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=CI2Rt, 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=I2Rt.  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=I2Rt 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=I2Rt,  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.

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=I2Rt, and learned how the current changes with parallel and series circuitry.