LPC Physics
Joule’s Law and the Electrical Equivalent of Heat
Joule’s Law and the Electrical Equivalent of Heat
Purpose:
To verify the conversion factor, 1 cal. = 4.18 Joules.
Equipment:
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Double-walled calorimeter
Heating coil with stirrer
Power Supply
Enviro-Safe Thermometer
Standard Temperature Probe and LabPro Kit
Rods and Clamps
2 DMMs
Balance
Stopwatch
400 ml beaker, ice, water
Patch cords, Alligator clips
Theory:
The work W done (or energy expended) per unit charge in moving a charge q from one
point to another is the potential difference, or voltage V
V 
or
W
q
W  qV
Eq. 1
The time rate of flow of charge is described in terms of current I and
I
q
t
Eq. 2
Hence, Eq. 1 may be written
W  qV  IVt
Eq. 3
which represents the work done or the energy expended in a circuit in time t. This is
often expressed as work or energy per time, or power P:
P
W
 IV
t
Eq. 4
The expended energy can be written in terms of the resistance R of the circuit or a
particular circuit element by Ohm’s law, V=IR. Using this relationship, Eq. 3 has the
various forms:
W  IVt  I 2 Rt 
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V 2t
R
Eq. 5
LPC Physics
Joule’s Law and the Electrical Equivalent of Heat
The electrical energy expended is manifested as heat energy, and is commonly called
joule heat or I2R losses, I2R being the power or energy expended per time.
Equation 5 shows how the joule heat varies with resistance:
1. For a constant current, I, the joule heat is directly proportional to the resistance,
I2R.
2. For a constant voltage, V, the joule heat is inversely proportional to the resistance,
V2 R.
The energy expended in an electrical circuit as given by Eq. 5 is in the units of
joules. The relationship (conversion factor) between joules and heat units in calories was
established by James Joule from mechanical considerations – the mechanical equivalent
of heat. You may recall that in his mechanical experiment, Joule had a descending
weight turn a paddle wheel in a liquid. He then correlated the mechanical (gravitational)
potential energy lost by the descending weight to the heat generated in the liquid. The
result was 1 cal = 4.18 J. A similar electrical experiment may be done to determine the
“electrical equivalent of heat”. By the conservation of energy, the heat equivalents of
mechanical and electrical energy are the same (i.e. 1 cal = 4.18 J).
Experimentally, the amount of electrical joule heat generated in a circuit element
of resistance R is measured by calorimetry methods. If a current is passed through a
resistance (immersion heater) in a calorimeter with water in an arrangement as illustrated
in Figure 1, by the conservation of energy the electrical energy expended in the resistance
is equal to the heat energy (joule heat) Q gained by the system:
electrical energy = heat gained
W Q
IVt  (m w c w  mcal ccal )(T f  Ti )
or
Eq. 6
where the m’s and c’s are the masses and specific heats of the water and calorimeter cup,
as indicated by the subscripts. Tf and Ti are the final and initial temperatures of the
system, respectively.1
DIGI 35A
V
C
-
+
G +
A
-
V
Figure 1
111
The theory section of this lab was shamelessly borrowed from:
Jerry D. Wilson. Physics Laboratory Experiments, 2nd Edition. Lexington MA: D.C. Heath and Company,
1986. Experiment 35.
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LPC Physics
Joule’s Law and the Electrical Equivalent of Heat
Experiment:
1. Measure the mass of the empty calorimeter.
2. Fill the inner calorimeter cup with 200 ml of water, cooled to about 10o C below
room temperature. Be sure to record this temperature as To.
3. Measure mass of the inner calorimeter cup and water.
4. Check your coil in the calorimeter such that it does not touch itself thus shorting some
of its elements.
5. Place the lid on the calorimeter. Make sure the stirring rod does not touch the coil
and short out the circuit. Suspend the thermometer (or temperature probe) such that it
does not touch the coil or interfere with stirring. NOTE: If the thermometer (or
probe) does not fit well in the cork or rubber stopper, use a wad of paper towels to
suspend it.
6. Hook up Joule's heating coil with one DMM as an ammeter and a second as a
voltmeter (see Figure 1). To get a good connection, it may be necessary to remove
the two knobs on the calorimeter and directly connect the circuit to the threaded
screws using alligator clips.
7. If using a temperature probe, follow Steps 7 - 11. If using a thermometer, skip to
Step 12.
8. Connect the AC adapter to the LabPro by inserting the round plug on the 6-volt
power supply into the side of the interface. Shortly after plugging the power supply
into the outlet, the interface will run through a self-test. You will hear a series of
beeps and blinking lights indicating a successful startup.
9. Attach the LabPro to the computer using the USB cable. The LabPro computer
connection is located on the right side of the interface. Slide the door on the
computer connection to the right and plug the square end of the USB cable into the
LabPro USB connection.
10. Connect a temperature probe to the LabPro.
11. Start the program Logger Pro3.3. If everything is correctly attached, then the
appropriate temperature charts and graphs should be displayed.
12. Currently, the experiment is set to collect for 180 seconds. You may wish to extend
the collection period by choosing Experiment > Data Collection and changing the
length of the collection time. If you still need more time, you can press Ctl+T to
extend the collection period by 270 seconds. However, it is not necessary to get all
the data in one run.
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LPC Physics
Joule’s Law and the Electrical Equivalent of Heat
13. IMPORTANT: Turn on the power only when the coil is under water so it doesn't
burn out.
14. With no ice present, turn on the power supply. Record the current, voltage and
temperature every 60 seconds until the water is heated to 10o C above room
temperature. Keep an accurate record of time. It is essential to stir vigorously and
continuously by raising and lowering the stirrer vertically throughout the
experiment. Take turns.
Analysis:
1. Graph the results of m w c w T  To w  mcal ccal T  To cal vs. IV (t  t o ) .
2. Draw the best straight line from your graph and calculate the slope and the
uncertainty in the value. Be sure to use error bars on your graph.
3. Determine the conversion factor from calories to Joules, i.e.: (J/cal) x the number of
cal = the number of Joules.
4. Discuss precision and error. How could the experimental procedure be altered to
give more accurate results?
Results:
Write at least one paragraph describing the following:
 what you expected to learn about the lab (i.e. what was the reason for conducting the
experiment?)
 your results, and what you learned from them
 Think of at least one other experiment might you perform to verify these results
 Think of at least one new question or problem that could be answered with the
physics you have learned in this laboratory, or be extrapolated from the ideas in this
laboratory.
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LPC Physics
Joule’s Law and the Electrical Equivalent of Heat
Clean-Up:
Before you can leave the classroom, you must clean up your equipment, and have your
instructor sign below. How you divide clean-up duties between lab members is up to you.
Clean-up involves:
 Completely dismantling the experimental setup
 Removing tape from anything you put tape on
 Drying-off any wet equipment
 Putting away equipment in proper boxes (if applicable)
 Returning equipment to proper cabinets, or to the cart at the front of the room
 Throwing away pieces of string, paper, and other detritus (i.e. your water bottles)
 Shutting down the computer
 Anything else that needs to be done to return the room to its pristine, pre lab form.
I certify that the equipment used by ________________________ has been cleaned up.
(student’s name)
______________________________ , _______________.
(instructor’s name)
(date)
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