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Mechanical Equivalent of Heat Includes 012-04331E Teacher's Notes Instruction Manual and and 5/94 Typical Experiment Results Experiment Guide for the PASCO scientific Model TD-8551A MECHANICAL EQUIVALENT OF HEAT © 1990 PASCO scientific $5.00 012-04331E Mechanical Equivalent of Heat Table of Contents Section ..........................................................................................................Page Copyright and Warranty ..................................................................................ii Equipment Return ............................................................................................ii Introduction ..................................................................................................... 1 Equipment........................................................................................................ 1 Measuring Temperature with the Thermistor .................................................. 2 History ............................................................................................................. 2 Operation ......................................................................................................... 3 Measuring the Mechanical Equivalent of Heat: Experiment................................................................................................. 4 Calculations ............................................................................................... 6 Worksheet .................................................................................................. 7 Maintenace....................................................................................................... 8 Thermistor Specifications: Temperature versus Resistance ................................................................. 9 Biography: Benjamin Thompson—Count Rumford of Bavaria................... 10 Teacher’s Guide.............................................................................................. 11 i Mechanical Equivalent of Heat 012-04331E Copyright, Warranty and Equipment Return Please—Feel free to duplicate this manual subject to the copyright restrictions below. Copyright Notice Equipment Return The PASCO scientific Model TD-8551A Mechanical Should the product have to be returned to PASCO Equivalent of Heat manual is copyrighted and all rights scientific for any reason, notify PASCO scientific by reserved. However, permission is granted to non-profit letter, phone, or fax BEFORE returning the product. educational institutions for reproduction of any part of Upon notification, the return authorization and this manual providing the reproductions are used only for their laboratories and are not sold for profit. Reproduc- shipping instructions will be promptly issued. tion under any other circumstances, without the written consent of PASCO scientific, is prohibited. NOTE: NO EQUIPMENT WILL BE ACCEPTED FOR RETURN WITHOUT AN Limited Warranty AUTHORIZATION FROM PASCO. PASCO scientific warrants this product to be free from defects in materials and workmanship for a period of one When returning equipment for repair, the units year from the date of shipment to the customer. PASCO must be packed properly. Carriers will not accept will repair or replace, at its option, any part of the product responsibility for damage caused by improper which is deemed to be defective in material or workman- packing. To be certain the unit will not be ship. This warranty does not cover damage to the product damaged in shipment, observe the following rules: caused by abuse or improper use. Determination of whether a product failure is the result of a manufacturing ➀ The packing carton must be strong enough for the defect or improper use by the customer shall be made item shipped. solely by PASCO scientific. Responsibility for the return of equipment for warranty repair belongs to the cus- ➁ Make certain there are at least two inches of tomer. Equipment must be properly packed to prevent packing material between any point on the damage and shipped postage or freight prepaid. (Dam- apparatus and the inside walls of the carton. age caused by improper packing of the equipment for ➂ Make certain that the packing material cannot shift return shipment will not be covered by the warranty.) in the box or become compressed, allowing the Shipping costs for returning the equipment, after repair, instrument come in contact with the packing will be paid by PASCO scientific. carton. Address: PASCO scientific 10101 Foothills Blvd. Roseville, CA 95747-7100 Phone: (916) 786-3800 FAX: (916) 786-3292 email: [email protected] web: www.pasco.com ii 012-04331E Mechanical Equivalent of Heat Introduction The principle of the conservation of energy tells us that if a Aluminum Cylinder given amount of work is transformed completely into heat, with embedded the resulting thermal energy must be equivalent to the Thermistor amount of work that was performed. Of course, since work is normally measured in units of Joules and thermal energy Counter is normally measured in units of Calories, the equivalence is not immediately obvious. A quantitative relationship is needed that equates Joules and Calories. This relationship is called the Mechanical Equivalent of Heat. Crank The PASCO scientific Model TD-8551A Mechanical Equivalent of Heat apparatus allows accurate determination Nylon Rope of the Mechanical Equivalent of Heat (to within 5%). The apparatus is shown in Figure 1. A measurable amount of work is performed by turning the crank, which turns the aluminum cylinder. A nylon rope is wrapped several times Mass around the cylinder so that, as the crank is turned, the (≅ 10 kg) friction between the rope and the cylinder is just enough to support a mass hanging from the other end of the rope. This Figure 1 Mechanical Equivalent of Heat Apparatus insures that the torque acting on the cylinder is constant and resistance of the thermistor, the temperature of the cylinder measurable. A counter keeps track of the number of turns. can be determined. By monitoring the temperature change of As the cylinder turns, the friction between the cylinder and the cylinder, the thermal energy transferred into the cylinder the rope converts the work into thermal energy, which raises can be calculated. Finally, the ratio between the work the temperature of the aluminum cylinder. A thermistor is performed and the thermal energy transferred into the embedded in the aluminum so that, by measuring the cylinder determines J, the mechanical equivalent of heat. Equipment The TD-8551A Mechanical Equivalent of Heat apparatus • Digital Ohmmeter for measuring the resistance of the ther- includes the items shown in Figure 2. mistor in the aluminum cylinder. (An analog meter can be used, but accuracy will be significantly sacrificed.) MANUAL Mechanical • Refrigerator (or some ice), for cooling the aluminum cyl- Instruction Equivalent inder below room temperature. Manual of Heat • known Mass of approximately 10 kg which can be sus- Apparatus pended from the nylon rope. (The apparatus comes with a container which can be filled with sand or dirt for the 10 kg mass; if this is done, you will need an accurate balance for Nylon Rope measuring this mass. Of course, you can fill the container Powdered Mass by adding sand in measured increments of 1-2 kg.) Graphite Container • Thermometer for measuring room temperature is conven- ient, though the thermistor can be used for this purpose. Rubber Band • Calipers and a Balance for measuring the mass and diame- ter of the aluminum cylinder if you wish these measure- Figure 2 Equipment ments to be part of the experimental process. (Approximate values are Mass: 200 ± 1.5 grams; Diameter: 4.763 ± 0.02 ➤ IMPORTANT: In addition to the Mechanical cm; Diameter including thickness of nylon rope: Equivalent of Heat apparatus, several other items are 4.94 ± 0.05 cm. These values can be used, but there is needed to measure the mechanical equivalent of heat. some variation, so your results will be more accurate if you These items include: make the measurements yourself.) 1 Mechanical Equivalent of Heat 012-04331E Measuring Temperature with the Thermistor Slip Rings soldered to the copper slip rings (see Figure 3) on the side of To the cylinder. The brushes provide an electrical connection Ohmmeter Banana between the slip rings and the banana plug connectors. By Jacks plugging an ohmmeter into these connectors, the resistance of the thermistor, and therefore it's temperature, can be monitored, even when the cylinder is turning. Although the temperature dependence of the thermistor is Brushes accurate and reliable, it is not linear. You will therefore Figure 3 Measuring the Cylinder Temperature need to use the table of Temperature versus Resistance that To measure the temperature of the aluminum cylinder, a is affixed to the base of the Mechanical Equivalent of Heat thermistor is embedded inside. A thermistor is a tempera- apparatus to convert your resistance measurements into ture dependent resistor. If the resistance of the thermistor is temperature readings. A more complete version of this known, its temperature can be very accurately and reliably table, covering a greater temperature range, is given at the determined. The leads of the thermistor in the cylinder are end of this manual. History It may not seem strange to us today that there is a thing his reasoning a step further, stating his belief that only if called energy that is conserved in all physical interactions. heat were a form of motion would it demonstrate the Energy is
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