An Educational Summary of "Resistive
Heating"
Mark Johnson
UBC Department of Physics and Astronomy,
2010
The following is taken from a lecture
designed to teach young physicists about the concept of joule heating. This lecture is beneficial to the
student that is learning about electricity and basic circuits, and is designed
to have the students doing a little bit of thinking on their own without being
completely lectured at. I have
passed a current through a hotdog and so cooked it; this experiment exemplifies
the concept of Joule Heating.
This is a link to the PowerPoint presentation used in lecture.
On the following page you will find some
notes that can be included into your own lecture, and basic instructions for
creating your own hotdog cooker.
How
Joule Heating was discovered:
In 1841 Joule heating, also known as
resistive heating, ohmic heating and electric heating, was discovered by James
Prescott Joule. He passed a
current through a wire of fixed length and observed that the wire increased in
temperature as the current was varied.
He then immersed the wire into a bath of water with fixed mass/volume
and recorded observations with different wire lengths and currents. Joule was able to derive the formula
Q=CI^{2}Rt, where I is current, R is resistance of the wire, t is the
time immersed in the water, and Q is the amount of energy transferred into the
water, measured in joules. C is a
constant, and not necessary to understand the basics of this
lecture, and is omitted from the rest of the lecture.
What
Causes Joule Heating?
Joule heating is "The process by which a
current is passed through a conductor and heat is released" (Wikipedia)
In a complete circuit, electrons move
around the circuit. Electrons are
negatively charged particles, and the ions (charged particles) in the resistor
are positively or negatively charged depending on the material. Often these electrons 'collide' with
ions, and the electrons share their kinetic energy with the ions when they
cause the ions to move about, or vibrate. The kinetic energy displays itself as and increase in temperature, and heat is observed.
Joule heating is exemplified by a java
application, available from the PhET website: "Battery-Resistor Circuit" http://phet.colorado.edu/simulations/sims.php?sim=BatteryResistor_Circuit
It is helpful for students to relate this
new concept to objects in their lives that use joule heating to operate. Have the class brainstorm some of these
objects.
Toaster
Oven
Incandescent
Light bulb
Curling
Iron/Clothes Iron
Electric
Kettle
Dryer
High voltage power transmission lines also
use the concept of joule heating and joule's energy equation to minimize the
amount of energy lost to heat. Q=I^{2}Rt. The resistance of the long distance wires cannot be adjusted
vey much, so the current and votage can be adjusted
to compensate. If using the V=IR
equation and subbing this into the Q=I^{2}Rt equation for I, we can see
that if the current, I, is reduced by ½, then the energy lost can be
reduced by a factor of 4 because of the squared term in the energy
equation. This is the reason that
power transmission lines carry such high voltages, usually not less than 110kV,
and as commonly as much as 230kV or more.
Experiment
Description:
We will use the concepts of joule heating to cook a hotdog. The power source that we will be using
is simply 120V supplied from a common electrical outlet. I have designed the apparatus so that
hotdogs can be connected in different ways. I can cook one hotdog, two hotdogs in parallel, and two
hotdogs in series. It is necessary
to explain to the class that this process works because of the ions contained
in the hotdogs, mostly from the salt.
The
Apparatus:
I
created the hotdog cooker ontop of a piece of 5/8" plywood,
with two 2 sets of three inch common nails through the plywood, 6.25". I bent over the tops of the nails to
create 'skewers' for the electrodes to enter the hotdogs. This bending process proved to be
difficult, as the nails were thick.
I had assistance and used multiple pairs of pliers and a blowtorch to
soften the nails. One must be
careful not to burn the wood while heating the nails.
Wiring
was added, so that the nails are connected together at their bases. Small swiches,
available from 'The Source (old Radio Shack) are used to make it so that the
circuits can be switched from series to parallel. See Fig.1 for the circuit diagram that I used. Using more than 2 hotdogs is practical,
but does not exemplify the addition of resistors in series and parallel, and
how that changes the cooking time.
Figure 1: Hotdog circuit diagram. The blue squares represent
switches. The red dots represent
the bent over nails.
I
painted the plywood black, so that the white wiring stands out for the
viewer. I added plexi-glass sides and top to protect the viewer from
unwanted electrical surges. I also
added a safety switch so that the power can only be activated when the lid is
closed, and another main power switch. (Thus two power switches for
safety). With 120 volts, this
experiment can prove quite dangerous if the proper precautions are not
taken.
Figure 2: picture of apparatus
Two
holes were drilled on one end of the apparatus so that dowells
can be inserted and the apparatus can stand up on end. This allows the class to view it
better, and allows better venting for the steam and smoke that will be created.
I found that when the
apparatus is not standing on end, the glass foggs up
very quickly, limiting the view of any viewers no matter how close.
The hotdogs that I used are schneiders all beef, I these wieners in trials as well as
in the lecture to ensure consistency.
I used a multimeter in the initial trials
to measure current. I only
measured the current in the one-wiener situation, as this was easy to to by connecting the multimeter in the place where the
second hotdog would normally be placed.
I measured the current only in my trials at home, I did not do it during
the class lecture, as it seemed like it was rather lengthy. Instead I presented the data from
previous trials to the class as the hotdogs were cooking.
Experimentation:
While at home, with only one hotdog
plugged in, I did various trials, measuring the current at various time
intervals until the dog stops cooking.
Table 1 shows the results of two of these trials. Also in Table 1 is the resiatance of the hotdog at various times. This resistance is calculated using
V=IR and the average current from 2 of the trials.
Time |
Trial 1 Current |
Trial 2 Current |
Avg. Current |
Avg. Resistance |
0 |
1.5 |
1.5 |
1.5 |
80 |
30 |
1.94 |
2.03 |
1.985 |
60.4534005 |
40 |
2.27 |
2.57 |
2.42 |
49.58677686 |
50 |
2.62 |
3.09 |
2.855 |
42.03152364 |
60 |
3.04 |
3.3 |
3.17 |
37.85488959 |
70 |
3.3 |
3.45 |
3.375 |
35.55555556 |
80 |
3.41 |
3.36 |
3.385 |
35.45051699 |
90 |
3.32 |
3.18 |
3.25 |
36.92307692 |
100 |
3.04 |
2.98 |
3.01 |
39.86710963 |
110 |
2.89 |
2.87 |
2.88 |
41.66666667 |
120 |
2.8 |
2.77 |
2.785 |
43.08797127 |
130 |
2.68 |
2.66 |
2.67 |
44.94382022 |
140 |
2.6 |
2.57 |
2.585 |
46.42166344 |
145 |
2.56 |
2.52 |
2.54 |
47.24409449 |
150 |
2.51 |
2.47 |
2.49 |
48.19277108 |
155 |
2.46 |
2.44 |
2.45 |
48.97959184 |
160 |
2.41 |
2.41 |
2.41 |
49.79253112 |
165 |
2.33 |
2.37 |
2.35 |
51.06382979 |
170 |
2.27 |
2.32 |
2.295 |
52.2875817 |
175 |
2.18 |
2.27 |
2.225 |
53.93258427 |
180 |
2.05 |
2.21 |
2.13 |
56.33802817 |
185 |
1.95 |
2.13 |
2.04 |
58.82352941 |
190 |
1.8 |
2.05 |
1.925 |
62.33766234 |
195 |
0.9 |
1.93 |
1.415 |
84.80565371 |
200 |
0.17 |
1.67 |
0.92 |
130.4347826 |
205 |
0.11 |
1.02 |
0.565 |
212.3893805 |
210 |
0.09 |
0.2 |
0.145 |
827.5862069 |
215 |
0.08 |
0.13 |
0.105 |
1142.857143 |
220 |
0.08 |
0.11 |
0.095 |
1263.157895 |
225 |
0.07 |
0.1 |
0.085 |
1411.764706 |
230 |
0.07 |
0.09 |
0.08 |
1500 |
235 |
0.07 |
0.08 |
0.075 |
1600 |
Table 1: Current in mAmps, Resistance in kOhms
Because the resistance varies with time, I
used the first 24 data points to create an average current and average
resistance. Those values were
0.002505Amps, and 50kOhms.
Notice that the current and resistance
values go to zero/infinity at the end of the experiment. This is because the hotdogs contact
with the nails dries up once the moisture boils. The ends of the hotdog around the nails burn and create an
awful smelling smoke.
When cooking two hotdogs in parallel, it
can be calculated using the resistance addition for parallel circuits and the
voltage law with joules energy law, that the total resistance is only half of
when there is one hotdog, but the total current is double, and the current
through each hotdog is the same as when there is only one hotdog, thus the
cooking time for each hotdog will be identical to when there was only one
hotdog. Make sure that the class
hypothesizes this, and then understands the math involved. This is one of the learning goals for
the lecture.
When cooking two hotdogs in series, it can
be calculated using the resistance addition for series circuits and the voltage
law with joules energy law, that the total resistance is twice that of when
there is one hotdog, and so the current is half of what it was originally. This means that when joules energy law
is applied, Q=I^{2}Rt, that the total energy absorbed is only ¼ of
what it was in the one hotdog case, so it will take 4 times as long to
sufficiently stop cooking. My
observations confirm this, at 13 minutes for a complete cook. This, like the parallel circuit is
important for the students to understand.
The math can get a little confusing for younger audiences, but with
proper subscripts the math becomes intuitive.
Experimentation
summary:
Three experiments were conducted, one
hotdog, two hotdogs in parallel, and two hotdogs in series. Two results were observed. In the first two cases, the same result
was observed, approx 3 minutes and 15 seconds of cooking time. In the third case, with two hotdogs in
series, it was observed that the cooking time was approximately 13 minutes, 4
times that of the other case. Ask
the students: What would have
happened with 3 hotdogs in series?
3 hotdogs in parallel? (as a test to see if they understand the math that was just
proved).
The concept of joule heating is used
often, in everyday kitchen appliances, and to transport electricity without
loss. Joule heating can also be
used to cook hotdogs, but a physiscist would not cook
his lunch in sieries as that
would be a waste of time.
Other
explorations using the hotdogs:
How
much does it cost to cook a hotdog?
It
is often enlightening to think about how much it costs to cook ones lunch. In this case, the hotdogs preparation
is very cheap.
In
British Columbia, electricity costs ~6.724 cents per kWhr. Challenge the students to come up with
a cost for their hotdog preparation.
Use: 120V, 0.002505Amps,
3min 15seconds, and 6.724cents per kWhr.
This
is easily calculated, and some students may figure it out right away. If not, these hints and solution can be
given.
1
watt = 1 volt x 1 amp
1
kilo-watt-hour = the amount of energy in kilo watts consumed per hour
3mins
15 sec = 3.25 minutes,
3.25min/60min = 0.0542 hours
=
120V x 0.002505Amps x 0.0542hours x $0.06724 /1000
=
$1.096 x 10^{-6}
This
cost would be double in Ontario, where coal burning, and triple in California
where power is bought and imported from other places that make power. (Transported at high voltages of
course!)
What
factors contribute to a materials resistance?
For
conductors, like hotdogs or simple copper wires, we find that they all conduct
with a different variety of abilities.
What determines a conductor's ability to conduct, or not conduct
(resistance)?
Obviously,
there are insulating materials that don't conduct at all, but we are not going
to get into that. We are only
dealing with conductors/typical resistors. Again, PhET has a great simulation
that expemlifies this.
Visit:
http://phet.colorado.edu/simulations/sims.php?sim=Resistance_in_a_Wire
Play
with LED's:
When
inserted into a hotdog, an LED will light up. Be careful about how far apart the legs of the LED are,
because if they are too far apart the LED will absorb too much current and will
break (another example of joule heating).
In my case, the ends of the nail/electrodes are 70mm apart. The LED legs are 2 mm apart, therefore they are using 3.4 volts of the available
120 volts. The hotdog
is being cooked by the other 116.6 volts. It can be calculated that if an LED has a 5.0V rating, it
will be damaged if the legs are separated by anymore than 2.91mm. It is amusing for the class if you
separate the legs by a lot more than 2.91mm (I did 3cm) and overload the LED on
purpose. It will glow a bright
color briefly, then sizzle and turn off.
IN
SUMMARY:
"Joule
heating is the process by which a current is passed through a conductor and
heat is released" (wikipedia), It is expempified
in many of our household appliances, and when cooking hotdogs by
electrocution. With this
experiment the audience has learned about the differences in energy expelled by
a series and a parallel resistance circuit. The audience has confirmed Joules
energy law: Q=I^{2}Rt, and
learned how the current changes with parallel and series circuitry.