PASCO TD-8551A User Manual

Includes

Teacher's Notes

and

Typical

Experiment Results

Instruction Manual and
Experiment Guide for
the PASCO scientific
Model TD-8551A

MECHANICAL

EQUIVALENT

OF HEAT

012-04331E

5/94

© 1990 PASCO scientific $5.00

012-04331E Mechanical Equivalent of Heat

T able 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

The PASCO scientific Model TD-8551A Mechanical
Equivalent of Heat manual is copyrighted and all rights
reserved. However, permission is granted to non-profit
educational institutions for reproduction of any part of
this manual providing the reproductions are used only for
their laboratories and are not sold for profit. Reproduc­tion under any other circumstances, without the written
consent of PASCO scientific, is prohibited.

Limited Warranty

PASCO scientific warrants this product to be free from
defects in materials and workmanship for a period of one
year from the date of shipment to the customer. PASCO
will repair or replace, at its option, any part of the product
which is deemed to be defective in material or workman­ship. This warranty does not cover damage to the product
caused by abuse or improper use. Determination of
whether a product failure is the result of a manufacturing
defect or improper use by the customer shall be made
solely by PASCO scientific. Responsibility for the return
of equipment for warranty repair belongs to the cus­tomer. Equipment must be properly packed to prevent
damage and shipped postage or freight prepaid. (Dam­age caused by improper packing of the equipment for
return shipment will not be covered by the warranty.)
Shipping costs for returning the equipment, after repair,
will be paid by PASCO scientific.

Equipment Return

Should the product have to be returned to PASCO
scientific for any reason, notify PASCO scientific by
letter, phone, or fax BEFORE returning the product.
Upon notification, the return authorization and
shipping instructions will be promptly issued.

ä

NOTE: NO EQUIPMENT WILL BE

ACCEPTED FOR RETURN WITHOUT AN
AUTHORIZATION FROM PASCO.

When returning equipment for repair, the units
must be packed properly. Carriers will not accept
responsibility for damage caused by improper
packing. To be certain the unit will not be
damaged in shipment, observe the following rules:

➀ The packing carton must be strong enough for the

item shipped.

➁ Make certain there are at least two inches of

packing material between any point on the
apparatus and the inside walls of the carton.

➂ Make certain that the packing material cannot shift

in the box or become compressed, allowing the
instrument come in contact with the packing
carton.

Address: PASCO scientific

10101 Foothills Blvd.
Roseville, CA 95747-7100

Phone: [phone]
FAX: [phone]
email: [e-mail]
web: www.pasco.com

ii

012-04331E Mechanical Equivalent of Heat

Introduction

The principle of the conservation of energy tells us that if a
given amount of work is transformed completely into heat,
the resulting thermal energy must be equivalent to the
amount of work that was performed. Of course, since work
is normally measured in units of Joules and thermal energy
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.

The PASCO scientific Model TD-8551A Mechanical
Equivalent of Heat apparatus allows accurate determination
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
around the cylinder so that, as the crank is turned, the
friction between the rope and the cylinder is just enough to
support a mass hanging from the other end of the rope. This
insures that the torque acting on the cylinder is constant and
measurable. A counter keeps track of the number of turns.

As the cylinder turns, the friction between the cylinder and
the rope converts the work into thermal energy, which raises
the temperature of the aluminum cylinder. A thermistor is
embedded in the aluminum so that, by measuring the

Aluminum Cylinder

with embedded

Thermistor

Counter

Crank

Nylon Rope

Mass

(≅ 10 kg)

Figure 1 Mechanical Equivalent of Heat Apparatus

resistance of the thermistor, the temperature of the cylinder
can be determined. By monitoring the temperature change of
the cylinder, the thermal energy transferred into the cylinder
can be calculated. Finally, the ratio between the work
performed and the thermal energy transferred into the
cylinder determines J, the mechanical equivalent of heat.

Equipment

The TD-8551A Mechanical Equivalent of Heat apparatus
includes the items shown in Figure 2.

Mechanical

Equivalent

of Heat

Apparatus

Nylon Rope

Powdered

Graphite

Rubber Band

Figure 2 Equipment

➤ IMPORTANT: In addition to the Mechanical
Equivalent of Heat apparatus, several other items are
needed to measure the mechanical equivalent of heat.
These items include:

MANUAL

Instruction

Manual

Mass

Container

• Digital Ohmmeter for measuring the resistance of the ther-

mistor in the aluminum cylinder. (An analog meter can be
used, but accuracy will be significantly sacrificed.)

• Refrigerator (or some ice), for cooling the aluminum cyl-

inder below room temperature.

• known Mass of approximately 10 kg which can be sus-

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
measuring this mass. Of course, you can fill the container
by adding sand in measured increments of 1-2 kg.)

• Thermometer for measuring room temperature is conven-

ient, though the thermistor can be used for this purpose.

• Calipers and a Balance for measuring the mass and diame-

ter of the aluminum cylinder if you wish these measure­ments to be part of the experimental process. (Approximate
values are Mass: 200 ± 1.5 grams; Diameter: 4.763 ± 0.02
cm; Diameter including thickness of nylon rope:

4.94 ± 0.05 cm. These values can be used, but there is
some variation, so your results will be more accurate if you
make the measurements yourself.)

1

Mechanical Equivalent of Heat 012-04331E

Measuring Temperature with the Thermistor

To

Ohmmeter

Figure 3 Measuring the Cylinder Temperature

Slip Rings

Banana
Jacks

Brushes

To measure the temperature of the aluminum cylinder, a
thermistor is embedded inside. A thermistor is a tempera­ture dependent resistor. If the resistance of the thermistor is
known, its temperature can be very accurately and reliably
determined. The leads of the thermistor in the cylinder are

History

It may not seem strange to us today that there is a thing
called energy that is conserved in all physical interactions.
Energy is a concept we have all grown up with. A hundred
and fifty years ago it was not so evident that there should be
an intimate, quantitative relationship between such appar­ently unrelated phenomena as motion and heat. The
discovery that heat and motion can be seen as different
forms of the same thing—namely energy—was the first and
biggest step toward understanding the concept of energy
and its conservation.

Count Rumford of Bavaria, in 1798, was the first to realize
that work and heat were related phenomena. At that time, it
was commonly believed that heat resulted from the flow of
a massless fluid-like substance called caloric. It was
believed that this substance resided in objects, and that
when they were cut, ground, or otherwise divided into
smaller pieces, the pieces could not hold as much caloric as
the original object. The resulting release of caloric was
what we experience as heat.

While boring cannon for the Bavarian government,
Rumford noticed that heat was produced even when the
boring equipment had become so dulled from use that it was
no longer boring into the iron. The heat therefore was not
dependent on the breaking up of the metal into smaller
pieces. In fact, this meant that a limitless amount of heat
could be produced from the iron and boring equipment, an
idea that was inconsistent with the belief that heat was the
result of the release of a substance that resided in the
material. Rumford realized that a connection existed
between the motion of the bore and the heat. He even took

soldered to the copper slip rings (see Figure 3) on the side of
the cylinder. The brushes provide an electrical connection
between the slip rings and the banana plug connectors. By
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
accurate and reliable, it is not linear. You will therefore
need to use the table of Temperature versus Resistance that
is affixed to the base of the Mechanical Equivalent of Heat
apparatus to convert your resistance measurements into
temperature readings. A more complete version of this
table, covering a greater temperature range, is given at the
end of this manual.

his reasoning a step further, stating his belief that only if
heat were a form of motion would it demonstrate the
properties he had observed.

It was not until the experiments of Joule in 1850, however,
that Rumford's ideas about the nature of heat gained popular
acceptance. Joule performed a variety of experiments in
which he converted a carefully measured quantity of work,
through friction, into an equally carefully measured quantity
of heat. For example, in one experiment Joule used falling
masses to propel a paddle wheel in a thermally insulated,
water-filled container. Measurements of the distance
through which the masses fell and the temperature change
of the water allowed Joule to determine the work performed
and the heat produced. With many such experiments, Joule
demonstrated that the ratio between work performed and
heat produced was constant. In modern units, Joule's results
are stated by the expression:

1 calorie = 4.186 Joule.

Joule's results were within 1% of the value accepted today.
(The calorie is now defined as equal to 4.184 Joule.)

It was this series of experiments that led Joule, along with
several others, to the more general theory that energy is
conserved in all physical processes.

➤ NOTE: See the short biography at the end of
this manual for more information on the life of
Benjamin Thompson—Count Rumford, of Bavaria.

2