity, it was unaffected by the mass of the object that had dropped
the 50 m. So one-half the velocity squared represents what we will call a specific
energy, or energy per kilogram. In addition, the potential energy at the top of the
falls could be expressed as a specific potential energy relative to the waters below.
The potential energy per pound mass would just be the acceleration of gravity times
the height of the falls. Typically, we will use lower case letters to represent specific
quantities and upper case letters to represent extensive quantities. Extensive quantities are dependent upon the amount of mass present. Specific quantities are also
referred to as intensive variables, though there are some intensive variables that
have no extensive counterpart, such as pressure or temperature.
p:e: ¼ mgh =m ¼ gh ¼ 9:8 50 ¼ 0:49 kJ=kg
It is also worth pointing out that Newton’s law of gravity states that
F¼G
m1 M 2
R2
ðEq: 1:1Þ
where m1 is the smaller mass and M2 is the mass of the Earth. We can find the
specific force on an object by dividing the gravitational force by the mass of the
object. For distances like 50 m on the surface of the Earth (R ¼ 6,378,140 m) we can
treat R as constant, but if the distance the gravitational force acts through is
comparable to the radius of the Earth, an integration would be required. Even on
the top of Mount Everest, the gravitational potential is within 0.25 % of that at Sea
Level, so gravity is essentially constant for all systems operating on the face of the
Earth.
6
1 Definitions and Basic Principles of Thermodynamics
1.3
Units and Dimensions
Any physical quantity can be characterized by dimensions. The arbitrary magnitudes assigned to the dimensions are called units. There are two types of dimensions, primary or fundamental and secondary or derived dimensions.
Primary dimensions are: mass, m; length, L; time, t; temperature, T
Secondary dimensions can be derived from primary dimensions such as: velocity
(m/s2), pressure (Pa ¼ kg/m s2).
There are two unit systems currently available SI (International System) and
USCS (United States Customary System) or English (E) system, and they are
discussed in this section.
1.3.1
Fundamental Units
Before going further it is a very good idea to discuss units for physical quantities
and the conversion of units from one system to another. Unfortunately, the field of
thermodynamics is beset with two popular systems of units. One is the International
System (SI) consisting of the kilogram, meter, and second. The other is the English
(E) system consisting of the pound-mass, foot, and second.
Starting with the SI system, the unit of force is the Newton. The unit of work or
energy is the Joule, and the unit of pressure is the Pascal. We have,
1 N ¼ 1 kg m/s2
1 J ¼ 1 N-m
1 Pa ¼ 1 N/m2
Now the acceleration of gravity at Sea Level on Earth is 9.8066 m/s2, so a 100 kg
mass will have weight 980.66 N. Also when we want to avoid spelling out very
large or small quantities we will usually use the standard abbreviations for powers
of ten in units of 1000. We have,
kilo ¼ 103
mega ¼ 106
giga ¼ 109
deci ¼ 101
centi ¼ 102
milli ¼ 103
micro ¼ 106
nano ¼ 109
For the English system we have
1.3 Units and Dimensions
7
lbm ⟹ 1 lbf (at Sea Level)
1 ft lbf ¼ 1 lbf 1 ft
1 British Thermal Unit (BTU) ¼ 778 ft lbf
1 psi ¼ 1 lbf/in.2
Note that the fact that 1 lbf ¼ 1 lbm at Sea Level on Earth, means that a mass of
100 lbm will weigh 100 lbf at Sea Level on Earth. The acceleration of gravity at Sea
Level on Earth is 32.174 ft/s2. Thus we have 1 lbf/(1 lbm ft/s2) ¼ 32.174. If we
move to another planet where the acceleration of gravity is different, the statement
that 1 lbm 1 lbf doesn’t hold.
Consider comparative weights on Mars. The acceleration of gravity on Mars is
38.5 % of the acceleration of gravity on Earth. So in the SI system we have:
W ¼ 0:385 9:8066 m=s2 100 kg ¼ 377:7 N
In the English system we have,
W ¼ 0:385 100 lbm ¼ 38:5 lbf
1.3.2
Thermal Energy Units
The British thermal unit (Btu) is defined to be the amount of heat that must be
absorbed by a 1 lb-mass to raise its temperature 1 F. The calorie is the SI unit that is
defined in a similar way. It is the amount of heat that must be absorbed by 1 g of
water to raise its temperature 1 C. This raises the question as to how a calorie
compares with a Joule since both appear to be measures of energy in the SI system.
James Prescott Joule spent a major part of his life proving that thermal energy was
simply another form of energy like mechanical, kinetic or potential energy. Eventually his hypothesis was accepted and the conversion factor between the calorie
and Joule is defined by,
1 cal ¼ 4.1868 J
The constant 4.1868 is called the mechanical equivalent of heat.
1.3.3
Unit Conversion
As long as one remains in either the SI system or the English system, calculations
and designs are simple. However, that is no longer possible as different organizations and different individuals usually think and work in their favorite system.
8
1 Definitions and Basic Principles of Thermodynamics
In order to communicate with an audience that uses both SI and English systems it
is important to be able to convert back and forth between the two systems. The basic
conversion factors are,
1 kg ¼ 2.20462 lbm
1 lbm ¼ 0.45359 kg
1 m ¼ 3.2808 ft
1 ft ¼ 0.3048 m
1 J ¼ 0.00094805 Btu
1 Btu ¼ 1055 J
1 atm ¼ 14.696 psi
1 atm ¼ 101,325 Pa
1 psi ¼ 6894.7 Pa
1 bar ¼ 100,000.0 Pa
1 bar ¼ 14.504 psi
The bar unit is simply defined by rounding off Sea Level atmospheric pressure to
the nearest 100 kPa. There are many more conversion factors defined in the
Appendix, but they are all derived from these basic few.
1.4
Classical Thermodynamics
Classical thermodynamics was developed long before the atomic theory of matter
was accepted. Therefore, it treats all materials as continuous and all derivatives well
defined by a limiting process. Steam power and an ability to analyze it and optimize
it was one of the main drivers for the development of thermodynamic theory. The
fluids involved always looked continuous. A typical example would be the definition of the density of a substance at a point. We have,
ρ ¼ lim
ΔV!0
Δm
ΔV
ðEq: 1:2Þ
As long as ΔV does not reach the size of an atom this works. Since classical
thermodynamics was developed, however, we have come to understand that all
gases and liquids are composed of very small atoms or molecules and a limiting
process that reaches the atomic or molecular level will eventually become discontinuous and chaotic. Nevertheless, the continuous model still works well for the
1.5 Open and Closed Systems
9
macroscopic systems discussed in this text and classical thermodynamics is based
on it.
At times, we will refer to an atomistic description of materials in order to
develop a method of predicting specific thermodynamic variables that classical
thermodynamics cannot predict. A typical example is the derivative that is called
the constant volume specific heat. This variable is defined as the rate of change of
the internal energy stored in a substance as a function of changes in its temperature.
Classical thermodynamics demonstrates that this variable has to exist and makes
great use of it, but it has no theory for calculating it from first principles. An
atomistic view will allow us to make some theoretical estimates of its value.
Therefore, at times we will deviate from the classical model and adopt an atomistic
view that will improve our understanding of the subject.
Classical thermodynamics is also an equilibrium science. The laws of thermodynamics apply to objects or systems in equilibrium with themselves and their
surroundings. By definition, a system in equilibrium is not likely to change.
However, we are generally interested in how systems change as thermal energy is
converted to and from other forms of energy. This presents a bit of a dilemma in that
the fundamental laws are only good for a system in equilibrium and the parameters
we want to predict are a result of thermal energy changes in the system. To get
around this dilemma, we define what is called a quasi-equilibrium process. A quasiequilibrium process is one that moves from one system state to another so slowly
and so incrementally, that it looks like a series of equilibrium states. This is a
concept that classical thermodynamics had a great deal of difficulty clarifying and
quantifying. Basically, a process was a quasi-equilibrium process if the laws of
equilibrium thermodynamics could characterize it. This is sort of a circular definition, but once again, we will find that the atomistic view allows us to make some
predictions and quantifications that identify a quasi-equilibrium process. Quasiequilibrium processes can occur very rapidly on time scales typical of human
observation. For example, the expansion of hot gases out of the nozzle of a rocket
engine can be well described as a quasi-equilibrium process with classical
thermodynamics.
1.5
Open and Closed Systems
In the transfer and conversion of thermal energy, we are interested in separating the
entire universe into a system and its environment. We are mainly interested in the
energy transfers and conversions that go on within the system, but in many cases,
we need to consider its interactions with the rest of the world or its environment.
Systems that consist of a fixed amount of mass that is contained within fixed
boundaries are called closed systems. Systems that pass the mass back and forth
to the environment are called open systems. Both open and closed systems allow
energy to flow across their borders, but the flow of mass determines whether they
are open or closed systems. Open systems also carry energy across their borders with
10
1 Definitions and Basic Principles of Thermodynamics
Weight
Work
Gas under pressure
(closed system)
System Boundary
Heat
Fig. 1.4 A closed system
the mass as it moves. Consider the simple compressed gas in the piston below as a
closed system (Fig. 1.4).
In analyzing the closed system, we are concerned about the changes in the
internal energy of the compressed gas as it interacts with its environment and the
transfers of mechanical and thermal energies across its boundary.
In analyzing open systems, the concept of a control volume comes into play. The
control volume is the boundary for the open system where the energy changes that
we are interested in take place; the thing that separates the open system from its
environment. Consider the following open system where we have now allowed
mass to flow in and out of the piston of our closed system above (Fig. 1.5).
The control volume looks a lot like our system boundary from before, and it
is. The only difference is that we now allow mass to flow in and out of our control
volume. Thermal and mechanical energy can still flow across the boundary, or in
and out of the control volume. The mass flowing in and out can also carry energy
with it either way.
1.6
System Properties
In order to characterize a system we have to identify its properties. Initially there are
three main properties that we are concerned with—density, pressure, and temperature all of which are intensive variables. We use intensive properties to characterize the equilibrium states of a system. Systems are composed of pure substances
and mixtures of pure substances. A pure substance is a material that consists of
only one type of atom or one type of molecule. A pure substance can exist in
multiple phases. Normally the phases of concern are gas, liquid, and solid, though
for many pure substances there can be several solid phases. Water is an example of
a pure substance that can readily be observed in any of its three phases.
A solid phase is typically characterized as having a fixed volume and fixed
shape. A solid is rigid and incompressible. A liquid has a fixed volume but no fixed
1.6 System Properties
11
Weight
Mass out
Work
Control
Volume
Compressed Gas
Mass in
Heat
Fig. 1.5 An open system
shape. It deforms to fit the shape of the container that it is in. It is not rigid but is still
relatively incompressible. A gas has no fixed shape and no fixed volume. It expands
to fit the container that it is in. To characterize a system composed of one or more
pure components and one or more phases we need to specify the correct number of
intensive variables required to define a state. Gibbs Phase Rule, named after
J. Willard Gibbs who first derived it, gives the correct number of intensive variables
required to completely define an equilibrium state in a mixture of pure substances.
It is:
V ¼CPþ2
ðEq: 1:3Þ
V ¼ Number of variables required to define an equilibrium state.
C ¼ The number of pure components (substances) present.
P ¼ The number of phases present.
So for pure steam at Sea Level and above 100 C, we have 1 component and
1 phase so the number of variables required to specify an equilibrium state is
2, typically temperature and pressure. However, temperature and density would
also work. If we have a mixture of steam and liquid water in the system, we have
1 component and 2 phases, so only one variable is required to specify the state,
either pressure or temperature would work. If we have a mixture like air that is
composed of oxygen, nitrogen, and argon, we have 3 components and 3 phases (the
gas phase for each component), and we are back to requiring 2 variables. As we
progress, we will introduce additional intensive variables that can be used to
characterize the equilibrium states of a system in addition to density, pressure,
and temperature.
12
1.6.1
1 Definitions and Basic Principles of Thermodynamics
Density
Density is defined as the mass per unit volume. The standard SI unit is kilograms
per cubic meter (kg/m3). The Standard English unit is pounds mass per cubic foot
(lbm/ft3). If the mass per unit volume is not constant in a system, it can be defined at
a point by a suitable limiting process that converges for engineering purposes long
before we reach the atomistic level. The inverse of density is specific volume.
Specific volume is an intensive variable, whereas volume is an extensive variable.
The standard unit for specific volume in the SI system is cubic meters per kilogram
(m3/kg). The standard unit in the English system is cubic feet per pound mass (ft3/
lbm).
1.6.2
Pressure
Pressure is defined as force per unit area. The standard unit for pressure in the SI
system is the Newton per square meter or Pascal (Pa). This unit is fairly small for
most engineering problems so pressures are more commonly expressed in kiloPascals (kPa) or mega-Pascals (MPa). The standard unit in the English system
really does not exist. The most common unit is pounds force per square inch (psi).
However, many other units exist and the appropriate conversion factors are provided in the Appendix.
Pressure as an intensive variable is constant in a closed system. It really is only
relevant in liquid or gaseous systems. The force per unit area acts equally in all
directions and on all surfaces for these phases. It acts normal to all surfaces that
contain or exclude the fluid. (The term fluid includes both gases and liquids.) The
same pressure is transmitted throughout the entire volume of liquid or gas at
equilibrium (Pascal’s law). This allows the amplification of force by a hydraulic
piston. Consider the system in the following figure. In Fig. 1.6, the force on the
piston at B is greater than the force on the piston at A because the pressure on both
is the same and the area of piston B is much larger.
In a gravity field, the pressure in a gas or liquid increases with the height of a
column of the fluid. For instance, in a tube containing a liquid held vertically, the
weight of all of the liquid above a point in the tube is pressing down on the liquid at
that point. Consider Fig. 1.7, then:
dp ¼ ρgdh
ZH
ρgdh
pð 0Þ ¼ Pð H Þ þ
0
ðEq: 1:4Þ
1.6 System Properties
13
Fig. 1.6 A hydraulic
amplifier
Moveable pistons
A
B
Liquid
Fig. 1.7 Pressure in a
liquid column
dp
dh
Thus, the pressure at the bottom of the container is equal to the pressure on the top
of the fluid in the container plus the integral of the weight of the fluid per unit area in
the container.
This raises an interesting concept. Often it is important to distinguish between
absolute pressure and gage pressure. The preceding equation calculates the absolute pressure. The gage pressure is simply the pressure exerted by the weight of the
column without the external pressure on the top surface of the liquid. It is certainly
possible to have a negative gage pressure, but not possible to have a negative
absolute pressure. A vacuum pressure occurs when the absolute pressure in a
system is less than the pressure in the environment surrounding the system.
A manometer is a very common way of measuring pressure (setup in Fig. 1.8). A
manometer works by measuring the difference in height of a fluid in contact with
two different pressures. A manometer can measure absolute pressure by filling a
closed end tube with liquid and then inverting it into a reservoir of liquid that is
open to the pressure that is to be measured. Manometers can also measure a vacuum
gage pressure. Consider Fig. 1.8 below:
The tall tubes on the right in each system are open to the atmosphere. System A
is operating at a small negative pressure, or vacuum, relative to the atmosphere.
System B is operating at a positive pressure relative to the atmosphere. The
magnitude of the pressure in each case can be calculated by measuring the height
difference between the fluids in the two sides of the U-tube and calculating its
weight per unit area. This is the difference in the pressures inside systems A or B
and the atmospheric pressure pushing down on the open columns on the right.
14
1 Definitions and Basic Principles of Thermodynamics
h2
System A
System B
h1
Fig. 1.8 Pressure measurement with manometers
1.6.3
Temperature
The other intensive variable to be considered at this point is the temperature. Most
everyone is familiar with temperature as a measure of coldness or hotness of a
substance. As we continue our study of thermodynamics, we will greatly refine our
concept of temperature but for now it is useful to discuss how a temperature scale is
constructed. Traditionally the Fahrenheit scale was established by defining the
freezing point of water at Sea Level pressure to be 32 F and the boiling point of
water to be 212 F under the same conditions. A thermometer containing a fluid that
expands readily as a function of temperature could be placed in contact with a
system that contained ice and water vapor saturated air. The height of the fluid in
the thermometer would be recorded as the 32 F height. Then the same thermometer
would be placed in a water container that was boiling and the height of the fluid in
the thermometer marked as the 212 F point. The difference in height between the
two points would then be marked off in 180 divisions with each division
representing 1 F. The Celsius scale was defined in the same way by setting the
freezing point of water at 0 C and the boiling point at 100 C. Water was chosen as
the reference material because it was always available in most laboratories around
the world.
When it became apparent that absolute temperatures were possibly more important than simple temperatures in the normal range of human experience, absolute
temperature scales were defined. The freezing point of water was defined as
273.15 K and the boiling point was defined as 373.15 K, to match up with the
Celsius scale. Note that the unit on the absolute scale is Kelvin, not degrees Kelvin.
It was named in honor of Lord Kelvin who had a great deal to do with the
development of temperature measurement and thermodynamics. The freezing
point of water was further defined as the equilibrium of pure ice and air saturated
water. However, it was difficult to attain this point because as ice melts it forms a
layer of pure water around itself, which prevents direct contact of pure ice and
air-saturated water. Therefore, in 1954, the two-point method was abandoned and
the triple point of water was chosen as a single standard. The triple point of water is
273.16 K, 0.01 K above the ice point for water at Sea Level pressure. A single point
can be used to define the temperature scale if temperatures are measured with a
constant volume, ideal gas thermometer. Basically, the ideal gas thermometer can
measure the pressure exerted by a constant volume of gas in contact with the system
1.6 System Properties
15
to be measured. It can also measure the pressure exerted by the gas when in contact
with a system at the triple point of water. The ratio of the two pressures gives the
ratio of the measured absolute temperature to the absolute temperature of the triple
point of water.
However, additional secondary standards are defined to simplify calibration over
a broad range of temperatures. The International Practical Temperature Scale is
defined by:
Triple point of equilibrium hydrogen
Boiling point of hydrogen at 33.33 kPa
Boiling point of hydrogen at 1 atm
Boiling point of neon
Triple point of oxygen
Boiling point of oxygen
Triple point of water
Boiling point of water
Freezing point of zinc
Freezing point of silver
Freezing point of gold
13.81 K
17.042 K
20.28 K
27.102 K
54.361 K
90.188 K
273.16 K
373.15 K
692.73 K
1235.08 K
1337.58 K
Once the absolute temperature scale in Kelvin was defined it became part of the
SI system. An absolute scale matching the Fahrenheit scale between the freezing
point of water and its boiling point has been defined for the English system. Since
there are 180 between the freezing and boiling points in the Fahrenheit scale and
100 over the same range in the Kelvin scale, the absolute scale for the English
system, where the unit of measurement is called a degree Rankine, is simply 1.8
times the number of Kelvin. So the freezing point of water on the Rankine scale is
491.67 R and the boiling point is 671.67 R. Absolute zero on the Rankine scale is
459.67 F. To convert back and forth the following formulas apply.
T K ¼ T C þ 273
T C ¼ T K 273
T R ¼ T F þ 460
T F ¼ T R 460
TR
TK
TF
TC
¼ 1:8T K
5
¼ TR
9
¼ 1:8T C þ 32
5
¼ ðT F 32Þ
9
ðEq: 1:5Þ
ðEq: 1:6Þ
16
1.7
1 Definitions and Basic Principles of Thermodynamics
Properties of the Atmosphere
Before going further, it will be useful to have a model for the atmosphere that can be
used for calculations. This is important to realize that the atmosphere at Sea Level
supports a column of air that extends upwards of 50 miles. Given the equation
derived earlier for the pressure in a column of fluid, we have as always to begin at
Sea Level.
dp ¼ ρgdh
Let ρ ¼ p=RT
Then
g
dp ¼ p dh
RT
ðEq: 1:7aÞ
Or by integration of the last term of Eq. (1.7a), we obtain
g
p ¼ pSL eRTh
ðEq: 1:7bÞ
To perform the integration, the above temperature has been assumed constant. This
is not quite true as the standard lapse rate for the Troposphere up to about 40,000 ft
is approximately 2 C per 1000 ft or 3.6 F per 1000 ft. This means that the air is
denser than the exponential model predicts. However, it is approximately correct
for the Troposphere particularly if only a limited range of elevations is considered
and the average temperature is used. The initial values at Sea Level for the standard
atmosphere are,
Pressure
Temperature
Density
Composition
Nitrogen
Oxygen
Argon
Carbon Dioxide
Ne, He, CH4, etc.
14.696 psi
59 F (519 R)
076,474 lbm/ft3
101.325 kPa
15 C (288 K)
1.225 kg/m3
Mole fraction (%)
78.08
20.95
0.93
0.03
0.01
A more extensive model of the atmosphere as a function of altitude is provided
in the Appendix. The relative composition is essentially constant up to the top of the
Troposphere.
References
1.8
17
The Laws of Thermodynamics
It is useful at this time to state the Laws of Thermodynamics. Later chapters will
expand on them greatly, but realizing there are four simple laws that all of the
analysis is built around will provide some structure to guide the way forward.
Zeroth Law of Thermodynamics: Two bodies in thermal contact with a third
body will be at the same temperature.
This provides a definition and method of defining temperatures, perhaps the most
important intensive property of a system when dealing with thermal energy conversion problems.
First Law of Thermodynamics: Energy is always conserved when it is
transformed from one form to another.
This is the most important law for analysis of most systems and the one that
quantifies how thermal energy is transformed to other forms of energy.
Second Law of Thermodynamics: It is impossible to construct a device that
operates on a cycle and whose sole effect is the transfer of heat from a cooler body
to a hotter body.
Basically, this law states that it is impossible for heat to spontaneously flow from
a cold body to a hot body. If heat could spontaneously flow from a cold body to a
hot body, we could still conserve energy, so the First Law would hold. But every
experiment that has ever been performed indicates that thermal energy always flows
the other way. This law seems obvious enough but the implications are very
significant, as we will see.
Third Law of Thermodynamics: It is impossible by means of any process, no
matter how idealized, to reduce the temperature of a system to absolute zero in a
finite number of steps.
This allows us to define a zero point for the thermal energy of a body be taken
under consideration and a subject of this matter is beyond the scope of this book.
References
1. Zohuri, Bahman, and Patrick McDaniel. 2015. Thermodynamics in nuclear power plant.
Switzerland: Springer Publishing Company.
2. Cengel, Yunus A., and Michael A. Boles. 2008. Thermodynamics: An engineering approach,
6th ed. Boston: McGraw Hill.
3. Elliott, J. Richard, and Carl T. Lira. 1999. Introductory chemical engineering thermodynamics.
Upper Saddle River, NJ: Prentice Hall.
4. Hseih, Jui S. 1975. Principles of thermodynamics. New York: McGraw Hill.
5. Moran, Michael J., and Howard N. Shapiro. 2008. Fundamentals of engineering thermodynamics, 6th ed. New York: John Wiley & Sons.
6. Van Wylen, Gordon J., and Richard E. Sonntag. 1978. Fundamentals of classical thermodynamics. SI Version 2e. New York: John Wiley & Sons.
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