Thermal Physics
PBL
Joel Teo (4S4)
Ng Chow Hui (4S3)
Ong Han Wee (4S4)
Introduction to problem task
Everyone has a ubiquitous propensity for a simple, nondescript substance known as
chocolate. Comprising a number of raw and processed foods produced from the seed of
the tropical Theobroma cacao tree, chocolate is delicious, scrumptious and simply
tantalizing. Chocolate is also versatile, and can be utilized in the solid or liquid state.
However, melting of such chocolate using commercial chocolate melters are a waste of
energy as they convert electrical energy to heat energy. Thus, in this problem based
learning, we will attempt to use only physics principles relating to solar insolation and
heat to create a solar chocolate melter that relies on the power of the sun such that our
chocolate melter would be eco-friendly.
In designing our chocolate melter, we considered the principles of thermodynamics and
heat transfer. It is commonly known that heat can be transferred via three methods;
conduction, convection and radiation. Knowledge on these three processes is imperative
as to change the chocolate from solid to liquid, we need to melt it, and melting is a
physical process which involves a great intake of heat to overcome the intermolecular
bonds between the molecules of chocolate without changing its temperature. Thus, to
ensure that the chocolate melts the fastest, we need to ensure that the rate of heat energy
flowing to the substance/chocolate is highest.
Out of the three modes of heat transfer, we as a group opine that conduction would be the
most worthless and inefficacious of all. Thus is because the chocolate is suspended in the
air via toothpicks, and since neither wood nor air is a good conductor of heat energy,
conduction in this case is virtually useless. Convection is slightly more useful in the sense
that if we are able to create a micro-environment which is unaffected by wind and
external factors, we can use convection currents to our advantage. However, in other
cases, convection is useless as it is merely the transfer of heat via hot air rising and cold
air sinking. Thus, we can only conclude that radiation, in the form of solar radiation,
would be the most important factor needed to melt the chocolate.
Prediction
We predicted that the chocolate was relatively easy to melt, since it melted very quickly
in our trails and we were very confident that our setup is able to focus the solar radiation
effectively to melt the chocolate
Design features
1.
2.
3.
4.
5.
Shiny metal tray as base
Chocolate is surrounded by mirrors and shiny surfaces
Chocolate is covered by glass dome
Two convex lenses are placed on top of the glass dome
A magnifying glass is held on top of the set up via a retort stand
Top View
Stand to support mirrors
Cardboard with
Aluminum Foil
Mirrors at 45 degrees
Retort Stand
Magnifying glass
Shiny metal tray
Glass dome
Side View
Magnifying glass
Convex Lens
Stand to support mirrors
Retort Stand
Mirrors at 45 degrees
Shiny metal tray
Chocolate
Glass dome
Cardboard with
Aluminum Foil
Below is a picture of the actual setup on the day itself. We removed the glass dome to
make things clearer to photograph.
Procedure
1. Place metal tray on ground
2. Position mirrors and the cardboard with aluminum foil at 45 degrees leaning on
stands
3. Place retort stand and the mirror on it
4. Adjust the arm of the retort stand so the magnifying glass at the tip of it is directly
over where the chocolate would be
5. Setup the data logger
6. Place the temperature sensor in the middle of the metal tray, beside the Styrofoam
where the toothpick with the chocolate would be placed
7. Obtain the chocolate with the toothpick and place it into the Styrofoam
8. Start the timing on the stopwatch
9. Cover the chocolate and the temperature sensor with a glass bowl
10. Place 2 convex lenses on top of the glass bowl
11. Wait until chocolate melts and stop the stopwatch, recording the time
12. Obtain readings from the data logger
13. Keep the setup
Trial result and design modification
Our trial was reasonably successful, where we managed to melt the chocolate less than
two minutes. What we did not predict is that other groups are able to melt the chocolate
faster than that so even with our design modification we were not able to melt it as fast.
We had made a change in our design after the trail, deciding to use mirrors instead of
aluminum foil. This is because we noticed that mirrors can reflect solar radiation better
than the aluminum foil and mirrors were available in the lab to be borrowed. The
aluminum foil was also slightly crumpled and this can increase its thermal emissivity.
This increase would reduce the amount of solar radiation reflected as more is absorbed.
However, we left one side of the setup with aluminum foil since we thought that we
should still maintain some part of the original setup.
Another change in our design was that we removed the wooden base that was originally
below the metal tray. The original purpose is because wood is a poor thermal conductor
and thus serves to reduce loss of thermal energy from the metal tray to the ground via
conduction. But that was with the assumption that the ground was cooler than the metal
tray, which is not the case since the ground had been baked under the hot sun previously
before we went on to setup, thus putting an insulator would have a reverse effect of
decreasing gain of thermal energy from the metal tray and setup from the ground,
something that we do not want. Therefore we removed the wooden board.
Application of physics concepts
In designing our chocolate melter, we considered to a large extent rudimentary physics
concepts, encompassing lenses, thermal emissivity and conductivity of substances and
reflection. Appended below are the details of each physics concept applied:
Firstly, in our design, we made sure the top surface whereby the chocolate chip is situated
is made of shiny, reflective stainless steel metal. Shiny stainless steel has high thermal
emissivity and is an excellent emitter of thermal radiation thus able to reflect incoming
solar insolation onto the chocolate chip.
Our next feature would be to surround the
Incident ray
chocolate by a series of mirrors supported
Mirror
by laboratory stands. Such a series of
0i = 45O
mirrors, when placed at the correct
positions (angle of inclination being 45
0r = 45O
degrees) would serve to reflect the solar
radiation from the midday sun directly
Reflected ray
above the ground. The initial angle of
Normal
midday sun’s ray to the ground is 90
degrees. Because of the angle the mirror is
45O
positioned the angle of incidence is 45
Ground
degrees, resulting in the angle of reflection
being 45 degrees to, and the solar radiation
bends towards the chocolate chip horizontally. With more solar radiation focusing on the
chocolate chip, it can melt faster, increasing the rate at which heat energy is gained.
Next, we covered the chocolate chip using a glass dome to trap a layer of insulating air
above and around the chocolate chip, thereby preventing the formation of convection
current and thus reducing heat loss to the surroundings. The layer of hot air above the
chocolate chip reduces the temperature gradient and thus minimizing heat loss from the
chocolate chip to the surroundings. In addition, the glass dome functions as a greenhouse
effect; when light rays enter the glass dome; they would have short wave radiation and
thus can enter with ease. However, the glass dome prevents light rays from escaping as it
prevents heat from escaping via radiation. This is because after impacting the ground, the
incoming light rays lose some of their energy and thus are shifted into long wave
radiation, which have less energy and are unable to pass through the glass dome.
The function of both convex lenses on top of the glass dome would be to converge
incoming light rays onto the chocolate chip, ensuring that the light rays which enter the
glass dome are not dispersed and scattered, but focused onto the chocolate chip. The
increase in intensity of these light waves would increase the amount of solar radiation
reaching the chocolate chip and the speed of it melting. The magnifying glass is used to
the same effect. Having read about the focusing power of magnifying glasses and having
personally utilized them to burn pieces of paper or dry leaves, we thought the magnifying
glass would be most useful in melting the chocolate in this case.
Data collected
Below are a table and a graph of our results on the actual day:
Temperature / o C of setup against time / s
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
80.00000
75.00000
o
C
70.00000
Temperature /
Time /
sec
65.00000
Temp / C
54.18421
54.92105
56.78947
58.66667
61.02541
63.55556
65.78947
67.05263
68.31579
69.84206
71.11111
72.55556
73.92105
74.49588
74.85859
60.00000
55.00000
50.00000
0
10
20
30
40
50
60
70
80
90
100 110 120 130 140
Tim e / s
From the above graph we can see that there is an overall increase in the temperature as
we left the setup under the sun. This would mean that our setup was successful in raising
the temperature of the air around the chocolate and that would mean that our setup was
successful in melting the chocolate, reaching temperatures as high as almost 75 o C.
We do note that the initial temperature is not the temperature of the environment since we
had setup before that and timing only starts when required and the chocolate is in place.
During this time the air inside the setup may have been warmed.
Comment on our result
The official time that we were awarded with is 131 seconds, placing us at the ninth place.
This time was based on the time the toothpick took to drop. However we feel that this
isn’t actually a very fair gauge on how fast the chocolate melts. This is since the length of
the toothpick used and angle of which the toothpick is positioned was not standardized.
We kept the toothpick as straight as possible and chose a short one so it can be placed
inside the bowl, but that affected our results. Thus when compared with other groups our
group was slower.
If the toothpick is longer or the angle of inclination is larger, it would affect the time
taken for the toothpick to drop. Because of the innate mass of the toothpick, a longer
toothpick would have more mass and thus more weight and more force would be applied
onto the chocolate, and the increment in pressure increases the rate of melting. Moreover,
a toothpick with larger mass would generate a greater moment about the chocolate, thus it
would drop first. If the angle of inclination is decreased, the further away the center of
gravity would be from the fulcrum and thus this implies that the moment generated is
greater and that the toothpick at a lower angle would drop first too.
Toothpicks
Fulcrum
With the help of the illustration on the left, the
toothpick on the left is twice the length of the one on
the right and thus the weight of it would also be twice
as much. Both are positioned at 60 degrees of angle of
inclination, so the moment, force multiplied by
perpendicular distance, generated by the weight at the
centre of gravity (which is twice as far from the fulcrum)
for the toothpick on the left is in fact four times as
much as the one on the right due to twice the
perpendicular distance and twice the weight. Therefore
this proves that the mass and thus length of the
toothpick does affect the result.
With the help of the illustration on the right, with the
Toothpicks
toothpick on the left being at an angle of inclination of
60 degrees and the toothpick on the right being at an
angle of inclination of 30 degrees, both being the same
length and thus same mass and weight, we would like
to prove that the angle of inclination of the toothpicks
does affect the result. Because of the difference in the
angle of incidence, the perpendicular distance of the
Fulcrum
weight to the fulcrum is greater, in this case by square
root of 3. Take the distance of the left toothpick be 1
unit, so at an angle of 60 degrees the diagonal would be 2 units, thus the vertical would
be root 3 units. Since the toothpick on the right is an inverse of the toothpick on the left
upon a 45 degrees line of symmetry, the vertical would be 1 unit, the diagonal still 2 units
and the horizontal distance root 3 units. Thus the horizontal distance is root 3 times larger,
and so will the moment generated by the toothpick. Thus this proves that angle of
inclination of the toothpick from the ground does affect the result.
Therefore we can conclude that without a standardized length of the toothpick and a
standardized angle of inclination, the resulting moment and force generated by the
toothpick has a vast difference. Because our group used a short toothpick and kept it as
straight as we can, we fall victim to this inconsistency, of which other groups with longer
toothpicks or with a smaller (even if it is only slightly) have an advantage over us and
their toothpick dropped in a shorter amount of time. Thus using this method of keeping
track of when the toothpick actually dropped is not a very good gauge on the extent on
melting of the toothpick.
Limitations of our experiment
Even though our solar chocolate melter is efficient in melting the chocolate, there are still
intrinsic limitations which cannot be ignored:
1. The machine is mainly based on the rudimentary principle on sunlight and
incoming solar radiation; thus essentially it is heavily dependent on weather
conditions. Thus, since weather is unpredictable; if it is cloudy and rainy, our
melter would not work.
2. The machine cannot be commercialized as it focuses incoming light rays onto one
chocolate, not many chocolates. Thus, extensive modifications must be done we
want to extrapolate our set up to mass melting of chocolate
Reflections
After the course of completing this PBL, in retrospect, we think this PBL was an eye
opener and was highly enriching, allowing us to learn and grown on two platforms.
Firstly, on the ubiquitous and cliché academic platform, we learnt more about the
applications of physics concepts and how they can be transferred from the classroom into
the world beyond. In addition, we also learnt about how capricious and whimsical
applying such physics concepts can be, as even though we contrived to the very best to
include as many concepts into our chocolate melter to make the chocolate melt
efficaciously, we were still unable to emerge victorious. Nevertheless, this failure was
seen as a learning opportunity and thus is still valuable in its own right. Moving on to the
other aspect of growth, we felt that this PBL has exposed flaws inherent in our individual
characters and made us more motivated to change them. For one, even though we knew
that Joel and Han Wee would not be present for chocolate melting day, we did not inform
the teacher till two days before the actual run, but by then scheduling another trial run
would not be convenient and in order. Such culminated in only one group member, Chow
Hui, being present, undermining the effectiveness and morale of our team. Thus, this
experience has thought us to be more responsible in my actions and inform the relevant
parties in the event of extenuating circumstances. This experience has also taught us the
importance of teamwork. If we had not discussed the idea for our setup, with only one
person available on the actual day we could not have even performed and made the setup
correctly and within the time limit for us to set up. And even though Chow Hui
understood how to do it, our group would have done better if all three of our members
were present. The absence of two of our members may be one of the reasons why we did
not manage to melt the chocolate efficiently. As a last word, we would like to thank Ms
Tan for giving us this interesting opportunity to do the PBL and we enjoyed the process
as a whole.