Heat: Energy in transit
EFEU May 2009
Heat: Energy in Transit
Renilde Nihoul
B BRUSSEL05
Renilde Nihoul
H.U.Brussel
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Heat: Energy in transit
EFEU May 2009
1 Introduction
Motivating pupils in science can be a challenge for teachers. This is especially true as the
pupils get older and science no longer has the novelty value that it had when they were
younger. Enhancing pupil‟s motivation is not a simple process. One of the most important
factors is creating a clear purpose for classroom activities. This can be done in a variety of
ways, including explaining daily life problems.
A lot of misconceptions about physical phenomena exist, including about heat. Pupils
(often) don‟t see the relation between the theoretical principles of physical phenomena
and situations of daily live. If we are able to give an answer at daily live questions by using
the theoretical principles they learned in physics lessons, they might be more interested in
these lessons.
Examples of such questions could be:
Will a snowman melt faster with a coat on or without a coat?
If you have a cup of coffee which is too hot to drink, should you
add cream to it immediately to cool it or let it stay black and sit for a
while before adding cream? (The object is to get it cool enough to drink
in the shortest possible time.)
Heat flow is normally from a high temperature toward a low
temperature region. How do you manage to cool your body on a July
day when the temperature is 39°C (compared to 37°C normal body
temperature)?
Will hot water freeze into ice cubes faster than cold water in
your freezer?
Is a metal teapot better than a porcelain one to keep the tea
hot?
...
Providing objective information alone is not enough. The pupils should investigate these
phenomenon‟s themselves to find out (and understand) the correct concepts behind the
observations.
First they have to discuss the (little) problem and try to formulate workhypotheses. Then
they set up a little experiment to find out in a scientific way, which workhypothesis is
correct.
In this way, we not only stimulate the interest of the pupils, but also their scientific skills.
Before explaining how to tackle this, the main principles of heat transfer are given.
2 Basics of Heat Transfer
Heat may be defined as energy in transit from a high temperature object to a lower
temperature object. If you place a hot object (f.i. a cup of coffee) or a cold object (a glass
of ice water) in an environment at ordinary room temperature, the object will tend toward
thermal equilibrium with its environment. That is, the coffee gets colder and the ice water
gets warmer. The temperature of each approaches the temperature of the room.
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H.U.Brussel
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Heat: Energy in transit
EFEU May 2009
Therefore we need some sort of exchange of energy between the system and its
environment. The following definition of heat can be used:
Heat (symbol Q) is energy that flows between a system and its environment by virtue of a
temperature difference between them.1
Figure 1 summarizes this view.
Environment
Environment
Environment
System
System
Q=0
Q>O
(a) TS < TE
System
(b) TS = TE
Q<0
(c) TS > TE
Figure 1: (a) If the temperature of a system is less than the temperature of its environment, heat flows into the
system until thermal equilibrium is obtained, as in (b). (c) If the temperature of a system is greater than that of
its environment, heat flows out of the system.
If the temperature TS of a system is less than the temperature of its environment TE, heat
flows into the system. By convention is Q positive in this case. It is a process by which the
internal energy of the system is increased. When TS > TE, heat flows out of the system, in
which case Q is taken to be negative.
Since heat is a form of energy, its units are those of energy, namely, the joule (J) in the SI
system. Other units are still in use today. The “calorie” is in common use as a measure of
nutrition.
1 cal = 4,186 J
The “British thermal unit” (Btu) is still commonly found as a measure of the ability of an air
conditioner to transfer energy (as heat) from a room to the outside environment. A typical
room air conditioner rated at 10 000 Btu/h can therefore remove about 107 J from a room
every hour and transfer it to the outside environment.
1 Btu = 1055 J
3 Misconceptions about heat
Heat is similar to work in that both represent a means for the transfer of energy. The
following figure of the interchange ability of heat and work as agents for adding energy to
a system can help to dispel some misconceptions about heat.
1
Resnick, R., Halliday, D., Krane, K. (1992) PHYSICS Volume 1, 4th Edition, John Wiley & Sons, New York
Renilde Nihoul
H.U.Brussel
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EFEU May 2009
Figure 2: The interchange ability of heat and work as agents for adding energy to a system. 2
If you are presented with a high temperature gas, you can‟t tell whether it reached that
high temperature by being heated, or by having work done on it, or a combination of the
two.
To describe the energy that a high temperature object has, it is not a correct use of the
word heat to say that the object “possesses heat”. It is better to say that it possesses
internal energy as a result of its molecular motion. Neither heat nor work is an intrinsic
property of a system. A system doesn‟t “contain” a certain amount of work. Instead, we
say that it can transfer a certain amount of energy as heat or work under certain specified
conditions. The word heat is reserved to describe the process of transfer of energy from a
high temperature object to a lower temperature one. You can take an object at low internal
energy and raise it to higher internal energy by heating it. But you can also increase its
internal energy by doing work on it, and since the internal energy of a high temperature
object resides in random motions of the molecules, you can‟t tell which mechanism was
used to give it that energy.
Some of the confusion about the precise meaning of heat results from the popular usage
of the term. Often heat is used when what is really meant is temperature or internal
energy. When we hear about heat in relation to weather, or when cooking instructions
indicate “heat at 200 degrees,” it is temperature that is being discussed. When someone
talks about the “heat generated” by the brake linings of an automobile or by briskly rubbing
the palms of your ands together, it is usually internal energy that is meant. When you rub
your hands together, they do work on one another, thereby increasing their internal energy
and raising their temperature. This excess energy can then be transferred to the
environment as heat, because the hands are at a higher temperature than the
environment.
So, don‟t refer to the “heat in a body” or say “this object has twice as much heat as that
body”. Avoid the use of the rather vague term “thermal energy” and the use of the word
2
Zemansky, M. (1970). The Use and Misuse of the Word „Heat‟. The Physics Teacher, 8, 295.
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“heat” as a verb, since this feeds the misconceptions. Introduce and use the concept of
internal energy as quickly as possible.
4 The mechanical equivalent of heat
In a classic experiment in 1850, James Joule showed the energy equivalence of heating
and doing work by using the change in potential energy of falling masses to stir an
insulated container of water with paddles.
Figure 3: Joule's arrangement for measuring the mechanical equivalent of heat. The falling weights turn paddles
that stir the water in the container, thus raising the temperature.3
The mechanical work, done by the falling weights, produces a measurable temperature
rise of the water. At that time, calories were the accepted unit of heat. It was originally
defined as the quantity of heat necessary to raise the temperature of 1 g of water from
14,5 to 15,5 °C. From the measured temperature increase of the water, Joule was able to
deduce the amount of calories of heat Q that would have produced the same temperature
increase. The work done on the water by the falling weights (in joules) therefore produced
a temperature rise equivalent to the absorption by the water of a certain heat (in calories),
and from this equivalence it is possible to determine the relationship between the calorie
and the joule. This experiment is noteworthy, not only for the skill, ingenuity, and its
precision, but also for the direction it provided in showing that heat, like work, could
properly be regarded as a means of transferring energy. In the 18th century, it was
believed that a material fluid, called caloric, was exchanged between bodies at different
temperatures!
5 Internal energy and the first law of thermodynamics
3
http://en.wikipedia.org/wiki/Image:Joule%27s_heat_apparatus.JPG
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Internal energy is defined as the energy associated with the random, disordered motion of
molecules. It is separated in scale from the macroscopic ordered energy associated with
moving objects; it refers to the invisible microscopic energy on the atomic and molecular
scale. For example, a glass of water at room temperature standing on a table has no
apparent energy, either potential or kinetic. But on the microscopic scale it is a seething
mass of high speed molecules travelling at hundreds of meters per second.
Figure 4: Internal energy of a glass of water at room temperature.4
U is the most common symbol used for internal energy. The change in internal energy
between equilibrium states 1 and 2 is:
ΔU = U2 – U1
The value of U1 depends only on the coordinates of the state 1(only on temperature for an
ideal gas). Similarly, U2 depends only on the coordinates of point 2. Such a function is
called a state function: it depends only on the state of a system and not at all on how the
system arrived at that state.
This brings us to the first law of thermodynamics, which can be stated as follows:
In any thermodynamic process between equilibrium states 1 and 2, the quantity Q – W
has the same value for any path between state 1 and 2. This quantity is equal to the
change in the value of a state function called the internal energy.
Mathematically, the first law is:
ΔU = Q – W
The change in internal energy of a system is equal to the heat added to the system minus
the work done by the system. In other textbooks you may find the first law written as:
ΔU = Q + W
It is the same law, namely the thermodynamic expression of the conservation of energy
principle. In this case, W is defined as the work done on the system instead of work done
by the system. For many processes (e.g. an internal combustion engine), the common
4
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/inteng.html#c2
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H.U.Brussel
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scenario is one of adding heat to a volume of gas and using the expansion of that gas to
do work. Therefore we prefer to use the first notation.
6 The transfer of heat
The transfer of heat between a system and its environment can take place by three
mechanisms: conduction, convection and radiation.
6.1 Conduction
If you leave a metal poker in a fire for any length of time, its handle will become hot.
Energy is transferred from the fire to the handle by conduction along the length of the
metal shaft. The atoms at the hot end, by virtue of the high temperature at that end, are
vibrating with large amplitude. These large vibrational amplitudes are passed along the
shaft, from atom to atom, by interactions between adjacent atoms. In this way a region of
rising temperature travels along the shaft to your hand.
The energy will be transferred because the higher speed particles will collide with the
slower ones with a net transfer of energy to the slower ones.
The rate of conduction heat transfer between two plane surfaces can be calculated.
Consider a thin slab of homogeneous material of thickness d and cross-sectional area A.
The temperature is T + ΔT (Thot) on one face and T (Tcold) on the other. The rate of heat
flow through the slab is:
directly proportional to A (the more area available, the more heat can flow per unit time)
inversely proportional to d (the thicker the slab, the less heat can flow per unit time)
directly proportional to ΔT (the larger the temperature difference, the more heat can flow
per unit time).
[To minimize the loss of heat from your house in winter: make the surface area smaller (a
two-story house is more efficient than a one-story house of the same total floor area); use
thick walls filled with insulation and, perhaps most important, move to a warmer climate.]
Mathematically, we can summarize this as:
Q= A T
t
d
With:
Q = heat transferred in time = Δt
κ = thermal conductivity of the barrier
A = area
ΔT = temperature difference
d = thickness of the barrier
A substance with a large value of κ is a good heat conductor; one with a small value of κ
is a poor conductor or a good insulator. In the case of solids, the properties of materials
that make them good electrical conductors (namely, the ability of electrons to move
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relatively easily throughout the bulk of the material) also make them good thermal
conductors.
Table 1 shows some representative values of κ.
Material
Conductivity, κ (W/m · K)
Metals
Stainless steel
14
Lead
35
Aluminium
235
Copper
401
Silver
428
Gases
Air
0.026
Helium
0.15
Hydrogen
0.18
Building materials
Polyurethane foam
0.024
Rock wool
0.043
Fiberglas
0.048
White pine
0.11
Window glass
1.0
Table 1: Some thermal conductivities5
Over the range of temperatures we normally encounter, we can regard κ as a constant,
but over wide temperature ranges it does show a slight variation with T. Gases transfer
heat by direct collisions between molecules, and as would be expected, their thermal
conductivity is low compared to most solids since they are dilute media.
6.2 Convection
If you look at the flame of a candle or a match, you are watching heat energy being
transported upward by convection. Heat transfer by convection occurs when a fluid, such
as air of water, is in contact with an object whose temperature is higher than that of its
surroundings. The temperature of the fluid that is in contact with the hot object increases
and (in most cases) the fluid expands. Being less dense than the surrounding cooler fluid,
it rises because of buoyant forces.
5
Resnick, R., Halliday, D., Krane, K. (1992) PHYSICS Volume 1, 4th Edition, John Wiley & Sons, New York
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H.U.Brussel
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Figure 5: Heat convection6
Convection can also lead to circulation in a liquid, as in heating a pot of water over a
flame. Heated water expands and becomes more buoyant. Cooler, denser water near the
surface descends and patterns of circulation can be formed.
Figure 6: Convection currents7
Atmospheric convection plays a fundamental role in determining the global climate
patterns and in our daily weather variations. Glider pilots and condors alike seek the
convective thermals that, rising from the warmer Earth beneath, keep them aloft. Huge
energy transfers take place within the oceans by the same process. The outer region of
the sun, called the photosphere, contains a vast array of convection cells that transport
energy from the interior to the solar surface and give the surface a granulated appearance
with a typical dimension of a granule being 1000 kilometres.
6
7
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.html#c2
http://www.physics.arizona.edu/
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Figure 7: The photosphere of the sun8
Heat-induced fluid motion in initially static fluids is known as free convection. For cases
where the fluid is already in motion, heat conducted into the fluid will be transported away
chiefly by fluid convection. These cases, known as forced convection, require a pressure
gradient to drive the fluid motion, as opposed to a gravity gradient to induce motion
through buoyancy.
It is difficult to quantify the effects of convection since it inherently depends upon small no
uniformities in an otherwise fairly homogeneous medium.
6.3 Radiation
Energy is carried from the sun to us by electromagnetic waves that travel freely through
the near vacuum of the intervening space. If you stand near a bonfire or an open fireplace,
you are warmed by the same process.
8
http://solarscience.msfc.nasa.gov/images/granules.jpg
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Figure 8: The sun at 5800K and a campfire at 800K9
The sun at 5800 K and a hot campfire at perhaps 800 K give off radiation at a rate
proportional to the 4th power of the temperature.
All objects emit such electromagnetic radiation because of their temperature and also
absorb some radiation that falls on them from the objects. The higher the temperature of
an object, the more it radiates. The energy is carried by photons of light in the infrared and
visible portions of the electromagnetic spectrum. When temperatures are uniform, the
radiative flux between objects is in equilibrium and no net thermal energy is exchanged.
The balance is upset when temperatures are not uniform, and thermal energy is
transported from surfaces of higher to surfaces of lower temperatures.
7 Heat Transfer Examples
7.1 With focus on radiation: the Greenhouse effect
The greenhouse effect refers to circumstances where the short wavelengths of visible light
from the sun pass through a transparent medium and are absorbed, but the longer
wavelengths of the infrared re-radiation from the heated objects are unable to pass
through that medium. The trapping of the long wavelength radiation leads to more heating
and a higher resultant temperature. Besides the heating of an automobile by sunlight
through the windshield and the namesake example of heating the greenhouse by sunlight
passing through sealed, transparent windows, the greenhouse effect has been widely
used to describe the trapping of excess heat by the rising concentration of carbon dioxide
9
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html#c2
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in the atmosphere. The carbon dioxide strongly absorbs infrared and does not allow as
much of it to escape into space.
Figure 9: The greenhouse effect10
A major part of the efficiency of the heating of an actual greenhouse is the trapping of the
air so that the energy is not lost by convection. Keeping the hot air from escaping out the
top is part of the practical "greenhouse effect", but it is common usage to refer to the
infrared trapping as the "greenhouse effect" in atmospheric applications where the air
trapping is not applicable.
The action of carbon dioxide and other greenhouse gases in trapping outgoing infrared
energy from the Earth, thereby warming the planet, is called the greenhouse effect. Those
gas molecules in the Earth's atmosphere with three or more atoms are called greenhouse
gases. The greenhouse gases include water vapour (H2O), ozone (O3), carbon dioxide
(CO2), and methane (CH4). Also, trace quantities of chlorofluorocarbons (CFC's) can have
a disproportionately large effect. Current analysis suggests that the combustion of fossil
fuels is a major contributor to the increase in the carbon dioxide concentration. It may
measurably increase the overall average temperature of the Earth, which could have
disastrous consequences. Because the potential consequences of global warming in
terms of loss of snow cover, sea level rise, change in weather patterns, etc are so great, it
is a major societal concern. On the other hand, proposed measures to reduce human
contributions to greenhouse gases can also have great consequences.
For more information: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
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7.2 Involving all three basic heat transfer mechanisms: cooling of the human
body.
Figure 10: Cooling of the human body11
This is a simplified model of the process by which the human body gives off heat. Even
when inactive, an adult male must lose heat at a rate of about 90 watts as a result of his
basal metabolism. One implication of the model is that radiation is the most important heat
transfer mechanism at ordinary room temperatures. This model indicates that an
unclothed person at rest in a room temperature of 23 Celsius would be uncomfortably
cool. The skin temperature of 34 °C is a typical skin temperature taken from physiology
texts, compared to the normal core body temperature of 37 °C.
What will happen if the ambient temperature is above the skin temperature? Even when
inactive, an adult male must lose heat at a rate of about 90 watts as a result of his basal
metabolism. This becomes a problem when the ambient temperature is above body
temperature, because all three standard heat transfer mechanisms work against this heat
loss by transferring heat into the body.
Figure 11: Cooling of the human body when the ambient temperature is above the skin temperature.
11
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/coobod.html#c1
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Our ability to exist in such conditions comes from the efficiency of cooling by the
evaporation of perspiration. At a temperature of 45 Celsius the evaporation process must
overcome the transfer of heat into the body and give off enough heat to accomplish a 90
watt net outward flow rate of energy. Because of the body's temperature regulation
mechanisms, the skin temperature would be expected to rise to 37°C at which point
perspiration is initiated and increases until the evaporation cooling is sufficient to hold the
skin at 37°C if possible. With those assumptions about the temperatures, one can
calculate that there will be a net input power of 109 watts to the body (by radiation). The
perspiration cooling must overcome that and produce the net outflow of 90 watts for
equilibrium.
8 Dealing with misconceptions by training the scientific method.
As mentioned before, some misconceptions about heat can stubbornly persist in pupils
mind. In order to explain how to deal with this misconceptions by training the scientific
method, we illustrate this concept with an example.
8.1 Step 1: Formulation of a problem
A problem (of a daily life situation) can be introduced by the teacher or by a pupil. For
instance:
I want to keep the tea as hot as possible, as long as possible in a teapot. Therefore, I
better choose a thick teapot? A metal teapot? …
8.2 Step 2: Formulation of workhypotheses
The pupils discuss the problem in small groups (3 – 4 pupils) and try to formulate
workhypotheses. The emphasis has to lay on the formulation of the hypotheses and not
on the “correct” formulation.
As a teacher, you try to stimulate the discussion by asking questions as: “What exactly do
you mean?, Why do you think that is?, How could you write this down?,…”. Don‟t give any
information with respect to content.
Discuss in class all the preconceptions made by the pupils. It is important they realise not
everyone has the same preconceptions. It is also important that they can practice to
express their visions. They have to become aware of their own visions.
Summarize all the visions of the pupils:
A metal teapot is better than a porcelain one to keep the tea
hot.
In a thicker teapot the tea will remain longer hot.
It doesn‟t matter which teapot you use (the tea will chill
anyway).
…
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8.3 Step 3: Experimental verification
Normally the teacher thinks out the experiment. However, it is important that the pupils
plan their own experiment so they see the experiment as a mean to answer questions and
not only as a recipe they have to follow.
At first, they will use their sensory perceptions to plan the experiment. Let them realise
that these sensory perceptions are valuable but they give only vague and superficial
information.
Then they ought to be able to translate the problem in measurable quantities. All
quantities that are important for the experiment need to be listed. Some of these quantities
need to be kept at a constant level during the experiment. Other quantities need to be
measured. The pupils should estimate the magnitude of the results in advance so they
can select the appropriate measuring instruments.
They can use the following scheme to think out their experiment.
Workhypothesis
What is the question?
Description and outline of the experiment Which experiment can answer that question?
Material list
Which equipment is necessary?
Procedure
How exactly is it done?
For the experiment with the teapot, this could be resolved as follows.
Tea can be replaced by boiling water;
In stead of a real teapot, we can use cups of different materials
(with the same volume);
To discover the effect of the thickness, we use cups of the
same material, but with a different thickness;
We measure the temperature with a thermometer, the time with
a chronometer and the volume with a pipette.
Procedure:
Fill the cups with equal volumes of boiling water (use the
different kind of cups).
Measure the temperature of the water at different points of time
(every 15 seconds).
Put the results in a convenient table and try to figure out which
cup is most suitable to keep the tea hot.
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8.4 Step 4: Reflection
When the experiment is finished, they have to select the work hypothesis confirmed by the
experiment and give one‟s motives for this choice. All the difficulties have to be put into
words.
If their own vision is in conflict with the outcome of the experiment, the pupils will be
intellectually challenged.
Selection of the hypothesis confirmed by the experiment: a
porcelain teapot will keep the tea longer hot than a metal teapot. The
thickness of the teapot is important. The tea will chill in every teapot,
but the time it takes to do so will be different.
Motivation of the selection
8.5 Step 5: Scientific explanation
The scientific explanation should start from the concrete problem, from a conceptual
approach and lead then to a mathematical formulation. The scientific explanation should
be told in a fascinating way so they will remember it longer.
The better you prevent an energy exchange between the hot
tea and the surrounding air, the longer the tea remains hot.
A metal pot is a very bad insulator.
(A complete explanation is not given here).
8.6 Conclusion
To deal with the existing misconceptions, let the pupils make their own experiments. By
practicing a scientific method they will be able to discover the „truth‟.
The link between the physical principles and situations of daily life will become clearer.
They might be more interested in physics lessons as they understand they can use these
theoretical principles to explain daily life problems.
Evaluate the concept afterwards. (Evalution of your practice is a powerful tool for
enhancing your teaching as well as their students' learning).
Did the strategie capture and retain the pupil‟s attention? How effective was this in
encouraging their scientific skills?
Hopefully the pupils will perceive themselves as participants in the journey of discovering
and learning and as co-operating detectives looking for and evaluating evidence. Let them
share your feelings of curiosity, enthusiasm and critical reflection!
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9 References
Balck, C., Cocquyt, B., Van Peteghem, R. (2005) Misvattingen fysica te lijf. Syllabus.
Universiteit Antwerpen – Centrum Nascholing Onderwijs.
Giancoli, D.C. (1999) Natuurkunde voor Wetenschap en Techniek. deel II: Golven en
Geluid; Kinetische Theorie en Thermodynamica; Elektriciteit en Magnetisme; Licht.
Academic Service, Schoonhoven.
Hathaway, D. (2008) Solar Physics. NASA's Marshall Space Flight Center
http://solarscience.msfc.nasa.gov/
Nave,C.R. (2005) HyperPhysics. Departement of Physics and Astronomy, Georgia State
University
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
Resnick, R., Halliday, D., Krane, K. (1992) PHYSICS. Volume 1, 4th Edition, John Wiley &
Sons, New York.
Zemansky, M. (1970). The Use and Misuse of the Word „Heat‟. The Physics Teacher, 8,
295
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H.U.Brussel
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