Joule is given credit for determining the mechanical equivalent of heat. His experiment
performed work on a container of water in such a way that all of the work was converted
into heat by friction. The temperature of the liquid was measured as work was done on the
system, and Joule discovered that the temperature increase was the same as if the same
amount of heat had been added to the system. Rather than repeat Joule's effort by
converting mechanical energy into heat, we will test whether the energy of a flowing
electrical current causes a similar response. To do this we will compare the
experimental and approximate theoretical values of the heat capacity of the system.
One set of data will be the temperature of the calorimeter versus time.
One data point will be taken every 2.5 seconds for 20 minutes. The resulting 480 points
will be plotted in such a way as to determine the heat capacity of the calorimeter cup.
The other data quantity that must be known is the electrical power supplied to the system.
As we will learn in class, the electrical power in watts due to a flowing electrical
current is given by: P = I V, where I is the current and V
is the voltage. By measuring both I and V, we can determine the input power. In order to
get the energy supplied, it is necessary to multiply the power by the elapsed time. Other
than the thermometer, the apparatus needed to perform this experiment is shown in the
following diagram:
The power supply is controlled by the lower knob. Be especially careful to only use the
0-12 V DC range. Also make sure that the larger upper control knob is set to its minimum
(i.e. fully counter clockwise) before turning on the power. The wiring connections shown
in the diagram should be followed. The current will be measured by the analog meter on the
power supply, and voltage will be measured by a Digital Multi Meter (DMM). On this meter,
you can choose either current or voltage measurement by pressing a button. Hence, the term
"multi meter". Notice that the DMM (which is used as a voltmeter today) has both
leads connected to the calorimeter. This meter is said to be connected in parallel with
the heater (within the calorimeter). The DMM should be set to DC Volts and 20 V maximum by
pushing the appropriate buttons on the front panel. Notice the stirring rod in the
diagram. It is used to gently stir the water so the entire cup is at the same temperature
while data is being taken. If you want good results, it is essential that you stir gently
and consistently for the entire twenty minutes. You can take turns stirring if necessary.
Once you have your experiment set up, ask your instructor to verify the
connections before proceeding.
Start LOGGERPRO, by double clicking JouleHeat.xmbl
in the PHY 184 folder. Measure the mass of the inner calorimeter cup. Place the
inner cup in the calorimeter and replace the cover. Measure the mass of the entire empty
calorimeter. Place cold water from a water cooler in the inner cup until it will just
barely cover the coil of heater wire and then quickly measure the mass of the entire
calorimeter plus water. Determine the mass of the water. After checking to see that the
power adjust knob is fully counterclockwise, turn on the DMM and the power supply. Start
Logger taking data. When "STOP" appears, quickly and smoothly advance the
adjust knob on the power supply until a current of between 3 and 4.5 A is observed on the
rightmost (current) meter. Check that the DMM is indicating a value less than 6.0 V, and
start gently stirring your water. Record the current and voltage values.
Once the experiment is over, return the power knob to its fully counter clockwise position, and turn off the power supply and the DMM. Again measure the mass of the calorimeter. Is there still the same amount of water in the cup? Also save your data on the hard drive as a text (.TXT) file. Now if something disastrous happens while trying to analyze your data, you can retrieve your data. If all has gone well, you should have a relatively straight line displayed on the screen. This is a graph of temperature vs. time.
Next you will determine the heat capacity C of the system (cup plus water). (Note: this is heat capacity not specific heat.) You need to create a graph of Temperature versus Energy Added (i.e. Q). The heat capacity, C, will then be related to the slope of the graph. Create a New Column called Energy Added. Energy Added is electrical power (current times voltage) multiplied by time. On your graph, change the Time axis to be Energy Added. If your entire line is reasonably straight, fit a best fit line to it. If the entire graph is not straight, select a portion that is straight before finding the best fit line. Record the equation of your best line and print your graph. How is the slope of this line related to the experimental value of the heat capacity C of the system? (Hint: consider dimensional analysis.) Calculate the experimental C.
Theoretically the heat capacity of he system is given by:
Calculate the theoretical C using the equation above, your mass data, and the known specfic heats.
Compare this experimental value to your theoretical value from the equation above. If the two values of C agree to within experimental error then the mechanical equivalent of electrical energy has been established experimentally. Comment on the closeness of agreement. If the discrepancy is rather large - like a factor of 4.2, be sure to consider the units that you have used.
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