Chapter 1 Applying Models to Thermal Phenomena
1
Contents
1-1 Where we are
headed in this
chapter
1-2 Phenomena, Data
Patterns,
Questions
1-3 Three-Phase
Model of Matter
1-4 EnergyInteraction
Model
1-5 Examples of
Particular
Models
1-6 Looking Back
and Ahead
1
Applying Models to Thermal
Phenomena
In the next two chapters we will introduce and gain a lot of experience using a
universally applicable model, perhaps the most powerful model in all of science.
We call this model the Energy-interaction Model. It literally applies to every kind
of interaction we have ever encountered, involving the smallest subatomic
particles to the evolution of our entire universe from the time of the Big Bang. It
can help us explain every kind of phenomena imaginable. This model incorporates
the Principle of Conservation of Energy. This principle, by itself, however, is not
a particularly easy tool to use. We need to turn it into a useful tool, a tool that we
can reason with, that we can answer various kinds of questions with, a tool that we
can readily use to construct explanations for all kinds of phenomena. That is, we
need to create a model that incorporates the principle of conservation of energy in
a way that we know how to apply it to particular phenomena we are interested in,
that we have questions about that we want answers to. As we develop and use the
energy-interaction model, we will also learn a lot about model-based reasoning
along the way. If you have not read the Appendix M1-Science and the Place of
Models in Science, especially the first three sections, you should do so now.
This is the first of two chapters in which the primary focus is on learning the
Energy-Interaction Model and how to use it to construct particular models of
various kinds of phenomena. We will encounter two other modes in these two
chapters as well, the Three-Phase Model of Pure Substances and the Intro SpringMass Oscillator Model (that will be substantially augmented and extended in later
chapters).
1-1 Where We Are Headed in this Chapter
We begin Chapter 1 talking about some phenomena you already know a lot about.
As we just previously said, the energy interaction model applies to every kind of
phenomena and every kind of interaction, so why start with what might seem to
be some pretty boring stuff you already know a lot about? Reason (1) is you do
know a lot about this phenomena, so you are not hit with stuff you don’t know
anything about right off the bat. Reason (2) is that there are some very interesting
parts of thermal phenomena that you probably can’t make much, if any, sense of
right now. That is, you can’t explain what’s going on, why it happens, or in
general, say much about it at all. We will see that by applying the EnergyInteraction Model to these seemingly very strange thermal phenomena, we can
make sense of them, we can explain what is going on, and we can answer all
kinds of questions about the phenomena (including some seemingly hard
questions on exams). To see the universal applicability of the Energy-Interaction
Model, we will also apply this model to several chemical reactions.
One rather simple kind of thermal phenomena you will immediately encounter in
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Chapter 1
Applying Models to Thermal Phenomena
the classroom activities involves the addition or removal of energy as heat to pure
substances. You have encountered this general class of phenomena (changing the
temperature of a substance and/or causing it to go through a phase change) in
general physical science courses as well as in your chemistry courses. So partly as
review, but also as an example of how models need to be extended and modified,
we introduce the Three-Phase Model of Pure Substances in this chapter.
On pages 5 & 6 we present some of the thermal phenomena to which we will be
applying our first two models: The Three-Phase Model of Pure Substances and
the Energy-Interaction Model. Often, in this section of each chapter we will also
present some of the more generalized data patterns that have evolved from many
scientific studies related to the same phenomena.
In this next section, we will also present some of the kinds of questions we will
want to be able to answer, the kinds of explanations we will want to construct,
and the kinds of predictions we can make using the models presented in the
chapter. As we do this throughout the course, we will become much more aware
of the limitations on the kinds of questions and explanations that the particular
models, in this case, the Energy-Interaction Model can help us with. We will
begin to get a much better feeling for when we can take an energy conservation
approach, i.e., apply the Energy-Interaction Model and when we must use a
different model.
Keep in mind that in Chapter 1 we deliberately restrict the range of phenomena to
which we are applying the Energy-Interaction Model to mostly thermal
phenomena (and a few examples of chemical reactions) and will wait until
Chapter 2 to apply the Energy-Interaction Model to mechanical interactions and
processes. It is easy to forget that this is the one model that can be usefully
applied to essentially any interaction or process that occurs in any branch of
physical and biological science.
Chapter 1 Applying Models to Thermal Phenomena
1-2
3
Phenomena, Data Patterns, and Kinds of
Questions and Explanations
Phenomena and Data Patterns
The principle of conservation of energy and the Energy-Interaction Model that
allows us to make effective use of it, applies to literally every kind of interaction.
Once it was realized that “heat-energy” (now called thermal energy) was not some
kind of special substance, but just one of the many ways energy increased or
decreased in interactions of matter, scientists began to appreciate the universality
of whatever it is that we give the label “energy” to.
It isn’t easy to define energy. During an interaction or process, energy decreases
in some “ways” and increases in “other ways.” In this course we use the phrase
“energy system” to label a “way” a physical system can “have” energy in the
Energy-Interaction Model. Scientists have found that during an interaction
between one physical system and another physical system, the energy in some
energy system(s) decreases and in other(s) it increases, but the net result is that
the total amount of energy in all systems remains constant.
Sometimes it was an apparent discrepancy in the energies “adding up” properly
that led to the discovery of new energy systems. That is, there were ways that
physical systems could have energy that were not previously known.
In a way, the idea of energy and its use as a conservation law as we and others
have presented it, really does seem to be the way our universe actually works.
That is, the model seems to be exactly how the universe works. And it works this
way in all circumstances. It works this way for all interactions. There appear to
be no exceptions. So if it works so well, why doesn’t it just answer all of our
questions?
It is true that the idea of energy conservation applies to every kind of interaction
imaginable. So that is not the problem. The problem comes with the kinds of
questions it can address and the kinds of answers it can be used to develop.
Kinds of Questions
The Energy-Interaction Model, like all conservation principles, allows us to make
very definite statements, predictions of all kinds of numerical parameters, and to
answer all kinds of questions regarding what the possibilities are when an
interaction occurs. What this kind of an approach cannot do is tell us much about
the details of what happens during an interaction or process.
For example, an energy conservation approach can tell us precisely how much
energy it takes to break apart some complicated molecule in order to rearrange its
4
Chapter 1
Applying Models to Thermal Phenomena
constituents into some desired product. But it can’t tell us how to cause the
rearrangement to happen. It can’t help us with the details of knowing what kinds
of catalysts we should try, for example, to speed-up the process.
What scientists have been able to do, however, is to create a systematic approach
to getting answers without having to know the messy details of how a process
proceeds. This approach is extended in Chapter 4, which addresses the models of
thermodynamics. Thermodynamics can be thought of as the art of getting answers
to the questions you are interested in without knowing “what you ought to know”
to be able to do it. It sometimes almost seems like magic.
One way to think about the way the Energy-Interaction Model is used is that it is
a “before and after” approach. We know some things before an interaction occurs
and we use the model to answer questions and predict numerical values certain
parameters will have after the interaction or process occurs. That is, we can know
the before and we can know the after, but we cannot know much about what goes
on during the process.
One way to get around this limitation is to redefine the interaction or process so
that the before and the after get closer together. Thermodynamics has all kinds of
other tricks to get by the limitations of “not knowing the details.”
But if this kind of approach has limitations as we have been describing, why don’t
we just develop theories and models that give us the details we want? There are
several kinds of reasons. First, detailed models work only for a small range of
phenomena, so you have to develop lots of different models, or at least variations
of models, for each new question. Second, models that address the fine details get
harder and harder to understand and use. High-speed numerical computers are
helping us out a lot here. There are plenty of questions that we need precise and
detailed answers to. For example, will the next big earthquake hit Northern
California? Details matter! Experts can get really detailed information from
models that make use of the tremendous computational power to answer these
questions. But the more complicated the model, the harder it is to understand. In
this course we concentrate on using a few simple models that you can build on
depending on the level of detail the situation requires.
The Energy-Interaction Model can’t do all our work for us, but it can answer
“before and after” kinds of questions for essentially every interaction of matter we
will encounter. This is why it is worth investing some mental energy in getting
really comfortable with using this model with many types of phenomena.
Chapter 1 Applying Models to Thermal Phenomena
5
Common SI Units Related to Energy
SI Unit
Construct
Abbreviation
Expressed in base units
Joule
Watt
Newton
Pascal
energy
power
force
pressure
J
W
N
Pa
kg•m2/s2 = N•m
J/s = kg•m2/s2
kg•m/s2
J/m3 = N•m2
Some common energy units and conversions to SI:
1 kWh = 3.6 MJ
1 erg = 10-7 J
1 cal = 4.184 J
1 food Calorie (big “C” calorie) = 1 kcal = 4.184 kJ
1 ft•lb = 1.36 J
1 eV = 1.602 x 10-19 J
1 BTU = 778 ft•lb = 252 cal = 1.054 kJ
Table of Melting and Boiling Points, Heats of Melting and Vaporization, and Specific Heats of Some
Common Substances (at a constant pressure of one atmosphere)
Substance Formula Melting Boiling Heat of melting Heat of Vap
point, K point, K kJ / kg kJ / mol kJ / kg kJ / mol
Specific heat Cp
J / K mol kJ / kg K
aluminum
bismuth
copper
Gold
ice (-10˚C)
Water
water vap
Al(s)
Bi(s)
Cu(s)
Au(s)
H20(s)
H20(l)
H20(g)
933
544
1356
1336
2600
1693
2839
3081
389.18
52.2
205
62.8
10.5
10.9
13
1.24
10790
722.5
4726
1701
291
151
300.3
33.5
273
373
333.5
6.01
2257
40.7
24.3
25.7
24.5
25.4
36.9
75.2
33.6
0.900
0.123
0.386
0.126
2.05
4.18
1.866
Lead
sodium
sodium
Pb(s)
Na(s)
Na(l)
600
2023
24.7
5.12
858
177.78
370.82
1154.4
114.8
2.64
4306
99
26.4
28.2
32.7
0.128
1.23
1.42
Silver
mercury
mercury
mercury
Ag(s)
Hg(s)
Hg(l)
Hg(g)
1234.93 2436
88.2
9.5
2323
250.6
234
630
11.3
2.3
296
59.1
25.4
28.3
28
20.8
0.233
0.141
0.140
0.103
tungsten
nitrogen
oxygen
Iron
W(s)
N2(g)
O2(g)
Fe(s)
3410
63.14
54.39
1535
5900
77
90.18
3000
184.1
25.7
13.9
33.86
.720
.444
4812
199.1
213.1
884.85
5.58
6.82
24.6
29.04
29.16
25.1
0.134
1.04
0.911
0.449
6
Chapter 1
Applying Models to Thermal Phenomena
Comparison of common temperature scales
Comment
Kelvin
Celsius
Fahrenheit
Absolute zero
0
−273.15
−459.67
Lowest recorded surface temperature on Earth
(Vostok, Antarctica - July 21, 1983)
184
−89
−128.2
Fahrenheit's ice/salt mixture
255.
−17.78
0
Ice melts (at standard pressure)
273
0
32
Average surface temperature on Earth
288
15
59
Average human body temperature ¹
310
36.8
98.2
Highest recorded surface temperature on Earth
(Al 'Aziziyah, Libya - September 13, 1922)
331
58
136.4
Water boils (at standard pressure)
373
100
212
Titanium melts
1941
1668
3034
5800
5526
9980
The surface of the Sun
.
Chapter 1 Applying Models to Thermal Phenomena
7
1-3 Three-Phase Model of Matter
(Model Summary #1)
Construct Definitions
Pure substances
We adopt the standard chemistry definition that a substance is any material with a
definite chemical composition. By “pure,” we simply mean that only one
chemical substance is present in the sample.
Three phases
By three phases we mean the standard phases of solid, liquid, and gases of pure
substances. We try to avoid the alternative phrase, “states of matter,” to avoid
confusion with “thermodynamic state” (see Chapter 4).i
Note that we are choosing which relevant features to include in our model and
which to exclude. The choices will definitely affect the level of detail we can
address in our questions and discuss in our explanations. At this time, we are
deliberately choosing to be more general to keep the model as simple as possible
and at the same time, applicable to as wide a range of phenomena as possible.
Solid, Liquid, Gas
These common phases have the meanings you learned in physical science and
introductory chemistry courses. Solids resist deformation and changes of volume.
Liquids resist to changes of volume, but the containers they fill determine the
shape of liquids. If the container is not full, there will be a surface that does not
touch the container.ii Gases are characterized by expanding to totally fill whatever
space they occupy. Gases and liquids are frequently called fluids, because they
can both flow.
Temperature
Temperature will take on more meaning as we move through the models in
Chapters 1-4. For this chapter, we need only the common meaning typically
taught in introductory physical science courses. We do not yet invoke a particle
model definition of temperature, which will be introduced in Chapter 3. At the
simplest level, temperature is a measure of the hotness of something. Temperature
is measured with thermometers of various types. Different temperature scales are
related by universal agreement on the values on the different temperature scales of
certain easily reproducible temperatures based on simple physical processes. The
temperature scales commonly used in the United States are the thermodynamic or
Kelvin scale, the Celsius scale and the Fahrenheit scale. By convention,
temperatures on the Celsius and Fahrenheit scale are written with the “degree”
symbol followed by an uppercase “C” or “F.” However, with the Kelvin scale, in
which the kelvin (note the lowercase “k”) is the SI unit of temperature, a
temperature value is written simply as a numeral followed by an uppercase “K,”
as is standard within the SI system.
If you are not already thoroughly familiar with the SI system of units, you need to
review this thoroughly. A good reference is the article from NIST located at
8
Chapter 1
Applying Models to Thermal Phenomena
http://physics.nist.gov/cuu/Units/introduction.html (NIST is the National Institute of
Standards and Technology. Founded in 1901, NIST is a non-regulatory federal agency within the
U.S. Commerce Department's Technology Administration.)
The Kelvin temperature scale (sometimes called the thermodynamic scale) has the
value zero at the “absolute zero” of temperature. It should always be used when
the value of the zero of temperature matters. It is also very helpful to remember
that the size of the kelvin is the same as the size of the Celsius degree.
Energy, Added as Heat or Work
At this point in our model development, energy is “something,” but not a material
thing, that can be transferred to or removed from substances as heat or work or
transferred from one substance to another as heat if one substance is at a higher
temperature (hotter) than the other. The transfer of energy as work involves one
object pushing or pulling another object through a distance in the direction of the
push or pull. (Note: we will frequently use the word object in a general sense, so
that the “object” could be a liquid, or sometimes even a gas.)
Phase change temperature and Change of Phase
Phase change temperature is the unique temperature at which a pure substance
changes from one phase to another phase. These temperature values depend on
the pressure, but if a value for the pressure is not specified, it is assumed to be one
atmosphere. Most (but not all) substances are solids at a standard pressure of one
atmosphere and at sufficiently low temperature. As energy is added as heat, the
substance changes from a solid to a liquid at a specific fixed temperature that is
unique to that particular substance, and then as heat is continually added, the
substance eventually changes from a liquid to a gas at a higher fixed temperature.
These fixed temperatures are referred to as the phase change temperatures. A few
substances at a standard atmosphere do not pass through a liquid phase, but
instead change directly from a solid to a gas, referred to as sublimation. Carbon
dioxide is a common example of this phenomenon.
In the simplest form of the Three-Phase Model of Matter, the phase changes occur
at the same temperature “on the way down” as “on the way up.” That is, the
temperature of the change from liquid to solid as energy is removed is the same as
the temperature of the phase change from solid to liquid as energy is added. Due
to this symmetry, the liquid-solid or solid-liquid phase change temperature can be
referred to as either the freezing or melting temperature. Likewise at the boiling
point, the phase change temperature can be referred to as the boiling or
condensation temperature. (In an activity, you will see that most pure substances
don’t behave exactly the same way “on the way up” as “on the way down.” This
seemingly strange behavior is actually rather common. In the classroom activities,
you will see how to extend and modify our simple Three-Phase Model of Matter
to account for this more detailed behavior.
Heats of melting, vaporization, and sublimation
Chemists typically refer to the amount of energy that must be added to convert a
standard amount of a pure substance from one phase to the next higher as the heat
of fusion and the heat of vaporization. Physics textbooks often refer to these
amounts of energy as “latent heats.” The table on page 5 provides values of these
heats for some common substances. Several useful references for this kind of data
Chapter 1 Applying Models to Thermal Phenomena
9
can be found at the NIST website: http://webbook.nist.gov/chemistry/ and through
your campus library at the on-line Handbook of Chemistry and Physics,
http://www.hbcpnetbase.com/ in Section 6: Fluid Properties: Enthalpy of
Vaporization and Enthalpy of Fusion. Both boiling and melting temperatures as
well as heats of vaporization and heats of fusion are given. Heats of fusion and
vaporization are referred to as Enthalpies because the measurements are made at
constant pressure. At constant pressure, as we will see in Chapter 4, changes in
the state function enthalpy, abbreviated “∆H,” are equal to transfers of energy as
heat. These energies are frequently tabulated as the amount of energy per mass or
as energy per mole of substance required to cause that amount of substance to
change phase. That is, they are reported as intensive quantities. (The distinction
between intensive and extensive properties is discussed more fully below in the
discussion of heat capacities.) If these heats are given as energy per mass, they
will have units of J/kg; if given as energy per mole, the units will be J/mol.
Thermal equilibrium
Thermal equilibrium means that the entire substance is at a single temperature.
During a process, the temperature of one part of a substance or object or system
can be at a different temperature than another part. When the temperature is not
the same throughout the substance or object, energy will be transferred internally
as heat in the direction to cause the system to come to the same temperature. An
isolated system will eventually reach thermal equilibrium to as close as we wish
to define it.
Mixed phase
If a substance is in thermal equilibrium and is at a phase change temperature, part
of the substance can be in one phase, perhaps a liquid, and another part can be in
an adjacent phase, perhaps a solid. A totally isolated substance can continue to
exist in a mixed phase forever if it is at a phase change temperature.
Heat capacity
At temperatures between the phase change temperatures, when energy is added to
a substance, the substance increases in temperature. The heat capacity of a
substance is a measure of the amount of energy that must be added to increase the
temperature of the substance a certain amount. The larger the heat capacity, the
larger the amount of energy that must be added to achieve the same increase in
temperature.
Heat capacity of a specific sample of matter is determined experimentally as the
ratio of the amount of energy added as heat to the sample to the change in
temperature of the sample. You probably recall from chemistry that there is often
a subscript “p” or “v” attached to experimentally determined values of heat
capacity, as in Cp and Cv. The subscript “p” means the measurement was carried
out at constant pressure and the “v” means it was carried out at constant volume.
(There is very little difference between Cp and Cv in the liquid phase or in the
solid phase, but there is a large difference in the gas phase. We will discuss this in
much more detail later in Chapter 4, and develop our model of matter to the point
that it can provide a thorough understanding of the origin of the similarities and
differences of observed heat capacities.)
10
Chapter 1
Applying Models to Thermal Phenomena
If energy is added to a substance or object as heat and if there are no phase
changes, then the energy transferred to the physical system as heat goes into
changing the temperature, and the heat capacity is simply the amount of energy
transferred, i.e., the heat, divided by the change in temperature:
C=
€
Q
dQ
or C =
ΔT
dT
Heat capacity is an extensive property. That is, it depends on the amount of
substance: if you double the amount of substance, then the value of the heat
capacity€doubles.
Specific heat capacity, or simply specific heat as it is commonly called, is an
intensive property. An intensive property of a substance does not depend on the
amount of substance. The two most widely used intensive expressions for heat
capacity are specific heat per unit mass and specific heat per mole, or molar
specific heat.
The SI units of heat capacity and specific heat:
heat capacity
J/K
specific heat per unit mass
J/kg K
molar specific heat
J/mol K
Meaning of the model Relationships
(Numbers below correspond to the numbered relationships on the Three-Phase Model of
Matter handout.)
1) Pure substances exist in one of three phases, depending on the temperature:
solid, liquid, and gas. Non-pure substances, e.g., solutions and composites,
require more complex models for analysis.
The statement above is the simplest statement that can be made regarding
ordinary matter at one atmosphere of pressure. It captures the behavior of the
vast majority of pure substances. Mixtures or composites, which are
composed of more than one kind of pure substance will often behave
differently as the temperature increases, because one component can begin to
change phase or even decompose chemically, before the other component
reaches its first phase change temperature.
The following information in this paragraph is interesting to know, but is not
important in terms of the understanding the model. The common exception to
the statement that all substances exist in all three phases is CO2, which does
not exist as a liquid at a pressure of one atmosphere, but does exist as a liquid
at higher pressures. Solid carbon dioxide passes directly from the solid phase
to the gas phase at its sublimation temperature when it is at one atmosphere of
pressure. Another exception is the common isotope of the element helium,
which does not exist as a solid, even if it is cooled to as close to the absolute
zero of temperature as we wish to define zero. It remains a liquid, albeit, a
very strange liquid (called a superfluid), all the way down to zero at one
atmosphere of pressure.
2) In order to change either the temperature or phase of a substance, energy must
Chapter 1 Applying Models to Thermal Phenomena
11
be added or removed. Often this energy is transferred to or from the substance
as heat, Q, but can also be transferred as work, W.
The first relationship discussed above, could be simply interpreted as a very
common data pattern that is observed for pure substances. The model part
really comes into its own with this 2nd and the following 3rd and 4th
relationships. This second relationship “establishes a reason” for why
substances don’t just willy-nilly change their temperature or change their
phase. Neither can happen unless energy is added or removed.
3) Changes of phase (solid⇔liquid and liquid⇔gas or at some values of
pressure, solid⇔gas (sublimation)) occur at specific temperatures, the phase
change temperatures (TMP, TBP, and TSP), which have particular values for
each pure substance. The values of these temperatures are the same “going
through” the phase change in “both directions.” Phase change temperatures
are, however, dependent on the pressure.
The amount of energy added or removed at a phase change (usually written as
∆H to signify constant pressure) is unique to each substance and has been
measured for most substances.
If the substance is in thermal equilibrium (i.e., if the substance is all at the
same temperature) at the phase change temperature, both phases will remain
at the phase change temperature as the phase change occurs. Mixed phases
can exist in thermal equilibrium only when the temperature has the value of
the phase-change temperature.
There is a lot of meaning packed into the three statements of this third
relationship. There is something unique about each kind of substance that
determines how much energy is required to cause the substance to change
phase. Also, in this simple model, the amount of change in energy is the same
(except for the algebraic sign) whether you go through the phase transition by
adding energy or by removing energy. Finally, there is a lot of meaning
packed into the last part of the statement regarding when and under exactly
what circumstances two phases can co-exist without one turning into the
other. Think about your cold soft drink about half filled with ice and half
filled with cola. If there is sufficient ice when the warmer cola is put in, and if
the drink is in a well-insulated container, some ice does melt, but then the cola
and ice seem to peacefully co-exist for quite some time. According to this
relationship, this can only happen if what condition holds? Only if both phases
are at the phase-change temperature. Additionally, this last part of the
relationship tells us what must happen if energy is added sufficiently slowly
so that the system is nearly in thermal equilibrium. What happens to the
temperature when energy is slowly added to the mixed phase? The
temperature remains at the phase change temperature until all of the substance
has changed phase. When you think about it, this is kind of weird. Normally,
when we heat something, the temperature rises. But in this special case of
mixed phases, the temperature does not rise. There is much predictive power
in this last relationship.
4) Changes of temperature of a substance occur when energy is added or
removed whenever the substance is not at a phase-change temperature.
12
Chapter 1
Applying Models to Thermal Phenomena
This last relationship tells us what we are already familiar with. When you add
energy, the temperature of the substance goes up. When the energy added is in
the form of heat, the change in temperature, ∆T, is related to the amount of
energy added by a property of the substance called heat capacity, C, that has a
particular value for each substance. Heat capacities have been measured for
most substances.
Graphical Relationship of the Three-Phase Model
The graphical representation reproduced below as well as on the blue summary
sheet at the end of the resource packet, nicely summarizes all of the relationships
of the model. It is very easy to be lulled into thinking this all makes sense, without
actually digging into the meaning. You need to ask questions like, what exactly is
the meaning of the horizontal portions of the graph. Can you explain in you own
words “what is going on” physically in your ice cola drink during a horizontal
portion of the graph? Which horizontal portion would correspond to your cold
drink? What about the three slanted portions of the graph? What exactly is
happening there? Where did the ice start out when you first put it into your cup?
When was your drink system in thermal equilibrium, or was it ever in thermal
equilibrium?
Can you picture what is happening in terms of this representation when you boil
water to make tea? How is this different from putting ice trays into the freezer
compartment of your refrigerator? How do the algebraic relationships relate to the
graph? Which parts? What is the relationship? These are the kinds of questions
you need to be asking yourself and getting confident about. You want to practice
using this representation enough so that it really does become a useful tool to
make sense of thermal phenomena and to be comfortable using it to construct
explanations for particular phenomena.
Energy Added or Removed (at constant pressure)
Chapter 1 Applying Models to Thermal Phenomena
1-4
13
Energy-Interaction Model
(Summary on Energy-Interaction Model
handout)
Construct Definitions
Energy and energy systems
The scientific meaning of energy is rather tricky to convey in a sentence or two.
There is a good reason for this: energy is an abstract concept that took scientists a
long time to figure out. Although the concept of energy is truly universal in the
sense that energy changes are associated with nearly all phenomena and
processes, energy is not related to a single property of matter. For example, we all
have an intuitive sense of “hotness” and we associate the concept of temperature
with this property of matter. We associate the concept of force with the intuitive
notion of push and pull. Energy, on the other hand, is associated with many
properties or conditions of matter including temperature, force, motion, atomic
level, mass, charge, and so on. It is the fact that energy is so universal that makes
it so difficult to define it precisely.
Another reason energy is difficult to pin down, is that the value of energy itself is
seldom of importance; rather, it is the changes in the values of energy that seem to
matter. In fact, we will see that change in energy is directly related to “how
much” interaction occurred.
The following are useful statements about energy. Taken together they constitute
a working definition of the construct (or concept of) energy. This concept will be
developed further throughout the course.
Statements that help define energy
1. Energy is an abstract concept that characterizes the interactions of matter.
2. The change in energy of a physical system is a quantifiable measure of the
degree of its interactions with other physical systems.
3. The importance of always being conscious of the word “change” as in the
phrase “change in energy” and of the way this idea is represented
mathematically cannot be overstressed. We signify “change in energy”
mathematically by writing “∆E.” The uppercase Greek symbol “∆” often is
used in science to indicate a change in some quantity. Does “∆E” look like
“E” to you? No, of course not. Yet students often mix this up on exam
questions because they don’t seem to “see” the difference between the
following two expressions:
14
Chapter 1
Applying Models to Thermal Phenomena
RIGHT
∆E1 + ∆E2 + ∆E3 + … = (net energy transferred into or out of
the physical system)
and
WRONG
E1 + E2 + E3 + … = (net energy transferred into or out of
the physical system)
Only one of these statements makes any sense–the first one! But if we wrote
the second one as:
RIGHT
E1 + E2 + E3 + … = Etotal
it would make perfect sense. Yet the statement
WRONG
∆E1 +∆E2 + ∆E3 + … = Etotal
would make absolutely no sense. The point is, whether we are talking about a
change in energy or the value of the energy matters a lot. You must always be
conscious of which you are thinking about and why it is the one you want to
think about!
4. Historically, many “forms” or “kinds” of energy have been identified.
Sometimes, the form of energy labels the interaction that resulted in a change
of energy, e.g., chemical, mechanical, or nuclear. It is often misleading to
think of there being different forms, kinds, or types of energy, even though we
have these “names of energy” in our vocabulary. Energy is energy, regardless
of how it manifests itself. Thus, instead of speaking of forms of energy or
kinds of energy, we speak of energy-systems. There is usually a one-to-one
correspondence between a historically identified type or form of energy and
what we will identify as an energy-system.
5. Energy is not a real thing that resides in systems, even though we often talk
about it as if it were a “real thing.” Be careful here. Remember there is
nothing at all physical about this “thing” we call energy, even when our
language sometimes suggests that there is.
6. Interactions are modeled by treating energy as something that resides in (can
be identified with) particular energy-systems. When interactions occur,
energy-systems change. Frequently, it is useful to envision energy as being
transferred into and out of particular energy-systems and from one energysystem to another as interactions occur. However, it is the changes in energysystems (and not the particular transfers among energy-systems) that are the
basis of the model.
Chapter 1 Applying Models to Thermal Phenomena
15
7. When an interaction occurs, there is a change in one or more energy systems.
For each energy system that changes, there is an observable (in the sense of
being detectable) and quantifiable change in some part of the physical system.
The magnitude of the change of each energy system is determined by the
change in its associated observable parameter. We will refer to this observable
parameter as the indicator associated with a particular energy system. The
questions of how to “divide up” the energy of some physical system and
which energy-systems to include in the model get to the heart of the modeling
process. The particular phenomenon under consideration will have salient
features that must also appear in the particular model. This is what is
illustrated in the center diamonds in Figures 1 & 2 on page M-9 and M-10 of
Appendix M1.
Systems
We have already introduced the word “energy system.” As is frequently the case
in both everyday and scientific language, the particular meaning of a word must
be obtained from the context in which it is used. We will also, for example, talk
about physical systems, particle systems, as well as energy systems, and doubtless
a few other kinds of system, and will, like other authors, not always include the
modifier, but simply refer to “the system.” Make sure you understand how the
word “system” is being used in particular discussions. In general, when we say
physical system it means exactly what you would think it would mean: some stuff
(objects, substances, apparatus, or just a beaker of water) that we wish to focus
on. The two-word phrase that we just previously introduced is the trickier one.
We don’t know of a better word to use. Our language encourages us to call the
“thing” we refer to as an “energy system” more than just “an energy.” But it is
misleading to call it by any of the historical names that arose when scientists did
not know that they were talking about the same thing. So in this course, energy
system has a special meaning that will become much more clear once you start
using it regularly in your classroom activities.
Closed and Open Physical Systems
There are two useful ways to express the principle of conservation of energy, one
corresponding to closed physical systems and the other to open physical systems.
Closed physical system
In a closed physical system, there is no transfer of energy into (or out of) that
physical system from some other physical system. (This condition would
generally preclude mass transfers as well, since mass transfers would also result
in energy transfers.) Another way to state the condition of being closed is that all
interactions occur within the one identified physical system. There are no
interactions with other physical systems.
Open physical system
In an open physical system, there can be a net transfer of energy into (or out of)
that physical system from some other physical system. Another way to state the
condition of being open is that interactions can occur between matter in the
identified physical system and matter in other physical systems (which might
simply be the environment.
16
Chapter 1
Applying Models to Thermal Phenomena
Energy Transfers: Heat, Q & Work, W
Even though energy is not a physical thing that can be transferred, it is
conventional and sometimes useful to model the process as if transfers of energy
actually take place among various physical systems. When energy is transferred
into a physical system from another physical system, it is customary to name the
energy transferred as either heat, or work. The name heat, Q, is given to energy
transfers that occur as result of a difference in temperatures. Heat “flows” from
the physical system at the higher temperature to the physical system at the lower
temperature. (We will use the word “heat” only in this sense. Note, however, that
historically, the word “heat” was also used to mean what is now more commonly
called thermal energy.) The notation ∆Q will never be used, since this implies a
change in a state quantity, which Q is not. However, the notation dQ will be used
to mean an infinitesimally small amount of energy transferred as heat.
When you are reading science journal articles or other textbooks, especially older
ones, be sure you understand how the authors are using the word “heat.” This is
important, because the concept of energy transfer as heat is very different from
the concept of thermal energy. We (and most modern authors) now restrict the use
of the word “heat” to its meaning as a transfer of energy between physical
systems as a result of temperature differences.
(The term work, W, is used to describe the energy transferred between physical
systems (objects), which exert forces on one another and move relative to one
another. We will examine this type of energy transfer in Chapter 2.)
One of the great advantages of an energy model is that we don’t have to be
concerned with the details of how energy transfers occur. We don’t need to have a
microscopic explanation, for example, of how friction causes increases in thermal
energy-systems and decreases in other non-thermal energy-systems. On a
microscopic scale, all kinds of energy transfers are taking place between
individual atoms and molecules. The energy transfers we are talking about that
occur between different physical systems are always the net transfers that occur as
a result of an interaction between those physical systems.
Processes and Interactions
One of the frequent ways beginning students go astray is to not be perfectly clear
in their own mind how the beginning and end of a process is defined or
determined. Sometimes, we think of an interaction instead of a process. The same
problem arises. What determines the beginning of the interaction and what
determines the end of the interaction?
Often there is a point in time that can be identified with the beginning and the end
of the interaction. This is not usually an actual clock time, such as 10 minutes
after one, but rather, something happens at a particular time. The something that
happens can be easily pictured in our mind and remembered. It is when the “ball
was “let go” or “just before the ball hit the ground.” Or perhaps it was when the
coffee pot was turned on and when the coffee pot was turned off. Something
physically happens that we make a conscious decision to identify with the
beginning of the time interval and something else happens that we use to identify
with the end of the time interval that corresponds to the interaction or process we
are interested in. It is crucial to always clearly identify these starting and ending
Chapter 1 Applying Models to Thermal Phenomena
17
“events,” which precisely determine the interval over which the process or
interaction occurs. We often use phrases like, “Determine the interval.” to
indicate precisely defining the beginning and end of a process.
State of a Physical System
Related to the discussion regarding the beginning and ending of a process or
interaction is the idea also mentioned previously that we are not concerned about
the details of the interaction in an energy conservation approach. In fact, all we
care about is how the state of the system changed from the beginning to the end of
the process or interaction. By state of the physical system we mean the values of
certain parameters that changed. For the Energy-Interaction Model we care only
about the indicators that tell us how much the energy changed in each energy
system. This notion of state of the physical system will become more obvious as
we work through more and varied phenomena using the Energy Interaction
Model.
Energy Systems Related to Thermal and Chemical Processes
When dealing with thermal and chemical processes from a macroscopic
perspective, it is convenient and useful to define energy systems that correspond
to the empirically determined heats, i.e., the ∆H’s, that correspond to the process
or interaction. These include heats associated with physical phase changes and
with the formation of various molecular species. The indicator for an energy
system associated with these processes would be the amount of substance that
changed phase or for a chemical reaction, the amount of substance that was
formed or that “disappeared.”
The general form of the expression for the amount of energy change in these
processes will be
∆E∆H = ±|∆m × (heat of the particular process, ∆H)|
The indicator for the energy change is the amount of substance that changed, ∆m.
If ∆H, which is typically given as an intensive quantity, has units of J/kg, then ∆m
will have units of kg. If ∆H is given as a molar quantity, with units of J/mol, then
∆m will have units of moles.
When there are no phase changes or chemical reactions occurring and heat is
added to a substance, its temperature changes with the amount of change
dependent on its heat capacity. The energy change associated with this process is
exactly equal to the heat, Q, added, since we have stipulated that there are no
other energy systems that are changing. From our discussion of heat capacity in
the Three-Phase Model of Matter we had
C=
Q
ΔT
Equating ∆E with Q and rearranging, we have an expression for the change in the
energy system associated with this process:
€
∆Eno ∆H = C ∆T.
Temperature is the indicator for this energy system.
18
Chapter 1
Applying Models to Thermal Phenomena
These two energy systems we have just defined are very useful for two reasons.
(1) They correspond to changes in indicators we can directly observe and (2)
depend on parameters, (∆H and C) that are tabulated for most substances.
Additionally, as we have defined them, during a physical or chemical reaction,
only one of them will be changing at a given time.
Both phase changes and chemical reactions involve the making and breaking of
atomic and/or molecular bonds. When heat is added to a substance and its
temperature changes, its thermal energy changes.
The two energy systems we have defined above are closely related to bond energy
and thermal energy we will develop from a particle perspective in Chapter 3, but
are not exactly the same. However, rather than use a different name for the energy
systems involving the empirically determined parameters, ∆H and C, and
macroscopic indicators, ∆m and ∆T, we will simply refer to them as the bond
energy system and thermal energy system, remembering that we will refine our
understanding of these processes in Chapter 3 and see how the macroscopic
energy systems we define here relate to the microscopically defined bond and
thermal energies using particle models.
So, to summarize, our Chapter 1 & 2 understanding of the constructs bond energy
system and thermal energy system is:
•
At a physical phase change, only the bond-energy system changes and the
change is given by
∆Ebond = ±|∆m × (heat of the particular phase change, ∆H)| ,
∆m is the indicator
•
Between phase changes, only the thermal-energy system changes and the
change is given by
∆Ethermal = C ∆T, ∆T is the indicator
•
In chemical reactions, there will typically be several bond energy changes,
corresponding to each of the molecular species present in either the
reactants or products. The energy change for each is given by
∆Ebond = ±|∆m × (heat of formation for the particular species, ∆H)|
The temperature is assumed to have the same value after the reaction as it
did before the reaction.
These energy systems, defined above, are the appropriate energy systems to use in
the Energy-Interaction Model whenever we are using empirically determined
values for the various ∆H’s and C’s. In the language of Appendix A1, the salient
features of the phenomenon are precisely the ∆H’s and C’s characterizing the
particular substance(s) and the indicators ∆m and ∆T. These salient features
appear in both the phenomenon and in the particular model we construct. It is this
particular model that we then use to create explanations and to make numerical
predictions.
Chapter 1 Applying Models to Thermal Phenomena
19
The algebraic signs of thermal and bond energies
It is very important to make sense of the algebraic sign of the change in the
energy system based on what physically is happening. This is actually very simple
to do, once you get the hang of it. However, it is easy to make a simple algebraic
slip-up when actually calculating numerical values. You should always check to
see if the final algebraic sign makes sense.
•
Any thermal energy-system for which the temperature increases during the
process will always have a positive change in energy. Likewise, any
thermal energy system for which the temperature decreases will always
have a negative change in energy. This is consistent with the simple notion
that thermal energy increases with increases in temperature, because at
higher temperatures there is “more vigorous” motion of the particles.
•
Any bond energy-system for which bonds are broken during the process or
interaction will always have a positive change in energy. Likewise, any
bond energy-system for which bonds are formed during the process or
interaction will always have a negative change in energy. This is
consistent with the common experience of having to add energy (and thus
increase the bond energy) to vaporize liquid water that is at 100 ˚C. The
bonds that had existed in the liquid phase disappear (are broken) in the
process of the liquid changing to a vapor. You will probably need to
struggle mentally with this last point: broken bonds have more energy than
intact bonds. Work on this until it “seems obvious” to you.
20
Chapter 1
Applying Models to Thermal Phenomena
Commonly Used Energy Systems
Energy system Indicator
Algebraic Expression
Thermal energy
temperature, T
∆Eth = C ∆T (assuming C is constant; ∆Eth will change at a
phase change if C changes, but we will ignore this
until we get to the Model of Thermodynamics)
Bond energy
mass of a
particular phase
∆Ebond = ±|∆m × (heat of the particular phase change, ∆H)|
(in phase changes)
Bond energy
(in chemical reactions)
(∆m in units of kilograms or moles)
amount of a
∆Ebond = ±|∆m × (heat of formation of the particular
particular molecular
molecular species, ∆H)|
species
(∆m in units of moles)
Mechanical Energy Systems
Gravitational PE
height
Translational KE
speed
Rotational KE
rotational speed
Elastic PE
displacement
from equilibrium
Spring-mass PE
displacement
from equilibrium
with mass attached
∆PEg = mgE ∆y
∆KE = 1/2 m ∆(v2)
(positive direction of y coordinate is up)
∆PEelastic = 1/2 k ∆(x2)
∆PEspring-mass = 1/2 k ∆(x2)
(x is measured from equilibrium
position)
(works for both hanging and
horizontal spring-mass systems.
x is measured from equilibrium
with mass attached )
Note: The mechanical energy systems listed here will be used in Chapter 2. They are listed here only for reference.
Useful Groupings of Energy Systems
Mechanical Energy
Sum of kinetic and potential energies associated with the physical “objects” as a
whole, not with the internal energies of the objects.
Internal Energy, U
Sum of kinetic and potential energies associated with the individual molecules/atoms
comprising a substance, as well as the energies associated with their atomic and
nuclear energies. In Chapter 1 we will mostly deal only with changes in the energies
associated with thermal and bond energies (chemical energies).
Chapter 1 Applying Models to Thermal Phenomena
21
Meaning of the Model Relationships
(Numbers below correspond to the numbered relationships Energy-Interaction Handout.)
1)
The heart of the Energy-Interaction Model is energy conservation, one
of a small number of powerful conservation principles used throughout
science. One way of expressing a conservation principle is that for an isolated
physical system there are certain physical properties that do not change during
an interaction or process. A process or interaction is determined by explicitly
indicating the start and end points of the process or interaction; i.e.,
identifying the beginning and end of the interval that defines the process or
interaction. The power of a conservation principle is that values of state
variables (variables like P, V, T, and n for a gas) need to be known at only
these two particular times (the ends of the interval), and not at intermediate
times during the interval during which the process or interaction takes place.
In particular, we need only know the values of the indicators of the various
energy systems at the ends of the interval. It is these values that allow us to
calculate actual energy changes.
2) The total energy of every physical system can be expressed as a sum of the
energies of separately identifiable energy systems. This division of the energy
into energy systems can be carried out in multiple ways. The energy
associated with a particular energy system can be expressed in terms of an
observable and measurable property of the physical system. We call these
properties indicators. The change in energy of each energy system can be
determined from the observed change in the indicator that occurs from the
beginning to the end of the time interval during which the interaction takes
place.
3)
Conservation of energy in a closed physical system (isolated with
respect to energy transfers from other physical systems):
The total energy of that physical system must remain constant during
the interaction or process. When internal interactions occur this conservation
principle can be expressed in terms of changes of energy systems: the changes
of the energies of all energy systems associated with that physical system must
sum to zero.
The sum of the increases in energy of those energy-systems that experience an
increase exactly equals the sum of decreases of the energy-systems that
experience a decrease. When we express this mathematically using the “∆”
symbol, a decrease in energy will result in a negative value for the change. So
another way of stating conservation of energy is to say that the sum of all the
energy changes is zero.
∆E1 + ∆E2 + ∆E3 + … = 0
4)
Conservation of energy in an open physical system:
During an interaction or process during which energy is added or
removed from the physical system as heat or work, the changes in energy of
all energy systems associated with that physical system must sum to the net
energy added (or removed) as heat and/or work. Equivalently, the change in
the total energy of that physical system must equal the net energy added (or
removed)
∆E1 + ∆E2 + ∆E3 + … = (net energy transferred into or out of
the physical system)
22
Chapter 1
Applying Models to Thermal Phenomena
Energy System Diagrams
Energy-system diagrams illuminate the types of energy transformations that occur
when two or more physical systems interact, or when a constraint is removed and
changes occur in two or more energy systems within a single physical system.
The diagram helps make clear the physical systems involved, the particular
energy-systems involved, and the changes in those energy-systems resulting from
the interaction. The initial and final states of the systems should be clearly
indicated on the diagram. These diagrams are “before-to-after” diagrams. That is,
they indicate the state of the systems before the interaction occurs and the state of
the systems after the interaction has occurred. (Note that there is one diagram that
includes both the initial and final states. The focus is the change that occurs
because of the interaction.) We use energy-system diagrams because they are
useful. They help us to systematically apply the energy conservation approach to
a particular physical situation using the Energy-Interaction Model.
Drawing Energy-System Diagrams When Modeling the Interaction as a
CLOSED System
Listed here are the conventions we adopt in this course.
1) The beginning and ending of the interaction is specified by explicitly writing
down a condition of the physical system that corresponds to the beginning and
end of the time interval over which the interaction occurs. These times are
referred to as the initial and final times.
2) The specific energy-systems that changed during the specified time interval
are indicated by circles and labeled sufficiently to identify the energy-system.
3) If transfers of energy to the environment are significant, due to friction, for
example, include the thermal system of the environment on the energy-system
diagram. That is, enlarge the boundary of the closed system to include the
environment.
4) The change in energy of each energy-system, whether an increase or decrease,
is indicated, when known, with an “up” or “down” arrow.
5) Changes in the observable parameter (indicator) associated with each energysystem that occur as a result of the interaction should be shown. If the quantitative
change in the value is known, it should be given. If not, an “up” or “down” arrow
can be used following the symbol of the indicator to indicate an expected increase
or decrease.
Chapter 1 Applying Models to Thermal Phenomena
23
Drawing Energy-System Diagrams When Modeling the Interaction as a
OPEN System
Listed here are the conventions we adopt in this course.
The important difference between open and closed systems is that energy from
outside the open physical system can be transferred into or out of the physical
system as heat, Q, or work, W. (By definition, these transfers do not occur for a
closed system.) The only difference, then, in the energy-system diagrams for the
two types, is that the diagram for an open system needs to explicitly show the
transfer of Q and/or W. This is done by drawing a dashed oval around all of the
energy-systems (to indicate the open physical system boundary) and drawing
arrows terminating on the boundary to show a Q or a W transfer.
Generic Example of an Energy System Diagram involving two physical
systems, three energy systems, and with Heat Input
Identification of beginning and end of
interval:
Physical system:
Physical thing 1
Physical thing 2
beginning
end
Physical thing 1
Ea ↓
Physical thing 1
Physical thing 2
Eb ↑
Ea ↓
Indicatora ↓
Indicatorb ↑
Indicatora ↓
Indicatora, initial =
Indicatora, final =
Indicatorb, initial =
Indicatorb, final =
Indicatora, initial =
Indicatora, final =
Comments:
heat
ΔE1,a + ΔE1,b + ΔE2,a = Q
1) What is shown in the diagram above is the minimum that must always be written down.
Most of the hard thinking will have been done to get to this point. Often, many
explanations of physical phenomena can be constructed using this diagram without going
further and substituting in explicit expressions for the individual change in energy terms
and numerical values for various parameters. Even if you are required to continue the
process through to a numerical result, you must do the mental work of constructing the
energy-system diagram to this point prior to doing any numerical calculations.
2) In an open-system diagram, the arrow showing energy transfer into the system is drawn
in the direction of energy flow and labeled with the words “heat” or “work,” and not “Q”
or “W.” This is to preserve the standard convention of calling Q and W positive when
energy is entering the physical system. Therefore, equations expressing conservation of
energy are always written as shown in the diagram, with Q and W always written on the
right side of the equation (without a negative sign, even if energy is leaving the physical
system). When numerical values are substituted in for Q or W, those values will be
written with a negative sign, if energy is leaving the physical system.
24
Chapter 1
Applying Models to Thermal Phenomena
General Process of Constructing an Energy-System Diagram
Listed here are some general questions you need to ask yourself as you use the
Energy-Interaction Model. The order suggested is logical, but it is often necessary
to cycle back to previous questions. The energy-system diagram is a tool to help
you use the Energy-Interaction Model. The energy-system diagram helps you
keep track of the many important details you need as you construct the particular
model corresponding to the particular physical situation you are interested in.
1) What happened? State the essence of the physical phenomenon of interest in
your own words. You don’t need to write this down, but you should have an
“internal dialogue” with yourself.
2) What is the boundary of the physical system you are modeling? Answer this
question by listing the physical things you intend to include in the physical
system. (Examples of “physical things” are: air, H2O, hand, heatpack, “all of the
chemicals”.) Energy systems are always energy systems of particular physical
things, so the energy systems you identify (in step (4)) will depend on the
physical things you decide to include within the boundaries of your overall
physical system. In some cases, it might be useful to identify two or more separate
physical systems, each with its own energy-system diagram.
3) What is the extent of the process or interaction? This means identifying the
beginning and end of the time interval corresponding to the process/interaction
that you defined and explicitly writing this on the diagram.
4) What energy systems do you include in your diagram? Answer: Which
indicators are changing? Each indicator that changes corresponds to an energy
system that changes. Put these energy systems into your diagram as labeled
circles (for example, “H2O Ethermal”). Include the indicator for each energy system
inside the labeled circle with an up or down arrow showing whether the indicator
increased or decreased during the process, if known. Show increases and
decreases in each energy system as up or down arrows next to the abbreviation for
the energy system. What you are doing here is picking out salient features from
the particular instance of a physical phenomenon that relate to energy to include
in the particular model you are constructing in order to answer questions, develop
explanations, make numerical predictions, etc. related to the particular
phenomenon you are interested in. Refer back to Appendix A1 for a general
discussion of this process.
5) What are the values of the indicators at the times corresponding to the ends of
the time interval you chose in step (3)? Record the initial and final values of the
indicators next to their respective energy systems. Remember that all of the initial
and final values of indicators should correspond to the same initial and final
times. (Note: It is not always necessary to identify specific initial and final values
for all indicators. Sometimes, depending on the question, you only care about the
change in the indicator (e.g., ΔT). At other times, you may only know that the
final value of the indicator is greater than (or less than, or equal to) the initial
value. The point is not to memorize a series of steps, but to be as specific as
possible about what you know. The diagram is not an end in itself, but a tool to
lead you through your analysis. The diagram helps you connect the particular
physical phenomenon to the particular model you are constructing.)
Chapter 1 Applying Models to Thermal Phenomena
25
6) Is the physical system in your particular model open or closed? If you are
modeling the phenomenon as an open physical system, draw a dashed oval
enclosing all of the energy systems, and use an arrow that stops or starts on the
oval to show heat or work entering or leaving the physical system. You may find
it necessary to go back to step (2) and modify the boundary of the physical
system.
7) Write an equation expressing energy conservation for your particular energysystem diagram, in terms of the ΔE’s. Each term in your conservation of energy
equation must correspond to an energy system in your diagram.
Units for Energy
The historical development of the energy concept separately as heat and
mechanical energy, as well as the widespread use of several different systems of
units, has created a multitude of energy units. But, energy is energy and all forms,
types, whatever, can and should be expressed in the same basic energy unit.
Fortunately, this is now becoming common. The SI unit of energy is the joule, J,
(rhymes with cool). All other energy units are related to the joule through an
appropriate conversion factor.
A concept closely related to energy is power–the time rate of energy change or
energy transfer. The SI unit of power is a joule per second and is given the name
watt, W.
Fortunately, essentially everyone within the scientific and technical community
has now embraced the International System (SI) system of units. We will
generally use SI units in this course. However, in those instances where non-SI
units are commonly used, we will use both, and expect you to be able to convert
back and forth. An advantage of working exclusively in SI is that you don’t have
to be concerned about unit conversions (and keeping track of them for that
purpose).
SI base units
The SI base units for mass, length, and time are kilogram (kg), meter (m), and
second (s). Other SI units can be expressed in base units when desired. For
example, a joule is a kg m2/s2.
SI unit of temperature
The kelvin (K), the SI unit for temperature, is another independent base unit. The
zero of the kelvin scale is at thermodynamic zero, the so-called “absolute zero” of
temperature. (Note that “kelvin” is used without the word “degree” attached.)
Although the zero of the Celsius, or centigrade, scale is not at absolute zero, the
kelvin is the same size as the Celsius degree. Thus, when dealing with
temperature differences, it is sometimes convenient to use Celsius degrees for ∆T.
For example, the SI unit for specific heat, J/kg K is equal to (and will sometimes
be written as) J/kg C°.
26
Chapter 1
Applying Models to Thermal Phenomena
SI Units related to energy:
SI Unit
Construct
Abbreviation
Expressed in base units
Joule
energy
J
kg•m2/s2 = N•m
Watt
power
W
J/s = kg•m2/s2
Newton
force
N
kg•m/s2
Pascal
pressure
Pa
J/m3 = N•m2
Some common energy units and conversions to SI:
1 kWh = 3.6 MJ
1 erg = 10-7 J
1 cal = 4.184 J
1 food Calorie (big “C” calorie) = 1 kcal = 4.184 kJ
1 ft•lb = 1.36 J
1 eV = 1.602 x 10-19 J
1 BTU = 778 ft•lb = 252 cal = 1.054 kJ
Chapter 1 Applying Models to Thermal Phenomena
27
1-5 Examples of Particular Models of Thermal
Phenomena
Example 1
Let us consider the physical situation of a pot of water left on an unattended
kitchen stove top. We might wish to estimate how long it would take for the 1.0
liter (1.0 kg) of water in the pan to boil away and heat the pan to dangerously high
temperatures, perhaps igniting the plastic handle. Let’s also suppose we have
previously determined the rate at which energy is transferred from the stove
burner to the pan by doing a simple experiment to see how long it takes to heat
the 1 kg of water in the pan 10˚C, giving a calculated power input to the water of
1.0 kW.
In this example we are both heating the water and changing its phase; thus we
know we will need to include both the thermal and bond systems of the water.
How about the pan’s energy systems? If the mass of the water (1.0 kg) is several
times larger than the mass of the pan (typically the case), the heat capacity of the
pan will be considerably less than the water, since the mass-specific heat of the
water is so much greater than steel or aluminum. What about transfer of energy to
the environment from the pan? This is tougher to estimate. We do know from
experience that water does boil when left on the burner for awhile. So the transfer
to the environment is definitely less than from the stove to the pan. We can
initially leave this out of the model and consider whether to put it in when we
have made the time calculation. What about the stove energy systems? Since we
know there is a heat input to the pan of 1.0 kW, it makes sense here to model the
water as an open system with the heat input from “the outside.”
So at this point, our energy-system diagram would look like this:
Physical system:
Identification of beginning and end of interval:
Beginning: liq water at 25 ˚C
End: water vapor at 100 ˚C
1.0 kg of water
water bond E
Ebond ↑
vap mass ↑
vapor mass initial = 0
vap m final = 1.0 kg
liq water
Ethermal ↑
heat
T↑
Tinitial = 25 ˚C
Tfinal = 100 ˚C
∆Ebond + ∆Ethermal = Q
|∆m ∆Hvap| + Cliq ∆Tliq = Q
(1.0Kg)(2257 kJ/kg) + (1.0kg) (4.18 kJ/kg ˚C)(75˚C) = Q
2,600 kJ = Q (keeping two significant figures)
Since the heat input is 1 kW or 1 kJ/s, it would take about 2600 sec or 43 min to boil away the water.
28
Chapter 1
Applying Models to Thermal Phenomena
Now we need to examine the reasonableness of our numerical predictions. First,
notice that the calculated change in energy of the bond system is about seven
times greater than the change in energy of the thermal system. This is at least
consistent with the values of heat capacities and heats of vaporization listed in the
data table. (We will develop a much deeper understanding of this difference
when we further develop our particle model of matter in Chapter 3.) This
difference in heats also implies that the water would come to boiling much
quicker than it would take to boil it away (something like 5 minutes compared to
38 minutes). Does this correspond to your personal experience when cooking? If
you haven’t noticed this considerable difference in times to heat water to boiling
and to boil it away, check it out. Earlier, we raised the question weather the pan
had an effect on the system. If we included the pan, what energy-system would
we need to add? How would this affect our prediction of the time to boil away all
of the water?
Chapter 1 Applying Models to Thermal Phenomena
1-6
29
Looking Back and Ahead
Let’s reflect on what we have done in the course up to this point. Our focus has
been on developing an energy model, which we’ve called the Energy-Interaction
Model, and on understanding how to apply it to some particular thermal
phenomena. We have used this model to begin to understand some of the more
general thermal properties of matter. We will continue to develop the EnergyInteraction Model as we apply it to new kinds of phenomena in Chapter 2.
Let’s think about how we have used the Energy-Interaction Model so far. If we
included all energy systems that were involved in the process or interaction, we
had a closed system and modeled the physical system as being composed of
several energy-systems, each of which might exchange energy with one or more
of the other energy-systems within the closed system. So, to make headway with
this approach, we had to be able to identify relevant energy-systems. So far, we
have considered bond and thermal systems explicitly. If we thought of the
physical system as being an open system, then in addition to exchanges of energy
among the energy systems within the physical system, we allow for the possibility
of energy entering (or leaving) the system.
The next step is to add additional energy-systems to our repertoire, so we can
handle other types of phenomena with different kinds of interactions. Fortunately,
there are not that many different energy-systems. So, after we have added just a
few more, we will be in a position to tackle questions about many more
phenomena than we could even deal with in one quarter or semester. But that is
precisely the power of this approach. It is so universal that you don’t need to be
shown how to use it for each different phenomenon. Once you are comfortable
with the approach, it becomes your own powerful tool, which you can use
anytime you need it.
What have we left out in what we have done so far? Think back over all of the
phenomena we have discussed and the questions we can answer with this
approach. Basically, we can get at the values of quantities, or more precisely the
changes in these values that occur as a result of the interaction, but we can’t get
information about the details of the interaction or what goes on during the
interaction.
When we want to know something about the details of an interaction or the
dynamics of the phenomenon, we will need to use an approach, or model, that
incorporates these details. But precisely because we have to incorporate more
detail, the models will not be nearly so general as the Energy-Interaction Model.
In Part 2 of the course we will devote considerable effort to understanding the
Newtonian model, which allows us to very accurately calculate motions of
objects. In Part 3 we focus on a very useful wave model of motion and field
models that allow us to make sense of electric and magnetic phenomena. We need
these detailed models because we want to be able to answer questions that the
energy-interaction model can’t help us with. But, alas, we will miss the simplicity
and generality of the energy model.
30
Chapter 1
Applying Models to Thermal Phenomena
Endnotes
i
Although we label this model the Three Phase Model of Matter, it is strictly
applicable only to pure substances. In addition, there are other phases of matter
(such as magnetic phases) that are not discussed as part of this model. Many
substances have several different solid phases due to different crystal structures.
Some authors define a fourth phase, the plasma phase, in which at least some of
the particles are ionized. In this simple model, we ignore these distinctions and
focus on only the three primary phases.
ii
In our simple model, we will ignore surface tension and capillarity. The effects
of gravity on changes in pressure in a liquid are ignored in this simple model, but
will be taken up in later chapters.