Digital Kenyon: Research, Scholarship, and Creative Exchange
Faculty Publications
Physics
2002
Nineteenth‐Century Measurements of the
Mechanical Equivalent of Heat
Tom Greenslade
Kenyon College, [email protected]
Follow this and additional works at: http://digital.kenyon.edu/physics_publications
Part of the Physics Commons
Recommended Citation
”Nineteenth-Century Measurements of the Mechanical Equivalent of Heat”, The Physics Teacher, 40, 243-248 (2002)
This Article is brought to you for free and open access by the Physics at Digital Kenyon: Research, Scholarship, and Creative Exchange. It has been
accepted for inclusion in Faculty Publications by an authorized administrator of Digital Kenyon: Research, Scholarship, and Creative Exchange. For
more information, please contact [email protected].
Nineteenth‐Century Measurements of the Mechanical Equivalent of Heat
Thomas B. Greenslade Jr.
Citation: The Physics Teacher 40, 243 (2002); doi: 10.1119/1.1474151
View online: http://dx.doi.org/10.1119/1.1474151
View Table of Contents: http://scitation.aip.org/content/aapt/journal/tpt/40/4?ver=pdfcov
Published by the American Association of Physics Teachers
Articles you may be interested in
Nanoscale specific heat capacity measurements using optoelectronic bilayer microcantilevers
Appl. Phys. Lett. 101, 243112 (2012); 10.1063/1.4772477
Nineteenth-Century Textbook Illustrations: A Frontispiece Puzzle
Phys. Teach. 47, 226 (2009); 10.1119/1.3098208
Construction of an innovative heating apparatus for ultrahigh vacuum platens used in high pressure
reaction cells
Rev. Sci. Instrum. 75, 983 (2004); 10.1063/1.1666993
Equilibrium structural model of liquid water: Evidence from heat capacity, spectra, density, and other
properties
J. Chem. Phys. 109, 7379 (1998); 10.1063/1.477344
The Gibbs–Thomson effect and intergranular melting in ice emulsions: Interpreting the anomalous heat
capacity and volume of supercooled water
J. Chem. Phys. 107, 10154 (1997); 10.1063/1.475322
This article is copyrighted as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
138.28.20.194 On: Sun, 11 Oct 2015 18:24:42
Nineteenth-Century
Measurements
of the Mechanical
Equivalent of Heat
Thomas B. Greenslade, Jr.
oday the measurement of the mechanical
equivalent of heat is a laboratory exercise in
which the student tries to come close to the
accepted value. How different was the attitude of the 19th-century physicists and engineers, for
which the value was a key link between mechanics and
thermodynamics, two seemingly separate domains of
physics. This article discusses some of the pioneering
experiments, translating them into modern nomenclature and units.
T
Definitions
You can raise the temperature of a system in two
ways. If the system is at a temperature below that of its
surroundings and it is connected to them by a thermal
link, energy in the form of heat will be transferred to
the system. The increase in the temperature of the system, ⌬T, is related to the quantity of heat transferred,
Q, by Q = mC⌬T, where m is the mass of the system
and C is a constant of proportionality determined by
the nature of the material of the system. If we let C
have the value of 1 cgs unit, m be 1 g, and ⌬T be 1⬚C,
centered about a value such as 15⬚C, then Q is measured in units of calories.
On the other hand, work can be done on the system to raise its temperature. This can be electrical
work, in which the power dissipated in a resistor during a given time is used to find the magnitude of the
work. Or, mechanical work can be done on the system, resulting in an increase in its temperature. This
work is measured in joules.
The ratio of the work necessary to raise the temper-
Tom Greenslade has a large collection of 19th- and early 20th-century physics books,
and his house is currently decorated with pieces of early physics teaching apparatus. In
May 2002, he will retire from Kenyon College after 38 years of teaching physics, but he
plans to keep on writing and will teach electronics part time.
Department of Physics
Kenyon College
Gambier, OH 43022
[email protected]
Thomas B.
Greenslade, Jr.
243
This article is copyrighted as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions.
Downloaded to IP:
138.28.20.194 On: Sun, 11 Oct 2015 18:24:42
THE PHYSICS TEACHER ◆ Vol. 40, April 2002
Table I. Some values obtained by various experimenters for the mechanical equivalent of heat.
Year
Experimenter(s)
Method
Results
1842
Mayer
Difference between CP and CV
3.58 J/cal
1843
Joule
Heating coil in stationary water
4.51
1843
Joule
Forcing water through small holes
4.14
1845
Joule
Compressing air
4.27, 4.42
1845
Joule
Free expansion of air
4.41, 4.38, 4.09
1845
Joule
Falling weights stirring water
4.79
1847
Joule
Falling weights stirring water or oil
4.203
1848
Joule
Falling weights stirring water
4.15
1849
Joule
Falling weights stirring water
4.1545
1849
Joule
Falling weights stirring mercury
4.1619
1849
Joule
Rubbing cast-iron disks together
4.1669
1860–61
Hirn
Percussive effects
4.17
1865
Hirn
Stirring water; use of dynamometer
4.234
1867
Joule
Heating coil in stationary water
4.295
1870–78
Joule
Stirring water; use of dynamometer
4.1538
Rowland
Stiring water; use of dynamometer
4.189
Work output of steam engine
4.1609
1877–78
1896
Reynolds & Moorby
1883
Griffiths
Heating coil in stationary water
4.195
1892
Miculescu
Stirring water; use of dynamometer
4.187
1895
Schuster & Gannon
Heating coil in stationary water
4.190
1899
Callendar & Barnes
Heating coil in flowing water
4.184
Modern defined value
ature of a system a given number of degrees to the
amount of heat transferred to the system that has the
same effect is called the mechanical equivalent of heat,
or Joule’s constant. The usual symbol is J, and the generally accepted value is 4.186 J/cal. As we shall see,
this is a difficult experimental value to obtain.
Overall View of Methods for
Measuring Joule’s Constant
The typical measurement of Joule’s constant involves some method of doing work on a fluid (usually
water, but occasionally mercury or sperm oil) and
finding the resulting increase in the temperature of the
fluid. Because a system at an elevated temperature
tends to leak heat through radiation, conduction, and
convection, precautions have to be taken to stop these
leaks. The alternative is to assume that the temperature
of the system falls below the true temperature in a way
predicted by Newton’s law of cooling and to apply appropriate corrections.
4.186
The methods of doing work on the water can be
arranged in a few broad categories:
1. Electrical and magnetic effects, such as resistive
heating of wires immersed in the fluid and
eddy-current heating.
2. Frictional effects, such as forcing a liquid through
small apertures, rubbing two pieces of metal together, and stirring liquids with paddle wheels.
3. Percussive effects, in which two massive bodies
make a partly elastic collision.
4. Thermodynamic effects, such as the compression
and expansion of gases and the difference between
specific heats of gases at constant pressure and constant volume.
Table I lists the majority of published measurements of the value of J up to the end of the 19th century. The number of significant figures listed reflects
that reported by the original experimenters.
THE PHYSICS TEACHER ◆ Vol. 40, April 2002
244
This article is copyrighted
as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
138.28.20.194 On: Sun, 11 Oct 2015 18:24:42
Fig. 1. Joule’s 1843 apparatus. The coil in the horizontal
tube is rotated in the field of an (unshown) electromagnet.1
Fig. 2. Joule used falling weights to do work at a constant rate on the coil shown in Fig. 1.1
Electrical and Magnetic Methods of
Obtaining Joule’s Constant
Before describing these experiments, it is well to remember that our present-day, well-standardized units
for electrical measurements did not exist in the 19th
century. There are references to the electrical equivalent of heat, as well as the more common mechanical
equivalent of heat. The two should have the same values, provided that proper electrical units are used.
1. Heating coil in stationary water. The earliest
measurement of the mechanical equivalent of heat by
James Prescott Joule (1818–1889) involved heating
water with a form of dynamo and noting the increase
in the temperature of the water.l The basic apparatus
is shown in Fig. 1. The crank on the right-hand side
drives the apparatus on the left-hand side at a rapid
rate of rotation, usually 600 rpm. The horizontal
cylinder on the left is a thermally insulated glass jar
filled with water. Inside is a coil of wire with its axis
parallel to the jar. The rotating-jar system is placed
between the poles of an electromagnet (not shown),
and the current from the resulting induced emf is
taken off by a commutator at the bottom of the
rotating shaft and fed to a galvanometer. The system
is thus an electrical generator, with a means of measuring the temperature increase of the rotating armature.
With this apparatus, Joule found that the “heat
evolved by the coil of the magneto-electric machine
[generator] is proportional to the square of the current.” This is the first explicit statement of Joule’s law,
which in today’s nomenclature would be written as
“the power dissipated by the current I though the coil
of resistance R is equal to I 2R.” In a given time t, the
temperature rise of the system, ⌬T, is proportional to
the energy dissipated, I 2Rt, measured in joules. Joule’s
constant is thus J = I 2Rt /mC⌬T, where mC is the sum
of the masses and specific heat capacities of the water,
the rotating coil of wire, and the glass jar. Joule used
weights adjusted to fall at a constant rate (Fig. 2) to
measure the work, and found that “1⬚ of heat per lb of
water is therefore equivalent to a mechanical force capable of raising a weight of 896 lb to the perpendicular
height of one foot.” Translated into modern terms,
1 BTU of heat is the equivalent of 896 ft-lb of work.
The corresponding value of J is 4.51 J/cal.
2. Heating coil in flowing water. The continuous
flow calorimeter was developed by Callendar and
Barnes for their 1899 determination of Joule’s constant.2 In Fig. 3, an electrical heater runs the length
of the long glass tube, and water is allowed to flow
through it at a constant and measured rate. The
temperature of the water is measured at the inlet and
outlet, giving the temperature increase ⌬T. In the
original apparatus, a vacuum jacket surrounded the
flow tube to minimize the transfer of heat to the surroundings. Laboratory apparatus manufacturers used
to supply continuous flow calorimeters to allow
introductory students to measure Joule’s constant,
and I have used this within the last 10 years for nonscience majors.
PHYSICS TEACHER ◆ Vol. 40, April 2002
245
This article THE
is copyrighted
as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions.
Downloaded to IP:
138.28.20.194 On: Sun, 11 Oct 2015 18:24:42
Frictional Effects Used to Obtain
Joule’s Constant
Fig. 3. Callendar and Barnes’ constant flow method of
determining J using electrical heating of the water.3
Fig. 4. Joule’s 1849 apparatus using steadily falling
weights to stir water. The cut shown is from Preston,5
and is slightly more compact than Joule’s original figure.
Note that the artist has both cords coming off the same
side as the shaft, which is obviously an error.
1. Forcing water through small apertures. In an
appendix to his 1843 paper on the electrical heating
of water,1 Joule mentioned an experiment in which
he noted that “heat is evolved by the passage of water
through narrow tubes.” He used a piston, pierced
with a number of small holes, being pushed by a
known force through water contained in a cylindrical
glass cylinder. His results, translated into modern
nomenclature, gave a value for Joule’s constant of
4.14 J/cal. This figure is accurate, only 1% below
the standard value of J, but Joule’s use of “about” in
reporting his results suggests a low precision.
2. Stirring water using falling weights. If only
one experiment on the mechanical equivalent of heat
is mentioned and illustrated in a textbook, it is
almost always the technique described in Joule’s classic 1849 paper,4 in which the mechanical energy
from slowly falling weights is used to stir a water
bath and raise its temperature. Joule had tried this
technique before in 1845 and had obtained a rough
value of 4.79 J/cal. A repetition of this experiment
in 1847 using water and then sperm oil as the resistive medium gave an average value for J of 4.203
J/cal.
Figure 4, from Joule’s original paper, shows the essential parts: A copper calorimeter filled with about
6.3 kg of water was fixed firmly in place. A brass paddle wheel with eight vanes rotated in the water, stirring
it and doing work on it. Joule concluded that 772.692
ft-lb of work was necessary to raise the temperature of
1 lb of water 1°F, corresponding to J = 4.1545 J/cal. A
modern experimenter would truncate some of Joule’s
extra significant figures.
Percussive Effects Used to Obtain
Joule’s Constant
Fig. 5. The apparatus used in Hirn’s 1865 percussive
method of determining Joule’s constant.
Only one experimenter used a large-scale collision
to obtain a value for Joule’s constant, but the experiment by the French engineer Gustave Adolphe Hirn
(1815–1890) was so heroic in scale that it needs to be
discussed in detail.6 Figure 5 shows the apparatus. An
anvil of stone (BB in the figure) of mass 941 kg was
suspended by ropes (see the side views) from a stout
THE PHYSICS TEACHER ◆ Vol. 40, April 2002
246
This article is copyrighted
as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
138.28.20.194 On: Sun, 11 Oct 2015 18:24:42
wooden framework about 2 m high. The hammer
(AA), a cylinder of iron with a mass of 350 kg, was
raised through a vertical distance of 1.116 m and released from rest. After the partly-elastic collision, the
iron hammer rebounded to a height of 0.87 m, and the
stone hammer reached a height of 0.103 m above its
equilibrium position. The experiment was done on a
cool day at an air temperature of about 8⬚C.
In between the anvil and the hammer was a cylinder of lead, partly flattened by the collision. Immediately after the collision, the cavity in the lead was filled
with a known mass of water whose temperature was
monitored. Corrections were made for the cooling of
the block during the time necessary to pour in the water. Although he assumed an exponential decrease in
the temperature, the data could have been fitted with a
linear decrease for the short time interval involved.
Greenslade6 gives the details of the calculations, leading to a value of J = 4.17 J/cal.
In a lecture demonstration at the Royal Institution
in 1862,7 John Tyndall showed that when a lead ball is
dropped four times from a height of 26 ft onto an iron
plate, the temperature of the ball increased. This is
probably the origin of the percussive method for measuring Joule’s constant used by Millikan and Gale
(1906) in their student laboratory handbook.8 A cardboard tube, closed at both ends and with an interior
length of 1 m, has birdshot (steel or lead) inside. The
temperature of the shot is taken at the beginning of the
experiment, and again after the tube has been inverted
100 times. In principle, this is the equivalent of dropping the shot 100 m; in practice the temperature rise is
nowhere as great as expected.9
Thermodynamic Methods Used to
Obtain Joule’s Constant
a. Specific Heat Differences. The first deliberate
method of measuring the mechanical equivalent of
heat seems to be the thermodynamic technique
employed by the German physician Robert Mayer
(1814–1878) in 1842. The specific heat capacity of a
gas depends on the physical conditions under which
work is done on it. The amount of work necessary to
raise the temperature of an enclosed volume of gas
under conditions of constant pressure is greater than
that under conditions of constant volume. This is
due to the fact that in the first case, work must be
Fig. 6. Joule’s 1845 apparatus used to measure the
effects of compressing a known volume of air to a
known final pressure.
done to expand the gas against the external pressure.
We can thus say that
MCP⌬T – MCV⌬T = P⌬V
is the work done by the gas on the surrounds as it
expands. In this expression, M is the mass of the gas,
⌬T is the temperature rise, and the two C values are
the specific heats. If we keep in mind that the two
sides of the equation are in different energy units, we
can write J = M(CP – CV )⌬T/P⌬V. Mayer did not
actually do the experiment, but relied instead on
somewhat inaccurate data. However, his value for
Joule’s constant of 3.58 J/cal is remarkably close to
the accepted modern value.
b. Compressing Air. In one of his 1845 papers,10
Joule used a hand pump to compress air into a cylinder and observed the resulting increase in temperature of the water. The apparatus is shown in Fig. 6.
Dry air from the calcium-chloride-filled container G
and at a temperature indicated by the water in container W was slowly pumped into the brass pressure
vessel R. Heat leaks from the water surrounding the
pressure vessel were reduced by containing it in a
double-walled container. The temperature of the
compressed air went up and increased the tempera-
PHYSICS TEACHER ◆ Vol. 40, April 2002
247
This article THE
is copyrighted
as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions.
Downloaded to IP:
138.28.20.194 On: Sun, 11 Oct 2015 18:24:42
ture of the water surrounding the pressure vessel.
The volume of the air initially in the pressure vessel
at atmospheric pressure was known, and the volume
of the compressed air was measured by releasing it in
a pneumatic trough at atmospheric pressure and
room temperature. The relationship pV = constant
enabled the initial and final pressures and volumes to
be known, and the net work done on the gas was the
area under the hyperbolic pressure-volume curve.
Corrections were made for frictional effects in the
cylinder and piston, and the values of Joule’s constant
for two runs were 4.27 and 4.42 J/cal, which Joule
regarded as acceptably close to his 1843 result of
4.51 J/cal.
c. Releasing compressed air. In a related experiment discussed in the same paper, compressed air in
a pressure vessel held in a water tank was allowed to
leak out slowly. The released air was allowed to travel
through a long length of tubing coiled up in the
water tank and was captured in a pneumatic trough
to estimate its final volume. Again, the starting and
final points on the pressure-volume graph were located, and the work calculated by the area under the
curve. This time Joule obtained 4.41, 4.38, and 4.09
J/cal. Today we would say that the air had undergone a throttling process and use the physical principle in our refrigerators.
Conclusion
It is my hope that physics teachers will be willing
to use portions of this material in their classes to help
break the cycle of problems that most students consider the reason for studying physics. Since we will certainly continue to rely heavily on the solution of problems as primary methods of teaching physics to students and assessing their grasp of ideas and their application, I have supplied a number of historical physical
situations that may be used as the basis for homework
and examination problems.11
Acknowledgment
The writing of this paper was inspired by work done
with Jason Summers, a physics major in the Kenyon
class of 1998.
References
1. James P. Joule, “On the calorific effects of magneto-electricity, and on the mechanical equivalent of heat,” Phil.
Mag. ser 3, xxiii (1843), reprinted in The Scientific Papers of James Prescott Joule (Taylor and Francis, London,
1884), pp. 123–159.
2. H.L. Callendar and Barnes, Phil. Trans. A (1899). The
original paper was not consulted, but there is a good discussion of it in J. K.Roberts, Heat and Thermodynamics
(Blackie, London, 1928), pp. 44–45.
3. Thomas Preston, The Theory of Heat, 2nd ed., revised by
J. Rogerson Cotter (MacMillan and Co., London,
1904), p. 321.
4. J.P. Joule, “On the mechanical equivalent of heat,”
reprinted in The Scientific Papers of James Prescott Joule
(Taylor and Francis, London, 1884), pp. 298–328.
5. Ref. 3, p. 301
6. G.A. Hirn, Theorie Mecanique de la Chaleur, premiere
partie: Exposition Analytique et Experimental, 2nd ed.
(Gauthier-Villars, Paris, 1865). See also Thomas B.
Greenslade, Jr., “A striking Joule’s constant determination,” Phys. Teach. 18, 208–209 (March 1980).
7. John Tyndall, Heat Considered as a Mode of Motion (D.
Appleton and Company, New York, 1873), pp. 54–55.
8. Robert Andrews Millikan and Henry Gordon Gale, A
Laboratory Course in Physics (Ginn, Boston, 1906), pp.
59–62.
9. Thomas B. Greenslade, Jr., “Joule’s constant revisited,”
Phys. Teach. 17, 530–531 (Nov. 1979).
10. J.P. Joule, “On the changes of temperature produced by
the rarefaction and condensation of air,” Phil. Mag. ser
3, xxiii, 369–383 (1845).
11. Thomas B. Greenslade, Jr., “Examination questions
based on historical apparatus,” Phys. Teach. 37, 172–173
(March 1999).
THE PHYSICS TEACHER ◆ Vol. 40, April 2002
248
This article is copyrighted
as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
138.28.20.194 On: Sun, 11 Oct 2015 18:24:42