Temperature, Heating, and
Thermal Energy- Sorting Things
Out!
By Patricia Westphal
Retired physics teacher, Neenah High School, Neenah,
Wisconsin
Summer 2003
Introduction
There are several good articles on the ASU listserv discussing the use of the modeling
strategies for describing the changes in the internal energy of a system, E, using the First Law
of Thermodynamics: E = Q + W. There is also discussion about energy transfer by working
in articles such as Making Work Work by G. Swackhamer. (See Appendix 6.) But there do not
seem to be many articles discussing Q, the energy transferred by heating. It is the purpose of
this paper to address this topic. However, before advancing, it is important to clarify a few
terms and to distinguish between them.
Internal Energy, Thermal Energy, and Temperature
Regardless of the state of matter—solid, liquid, gas, or plasma—we visualize matter as
a collection of jiggling particles—molecules, atoms, or ions. In which state the matter exists
depends upon the rate of this random, chaotic motion. We refer to this haphazard motion as
thermal motion and the energy associated with the body as its thermal energy.
When you touch a hot cup of tea, energy is transferred to your hand because the cup is
hotter than your hand. On the other hand, when you hold an ice cube in your hand, energy is
transferred from your hand to the ice cube because your hand is warmer than the cube. These
energy transfers result in a change in the thermal energy in your hand. The direction of energy
transfer is described by the Second Law of Thermodynamics and is always from the warmer
body to the colder one. The quantity that describes how warm or cold a body is, with respect
to a standard object, is called temperature. More precisely, temperature is a measure of the
average translational kinetic energy of those random, chaotic particles in the object.1 As
temperature changes, the properties of a material such as its size, its color, its electrical or
1
For a more detailed account of the kinetic molecular theory derivation of the relationship of temperature to the
average kinetic energy of a molecule, you can refer to Giancoli, Physics (3rd Ed.) Chapter 13 or Serway & Faughn
College Physics (5th Ed.) Chapter 10.
Thoughts on Heating
1
magnetic behavior, or its optical properties may also change. The common liquid-in-glass
thermometer relies on differences in the amount of expansion of the liquid and the glass to
create a measuring device.
On the scale bearing his name, Anders Celsius chose the reference temperature of a
container of water freezing to ice to be 0oC. Meanwhile, a container of boiling water was
chosen to be 100oC. The interval between the levels of the liquid-in-glass thermometer was
divided into 100 even spaces to create a centigrade or Celsius scale. Arithmetic formulas can
be use to relate temperatures on one scale to those on another, such as the Fahrenheit scale or
the Absolute scale. Each scale chooses a different value for the freezing and boiling point of
water. The Celsius and Absolute scales choose to divide the range into 100 parts while the
Fahrenheit scale divides the range into 180 parts, making a Celsius degree equal to 1.8 Fo.
Temperature, however, is not the same thing as thermal energy. When two blocks of
copper at the same temperature of 150oC, one with a mass of 1.0 kg and the other with a mass
of 5.0 kg, are placed on identical slabs of ice at 0oC, the larger copper block melts more of the
ice. The temperatures (and, therefore, the average translational kinetic energies) of both
copper blocks were the same, but the thermal energy they each transferred to the ice was
different. Thermal energy is measured in joules while temperature is measured in degrees or
kelvins. Thermal energy depends upon more than the temperature.
In addition to the energy of jiggling particles in a substance, there is energy in other
forms, namely the energy between atoms or molecules and the energy within molecules. These
inter- and intramolecular energies are bond energies and other particle interaction energies.
Cataloguing these interactions as energies due to position or shape or motion give rise to terms
like gravitational, elastic, and kinetic energies. The sum of all of the bond energies, interaction
energies, and jiggling energies will be referred to as the internal energy2 of the system. The
internal energy is a state variable of the system. Changes in the internal energy can be
monitored because the changes result in changes in other state variables like temperature and
pressure. In this context, a change in a system’s internal energy, Einternal, will be the sum of
all changes-- Egrav + Ekinetic + Eelastic + Ethermal + Eelectrical , etc.
Where does “heat” come in?
Energy is transferred from a hot body to a cooler one because the objects are at
different temperatures. This process is called heating. Heating, then, is the transfer of energy
due to a temperature difference between the system and the surroundings. Due to the heating
process, one or more properties of the system may change. Such changes might be
temperature changes, state changes, or other physical and chemical changes.
Specific Heat
2
Many texts use the terms thermal energy and internal energy interchangeably. These texts define internal
energy as the energy of all the molecules in all forms including energy of molecular motion and all types of
bonding. In these texts kinetic energy, elastic energy, gravitational energy, and electric energy are different forms
of energy. This fosters the idea that each kind of energy is fundamentally different from the others. It is this idea
that I wish to dispel with this modeling strategy.
2
Thoughts on Heating
When a particular immersion heater is used to heat a 100-g sample of water for a
measured period of time, the temperature of the sample increases by 30Co. But if the same
heater is used to warm a 100-g sample of ethanol for an identical period of time, the
temperature change is only 17Co. The same energy transfer does not result in the same
temperature increase. The temperature increase is related only to a change in the average
translational kinetic energies of the molecules in the sample. Other molecular energy changes,
such as rotational or vibrational changes, are not reflected in the increased temperature.
Generally, when energy is transferred to a substance a combination of these effects occurs,
only part of which is reflected by the temperature change. We can define a useful quantity for
each substance called its specific heat, c. The specific heat is the change in thermal energy,
Ethermal, required to change the temperature of 1 kg of the material by 1 Co.
c
Ethermal
m  T
Water requires 4186 J to raise the temperature of 1 kg by 1 Co whereas aluminum requires only
900 J for the same task and lead requires a mere 128 J. The very large value for water makes it
a useful cooling agent in power plants and automobile engines. Water can absorb (or store) a
large amount of energy per unit of mass while producing only small temperature changes. The
weather effect of this storage capacity for water is seen when comparing average summer and
winter temperatures in the Southern Hemisphere with those of the Northern Hemisphere. A
quick look at the globe reveals that the proportion of water to land is much larger in the
Southern Hemisphere. Due to the large absorbing or storage capacity of the oceans, summer
and winter temperatures have smaller ranges in this hemisphere. Temperature fluctuations
across continental Asia and North America are much more severe. The small specific heat of
sand explains the wide daily temperature fluctuations of the deserts, too.
Latent Heat
Depending upon conditions of temperature and pressure, adding energy can increase
the molecular motion to a point that bonds break and the rigid structure of the solid is replaced
with the fluid arrangement of the liquid. If more energy is added, the temperature increases
(increased average random kinetic energy). Continued heating, transferring more energy to the
sample, may cause the liquid to change to the gaseous phase. If heating continues, the
molecular motion increases. At some point, enough energy may even be added to tear the
particles asunder creating the plasma state.
The latent heat of fusion is the energy that must be transferred per unit of mass to break
the bonds holding the solid together, if the sample is already at its melting temperature.
Ethermal
m
In a similar fashion, the latent heat of vaporization is the energy that must be transferred per
unit of mass to convert the liquid to its gaseous state at its boiling temperature.
L fusion 
Lvaporization 
Thoughts on Heating
Ethermal
m
3
It is probably not a good idea to refer to this energy as a chemical energy even though it is the
energy associated with bond changes. Chemistry teachers make a distinction between
chemical and physical changes. Changes of state are physical changes and referring to the
energy accompanying a physical change as Echemical may introduce an element of confusion that
is unnecessary3.
Expansion
When the temperature of a substance is increased, its molecules exert forces upon each
other to move them farther apart, resulting in expansion. For solids and liquids the expansion
may not be very noticeable unless you make careful measurements. But if the filling in your
tooth is not made to expand in the same way as the natural tooth enamel, the pain you feel is
very noticeable indeed. The size of expansion cracks in sidewalks and roadways also indicates
that this expansion is not a trivial matter. The change in length for a solid is given by L =
LoT where  is the experimentally determined coefficient of linear expansion; Lo, is the
original length of the solid; and T is the temperature change. Volume changes for solids and
liquids can be determined using the relationship: V = VoT Here,  is the experimentally
determined coefficient of volume expansion. ( is approximately equal to 3 for solids.)
Gases provide an interesting case. Instead of requiring different coefficients of
expansion for different materials as for solids and liquids, changes in gas volumes depend upon
pressure as well as temperature but are independent of the identity of the gas or its purity. The
combined gas laws and the ideal gas law provide ways to calculate changes in volume with an
accompanying temperature and/or pressure change. The ideal gas law is written:
PV= nRT
where P is pressure, V is volume, n is the number of moles of gas, and T is temperature
8.314 J
measured on the absolute scale in kelvins. R, the universal gas constant, is
. The
mol  K
internal energy of a monatomic ideal gas is a particularly nice quantity because it depends only
upon the number of moles of gas and the absolute temperature of the sample. A monatomic
ideal gas has no bonds! So its only internal energy is kinetic energy of the atoms. Since Einternal
= Ekinetic = 3/2 nRT, changes in the internal energy of a monatomic ideal gas are given by the
equation:
Eint ernal 
3nRT
2
This might be an opportune time to remind ourselves that monitoring a system’s energy assets and the transfer of
those assets is a bookkeeping system that we, as observers of nature, have imposed to try to keep track of changes.
We are often successful in efforts to predict things like final temperatures of mixtures or the final speed of an
object by using this asset accounting model. Sometimes we are so successful that we forget that this cataloguing
process was our invention.
3
4
Thoughts on Heating
Thermodynamics
The word thermodynamics comes from Greek words meaning “movement of heat”.
Early in the nineteenth century, study of thermodynamics began during a time period parallel
with Dalton’s advancement of the atomic model. It is not surprising, then, that the study of
thermodynamics began with an investigation of macroscopic system changes like work and
changes in kinetic energy, gravitational energy or other system energy assets. At this period in
history, many were not convinced of the existence of molecules. And for those who supported
their existence keeping track of the molecular energies was thought to be, at best, difficult, or,
at worst, impossible. Your classroom binder consists of several hundred pages of paper. The
molecules in those papers have internal energies due to the temperature of the pages. The
bonds store energy, which could be released by burning. Those bonds represent electric
energies by virtue of the charges on the electrons and the fields they create. The nuclei are
held together by huge energies associated with the strong force and the closeness of the
particles. According to Einstein, by virtue of mass, the particles have stored energy. All of
these forms of energy constitute the internal energy.
If you drop your folder to the floor, it changes height as it increases its velocity toward
the floor. But gravitational and kinetic energy assets are not part of the book’s internal energy
assets. The height and velocity are measured relative to the earth. To include these energy
assets with those of the book as internal energies, we must choose a larger system—one
including the earth. A system is the atoms, molecules, and objects you choose to describe or
study. Everything else is considered to be the surroundings. Together, the system and the
surrounding make up the universe. Because measuring the internal energy of a system is
impossible except for very simple systems, like the monatomic ideal gas, we are concerned
with changes in internal energy.
James Prescott Joule (1818-1889), in his quest to design more efficient engines for his
family’s brewery, continued work begun by Benjamin Thompson (Count Rumford) and Sir
Humphrey Davy 25 years earlier. Joule constructed a simple electric generator, which was
driven by a falling weight. The generated current raised the temperature of a piece of wire,
which was immersed in a container of water (an immersion heater!). The energy transferred
to the generator by the falling weight (by applying an external force to the generator shaftworking) produced a change in the thermal energy of the water (by heating). As he refined his
process, Joule reported in 1849:
1st That the quantity of heat produced by the friction of bodies, whether solid or liquid, is
always proportional to the quantity of [energy] expended. And 2 nd That the quantity of heat
capable of increasing the temperature of a pound of water … by 1 oFahr. requires for its
evolution the expenditure of a mechanical energy represented by the fall of 772 lb through the
distance of one foot.
Today, refinement of Joule’s discovery is often stated as the First Law of
Thermodynamics. For a selected system, the change in the internal energy of the system
equals the sum of the energies transferred by working or heating. The energy transferred by
Thoughts on Heating
5
working is symbolized by a W and requires an external force to act across the system boundary
through some distance, with a force-component in the direction of the distance. The energy
transferred by heating, symbolized with a Q, is due to a temperature difference between the
system and its surroundings. The internal energy change is then given by:
E = Q + W
Energy transferred into the system is positive and increases the internal energy of the
system. Energy transferred out of the system is negative and decreases the internal energy.
If the system is chosen large enough so that all energy assets are redistributed within
the system, E doesn’t change. If E = 0, energy is conserved. This means the total internal
energy of the system does not change. This is not the same meaning of conservation of energy
that is used in public media. “Conserving energy”, as we often hear it used, refers to
maintaining supplies of a particular resource as we are asked to reduce consumption of oil or
natural gas. Students come to us believing that to conserve something means to make is usage
zero! It requires many examples and lots of discussion to convey the message that
conservation of a quantity (like energy or momentum) means that the total of the assets before
and after a particular process is the same—but not necessarily zero. We must point out that
energy is always conserved if the system is chosen appropriately.
With this introduction to the vocabulary and its application to the First Law of
Thermodynamics, let us continue by examining some of the topics traditionally encountered in
a study of energy transfers due to temperature differences (heating).
Methods and Rates of Energy Transfer by Heating
If two or more bodies of different temperature are in thermal contact, those that are hot
become cooler and those that are cool become warmer. They come to thermal equilibrium or
the same temperature. This equalization of temperature can be accomplished by conduction,
convection, or radiation.
Conduction
Anyone who has held a metal fork into a camping fire to roast marshmallows knows
that the metal handle quickly gets hot. Replacing the fork with a branch of green wood is
much more comfortable for the camper. The transmission of energy along the fork to the
camper’s hand occurs by conduction. On the atomic level, we picture the increased motion of
the metal atoms in the fire causing them to bump into their neighbors farther up the length of
the fork. The transfer of energy up the handle is accomplished by electron and molecular
collisions.
The branch transmits the energy much more slowly allowing us to roast the
marshmallows more comfortably. The rate of energy transmission is related to the electrical
bonding of the material’s structure. Metals have “loose” outer electrons, which are useful for
electrical energy and thermal energy transfer. Materials like wood, Styrofoam, and paper do
6
Thoughts on Heating
not have loose electrons and are not good conductors. They are insulators. Liquids and gases
are also, generally, poor conductors or good insulators.
The rate of energy transfer by conduction has been quantifiably measured and is given
by the relationship:
Ethermal kAT

P 
t
l
where k is a property of the material called its thermal conductivity in units of
J
,
s mCo
A is the cross-sectional area of the conductor,
T is the temperature difference across the two sides of the conductor, and
l is the thickness of the conductor.
The symbol for the rate of energy transfer is P, for power, and the measuring units are watts.
Convection
Energy transfer by fluids (liquids and gases) is predominantly by convection. Warming
of fluids causes them to expand and reduces the density of the fluid. When it becomes less
dense than the surrounding fluid, the mass is buoyed upward. For example, we have all heard
that warm air rises. The pressure below the region of warmed air is higher than the pressure
above the air. The pressure difference creates a buoyant force. When the buoyant force is
greater than the weight of the heated air, it moves upward. This energy transfer mechanism is
not as easily quantified as conduction was.
However, this transfer process can help us to understand some weather phenomena by
using the First Law of Thermodynamics. Why do expanding air masses cool? Consider the
system to be a very large mass of heated air. As the air is heated it expands. To expand, it
must apply a force to the surrounding air to push it aside. The result is to lower the internal
energy of the mass of air and its temperature drops.
It is a common error to say “heat is produced by molecular collisions with one
another.” This is not true. One of the postulates of the Kinetic Molecular Theory is that
molecular collisions are elastic. This means both kinetic energy and momentum are conserved
during molecular collisions. Temperature is a measure of their kinetic energies (not of their
collision rates). Since the kinetic energies remain the same, collisions do not change the
sample’s temperature. In short, because energy is transferred to a sample of gas by heating, the
molecular motions and collisions increase. We can say that because they are heated, molecules
collide more often. We cannot say because they collide more often, the molecules are heated.
This latter statement confuses the effect with the cause.
Radiation
The empty region of space between the earth and the sun is not filled with solids,
liquids or gases. Then, how does energy get transferred from the sun to the earth across the
kilometers of space? The third process, radiation, is responsible for the transfer. Strictly
Thoughts on Heating
7
speaking, the energy of a radiant body is transferred by emitting quanta of energy. The
radiation can also be described using a model of electromagnetic waves propagating through
space. It is absorbed to change an object’s thermal energy when it strikes an object like the
earth. Radiant energy is entirely different from thermal energy or molecular motion and
should be considered separately (in another paper). A better representation of the First Law of
Thermodynamics would represent this more correctly as Einternal = Q + W + R, where R is the
transfer of energy by radiation.4
Re-examining Traditional “Heat” Problems
Heat is not contained by objects or systems so using the word, heat, as a noun when
instructing students to “calculate the heat required to …” is confusing to students. The correct
noun is, again, energy. In this case the energy transferred becomes the thermal energy of the
increased molecular activity that results with the temperature increase. Let’s examine a
problem of this traditional type with an alternative wording and treatment.
Problem: Energy is to be transferred to a cup of water to increase the water’s temperature.
How many joules of energy must be added to produce a 30Co increase for 200 g sample of
water?
Flow Diagram
Cool water
Warm Water
Ethermal
Ethermal
System:
water
Q
4 units
3 units
1 unit
Energy Sentence: Ethermal = Q = mcT
Analysis: The number of units drawn on the bar graphs and transfer arrows is arbitrary but they should represent,
in a semi-quantitative way, the changes for the chosen water system. The cool water has some thermal energy
initially due to molecular motions. As energy is added during heating, which is represented as Q, the thermal
energy of the water increases. The energy sentence can be written using the First Law of Thermodynamics:
E = Q + W with W= 0.
Solving for Q, using Q = mcT, provides the answer to the question: 200.g (4.186 J/gCo) 30 Co = 25,000J.
4
For those who are interested, the rate at which a body radiates or absorbs energy by radiation depends upon the
nature of the body and the difference between its absolute temperature and that of the surroundings. The rate of
4
4
 Tsurr
) .  is the Stefan-Boltzmann constant; is the emissivity
transfer is given by the equation: P =  A(Tobj
property of the material; A is its area; and the temperatures, T, must be on the absolute scale. For further
reference, consult Serway & Faughn, College Physics, Ch. 11)
8
Thoughts on Heating
Another typical “heat problem” involves putting a hot object into a cooler container of water
and using the appropriate models to predict the final temperature of the system, find the
specific heat of one of the objects or the mass of one of the objects. Let’s look at how one of
these problems might be addressed using this modeling strategy.
Problem: When 220-g of a metal are heated to 330oC and then plunged into a 100 g
aluminum cup containing 150 g of water at 12.5oC, the final temperature is 33.8oC. Assuming
10% of the energy of the hot metal is transferred to the surrounding air, what is the specific
heat of the metal?
System: metal, aluminum cup, water, air
Eth-water Eth-cup Eth-metal Eth-air
Eth-water Eth-cup Eth-metal Eth-air
System: metal,
Al cup, water, air
7 units
7 units
Energy Sentence:
Eth-water+ Eth-cup+Eth-metal + Eth-air= 0
Analysis: Since thermal energy is more than temperature, the thermal energies of substances are not drawn to be
the same size bars. However, care has been taken to show the same number of energy units in the initial and final
states since W and Q are both zero. (No arrows show energy transfer for the flow diagram in the center.) It is
important that the water and the cup show an increase in thermal energy as the temperature increases, while the
thermal energy of the unknown metal decreases. The increase in the thermal energy of the air is 10% of the
change for the hot metal from the given information.
(mcT)water + (mcT)cup + (mcT)metal. + 0.10 (mcT)metal. = 0
+ term
+ term
- term
+ term
(150 g)(4.186 J/gCo)(21.3 Co) + (100 g)(0.900 J/gCo)(21.3Co) + (220 g)(c)(-296 Co) + 0.10 (220 g)(c)(296 Co) = 0
c = 0.261 J/gCo
Notice that only the term for the unknown metal is negative since the thermal energy of all of the other parts of
the system increased.
The use of this modeling strategy will seem awkward to teachers, at first, because we are
conditioned to calculating heat as if it were a property or real “thing”. But the only real
accounting tool that we need is energy. Students find it very natural to think in terms of energy
assets and transfer processes. Transfers into or out of the system will change the total internal
energy of the system. Transfers within the system are actually just redistributions of the assets,
which when related to the financial asset analogy, are easily within the grasp of even middle
Thoughts on Heating
9
school students. Consider this problem where some of the kinetic energy assets of the bullet in
the system are redistributed as thermal energy of items in the system.
Problem: A 15-g lead bullet traveling at 500 m/s passes through a thin iron wall and
emerges at a speed of 250 m/s. If the bullet absorbs 50 % of the energy provided by the
change in the bullet’s kinetic energy, what will be the temperature rise of the bullet? Assume
the ambient temperature is 20.oC.
System: bullet, wall, air
Ekin-bullet Eth-bullet Eth-wall Eth-air
Ekin-bullet Eth-bullet Eth-wall Eth-air
System: bullet,
wall, air
Energy Sentence:
Ekin-bullet+ Eth-bullet+Eth-wall + Eth-air= 0
Analysis: Notice again that the total number of energy units in the initial graph and final graph is the same though
the number is arbitrary. The kinetic energy of the bullet decreases (and will be a negative term). All of the other
terms are positive. Detailed information is not available to determine the temperature change of the wall. But the
information says 50% of the kinetic energy decrease for the bullet is the thermal energy gained by the bullet.
50% (Ekin) = mcTbullet
0.50 * [½ (15 x 10-3kg)(500 m/s)2-½ (15 x 10-3kg)(250 m/s)2] = (15 x 10-3kg)(128 J/kg Co) (T)
T = 366 C0
but lead melts at 327oC
This discovery means that the thermal energy of the bullet must be described as raising all 15 g to 327oC and the
extra transferred energy will result in the melting of part of the bullet. The temperature change is, therefore, from
20oC to 327OC or 307 Co.
50% (Ekin) = mcT + m’Lfusion
0.50 * [½ (15 x 10-3kg)(500 m/s)2-½ (15 x 10-3kg)(250 m/s)2] = (15 x 10-3kg)(128 J/kg Co) (307Co) + m’ (2.5 x 104J/kg)
m’ = 0.0045 kg or 4.5 g of the bullet will melt
If you progress to discuss thermodynamics (transfer of energy by heating) to other areas, you
might include such details as the work done by a heated solid as it expands against its
surroundings. In the example that follows a piece of aluminum is heated. During the energy
transfer, the internal energy of metal increases (by an amount equal to mcT) but it also
decreases by an amount equal to the work done by the block as it expands against the
10
Thoughts on Heating
atmosphere around it. The decrease in the internal energy due to working on the surrounding
atmosphere is the area under the pressure-volume graph for the process.
Problem: What is the change in the internal energy of a 5.0 kg sample of aluminum that is
heated to change its temperature by 110 Co?
System: Aluminum
W = - area under PV graph
Q =mcT
Eth-Al
Eth-Al
System:
aluminum
Energy Sentence:
EAl = Q + W
Analysis: Energy is transferred to the aluminum by heating, which increases the internal energy of the system
when raising the temperature of the aluminum. This energy transfer has a positive sign. But since the aluminum
expands against the atmosphere, the work it does by pushing away the surroundings decreases the internal energy
assets of the system.
Finding the work, we draw the P-V graph for the process and find the area under the curve.
V= 3VoT for expanding solids
Vo = m/
Therefore, V= 3 (24 x 10-6/co)(5.0 kg/2.7 x 10-3kg/m3)(110 Co)
V= 1.5 x 10-5 m3
Patm
The work is – area of the rectangle: W = -(1.013 x 105Pa)(1.5 x 10-3m3)
V
W = - 1.5 Joules
Q = mcT = 5.0 kg (900 J/kg Co)(110 Co) = +5.0 x 105J
The internal energy change, E, equals Q + W but W’s contribution is too small to detect significantly.
E = + 5.0 x 105J.
Thoughts on Heating
11
Summary
Treating the process of heating in this way will take more practice for the teacher who
has spent years calculating the “heat to…” than it does for the student. For the student, the
treatment of energy using bar graphs and flow diagrams to monitor energy is very natural.
Conservation of energy occurs whenever there is no net transfer of energy into and out of a
system. On the other hand, transferring energy by working and/or heating changes the
system’s energy assets in a natural way. The statement of the First Law of Thermodynamics,
Einternal = Q + W, is no more than an accounting ledger. These path-dependent processes (Q
and W) may produce changes in the system. Changes in temperature, pressure, volume, and
other state functions may result.
To what level you carry the discussion will, of course, depend upon the students with
whom you work. If you work with AP physics students, expanding the discussion to engines
that use an input of heat to create an output of work is a small step. It is very reasonable to
determine the engine efficiency as a ratio of output work to the input heat. (Of course, the
transition to the efficiency represented by 1 
Tc
for the Carnot engine still requires a
Th
significant leap.) With a background in ideal gases, even the bridge to adiabatic, isothermal,
isovolumetric, or isobaric system changes is not daunting for high school students using this
approach.
As a final word, I agree with Gregg Swackhamer when he concludes with the statement
that “top billing… must go explicitly to energy storage and exchanges”. The changes in
teaching strategies proposed in his paper and this one are not a simple instance of semantics.
Instead, they constitute a different way of “understanding” energy5. Work and heat are not
separate from energy. Both are transfer processes that affect the distribution of energy assets
and that are intricately dependent upon system choice. To quote a fellow modeler from
Oshkosh North HS, Jeff Elmer, “a joule is a joule is a jewel!” (misspelling mine )
5
As a post-script, about this time in my teaching of this unit, some student will ask me how I would define energy
after all of this discussion. This is an approximation of the definition I give: Energy is a measure of the
capability to produce change. By identifying the nature or source of the change (change of motion, position,
shape, temperature, etc.) one can provide the means of energy storage or transfer. Energy is a means of
interaction between objects that have internal structures in contrast with forces that are interactions between
point particles without internal structure. Scientists have created this “energy-accounting” to predict future states
of a system. The model has been very useful and successful, but it has sometimes required “remodeling”. How
do you define energy?
12
Thoughts on Heating