Century Measurements of the Mechanical Equivalent of Heat

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2002

Nineteenth‐Century Measurements of the Mechanical Equivalent of Heat

Tom Greenslade Kenyon College, [email protected]

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Recommended Citation ”Nineteenth-Century Measurements of the Mechanical Equivalent of Heat”, The Physics Teacher, 40, 243-248 (2002)

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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

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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 the system. The increase in the temperature of the sys- equivalent of heat is a laboratory exercise in tem, ⌬T, is related to the quantity of heat transferred, which the student tries to come close to the Q, by Q = mC⌬T, where m is the mass of the system Taccepted value. How different was the atti- and C is a constant of proportionality determined by tude of the 19th-century physicists and engineers, for the nature of the material of the system. If we let C which the value was a key link between mechanics and have the value of 1 cgs unit, m be 1 g,and ⌬T be 1ЊC, thermodynamics, two seemingly separate domains of centered about a value such as 15ЊC, then Q is meas- physics. This article discusses some of the pioneering ured in units of calories. experiments, translating them into modern nomencla- On the other hand, work can be done on the sys- ture and units. tem to raise its temperature. This can be electrical work, in which the power dissipated in a resistor dur- Definitions ing a given time is used to find the magnitude of the You can raise the temperature of a system in two work. Or, mechanical work can be done on the sys- ways. If the system is at a temperature below that of its tem, resulting in an increase in its temperature. This surroundings and it is connected to them by a thermal work is measured in joules. link, energy in the form of heat will be transferred to 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.

◆ This article THEis copyrighted PHYSICS TEACHER as indicatedVol. 40,in the April article. 2002 Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions.243 Downloaded to IP: 138.28.20.194 On: Sun, 11 Oct 2015 18:24:42 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 1877–78 Rowland Stiring water; use of dynamometer 4.189 1896 Reynolds & Moorby Work output of steam engine 4.1609 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 4.186

ature of a system a given number of degrees to the The methods of doing work on the water can be amount of heat transferred to the system that has the arranged in a few broad categories: same effect is called the mechanical equivalent of heat, or Joule’s constant. The usual symbol is J, and the gen- 1. Electrical and magnetic effects, such as resistive erally accepted value is 4.186 J/cal. As we shall see, heating of wires immersed in the fluid and this is a difficult experimental value to obtain. eddy-current heating. 2. Frictional effects, such as forcing a liquid through Overall View of Methods for small apertures, rubbing two pieces of metal to- Measuring Joule’s Constant gether, and stirring liquids with paddle wheels. The typical measurement of Joule’s constant in- 3. Percussive effects, in which two massive bodies volves some method of doing work on a fluid (usually make a partly elastic collision. water, but occasionally mercury or sperm oil) and 4. Thermodynamic effects, such as the compression finding the resulting increase in the temperature of the and expansion of gases and the difference between fluid. Because a system at an elevated temperature specific heats of gases at constant pressure and con- tends to leak heat through radiation, conduction, and stant volume. convection, precautions have to be taken to stop these leaks. The alternative is to assume that the temperature Table I lists the majority of published measure- of the system falls below the true temperature in a way ments of the value of J up to the end of the 19th cen- predicted by Newton’s law of cooling and to apply ap- tury. The number of significant figures listed reflects propriate corrections. that reported by the original experimenters.

THE PHYSICS TEACHER ◆ Vol. 40, April 2002 This article is copyrighted244 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 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 arma- ture. With this apparatus, Joule found that the “heat Fig. 1. Joule’s 1843 apparatus. The coil in the horizontal tube is rotated in the field of an (unshown) electromag- evolved by the coil of the magneto-electric machine net.1 [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 “1Њ of heat per lb of water is therefore equivalent to a mechanical force ca- Fig. 2. Joule used falling weights to do work at a con- pable of raising a weight of 896 lb to the perpendicular stant rate on the coil shown in Fig. 1.1 height of one foot.” Translated into modern terms, 1 BTU of heat is the equivalent of 896 ft-lb of work. Electrical and Magnetic Methods of The corresponding value of J is 4.51 J/cal. Obtaining Joule’s Constant 2. Heating coil in flowing water. The continuous Before describing these experiments, it is well to re- flow calorimeter was developed by Callendar and member that our present-day, well-standardized units Barnes for their 1899 determination of Joule’s con- for electrical measurements did not exist in the 19th stant.2 In Fig. 3, an electrical heater runs the length century. There are references to the electrical equiva- of the long glass tube, and water is allowed to flow lent of heat, as well as the more common mechanical through it at a constant and measured rate. The equivalent of heat. The two should have the same val- temperature of the water is measured at the inlet and ues, provided that proper electrical units are used. outlet, giving the temperature increase ⌬T. In the original apparatus, a vacuum jacket surrounded the 1. Heating coil in stationary water. The earliest flow tube to minimize the transfer of heat to the sur- measurement of the mechanical equivalent of heat by roundings. Laboratory apparatus manufacturers used James Prescott Joule (1818–1889) involved heating to supply continuous flow calorimeters to allow water with a form of dynamo and noting the increase introductory students to measure Joule’s constant, in the temperature of the water.l The basic apparatus and I have used this within the last 10 years for non- is shown in Fig. 1. The crank on the right-hand side science majors.

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

Fig. 3. Callendar and Barnes’ constant flow method of through narrow tubes.” He used a piston, pierced determining J using electrical heating of the water.3 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 clas- sic 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 Fig. 4. Joule’s 1849 apparatus using steadily falling weights to stir water. The cut shown is from Preston,5 in 1847 using water and then sperm oil as the resis- and is slightly more compact than Joule’s original figure. tive medium gave an average value for J of 4.203 Note that the artist has both cords coming off the same J/cal. side as the shaft, which is obviously an error. Figure 4, from Joule’s original paper, shows the es- sential 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 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 Fig. 5. The apparatus used in Hirn’s 1865 percussive (1815–1890) was so heroic in scale that it needs to be method of determining Joule’s constant. 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 This article is copyrighted246 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 8ЊC. In between the anvil and the hammer was a cylinder of lead, partly flattened by the collision. Immedi- ately 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. Fig. 6. Joule’s 1845 apparatus used to measure the Greenslade6 gives the details of the calculations, lead- effects of compressing a known volume of air to a ing to a value of J = 4.17 J/cal. known final pressure. In a lecture demonstration at the Royal Institution in 1862,7 John Tyndall showed that when a lead ball is done to expand the gas against the external pressure. dropped four times from a height of 26 ft onto an iron We can thus say that plate, the temperature of the ball increased. This is ⌬ ⌬ ⌬ probably the origin of the percussive method for meas- MCP T – MCV T = P V uring Joule’s constant used by Millikan and Gale (1906) in their student laboratory handbook.8 A card- is the work done by the gas on the surrounds as it board tube, closed at both ends and with an interior expands. In this expression, M is the mass of the gas, length of 1 m, has birdshot (steel or lead) inside. The ⌬T is the temperature rise, and the two C values are temperature of the shot is taken at the beginning of the the specific heats. If we keep in mind that the two experiment, and again after the tube has been inverted sides of the equation are in different energy units, we ⌬ ⌬ 100 times. In principle, this is the equivalent of drop- can write J = M(CP – CV ) T/P V. Mayer did not ping the shot 100 m; in practice the temperature rise is actually do the experiment, but relied instead on nowhere as great as expected.9 somewhat inaccurate data. However, his value for Joule’s constant of 3.58 J/cal is remarkably close to Thermodynamic Methods Used to the accepted modern value. Obtain Joule’s Constant a. Specific Heat Differences. The first deliberate b. Compressing Air. In one of his 1845 papers,10 method of measuring the mechanical equivalent of Joule used a hand pump to compress air into a cylin- heat seems to be the thermodynamic technique der and observed the resulting increase in tempera- employed by the German physician Robert Mayer ture of the water. The apparatus is shown in Fig. 6. (1814–1878) in 1842. The specific heat capacity of a Dry air from the calcium-chloride-filled container G gas depends on the physical conditions under which and at a temperature indicated by the water in con- work is done on it. The amount of work necessary to tainer W was slowly pumped into the brass pressure raise the temperature of an enclosed volume of gas vessel R. Heat leaks from the water surrounding the under conditions of constant pressure is greater than pressure vessel were reduced by containing it in a that under conditions of constant volume. This is double-walled container. The temperature of the due to the fact that in the first case, work must be compressed air went up and increased the tempera-

◆ This article THEis copyrighted PHYSICS TEACHER as indicatedVol. in 40, the April article. 2002 Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions.247 Downloaded to IP: 138.28.20.194 On: Sun, 11 Oct 2015 18:24:42 ture of the water surrounding the pressure vessel. Acknowledgment The volume of the air initially in the pressure vessel at atmospheric pressure was known, and the volume The writing of this paper was inspired by work done of the compressed air was measured by releasing it in with Jason Summers, a physics major in the Kenyon a pneumatic trough at atmospheric pressure and class of 1998. room temperature. The relationship pV = constant enabled the initial and final pressures and volumes to References be known, and the net work done on the gas was the 1. James P. Joule, “On the calorific effects of magneto-elec- tricity, and on the mechanical equivalent of heat,” Phil. area under the hyperbolic pressure-volume curve. Mag. ser 3, xxiii (1843), reprinted in The Scientific Pa- Corrections were made for frictional effects in the pers of James Prescott Joule (Taylor and Francis, London, cylinder and piston, and the values of Joule’s constant 1884), pp. 123–159. for two runs were 4.27 and 4.42 J/cal, which Joule 2. H.L. Callendar and Barnes, Phil. Trans. A (1899). The regarded as acceptably close to his 1843 result of original paper was not consulted, but there is a good dis- 4.51 J/cal. cussion of it in J. K.Roberts, Heat and Thermodynamics (Blackie, London, 1928), pp. 44–45. c. Releasing compressed air. In a related experi- 3. Thomas Preston, The Theory of Heat, 2nd ed., revised by ment discussed in the same paper, compressed air in J. Rogerson Cotter (MacMillan and Co., London, a pressure vessel held in a water tank was allowed to 1904), p. 321. leak out slowly. The released air was allowed to travel 4. J.P. Joule, “On the mechanical equivalent of heat,” through a long length of tubing coiled up in the reprinted in The Scientific Papers of James Prescott Joule water tank and was captured in a pneumatic trough (Taylor and Francis, London, 1884), pp. 298–328. to estimate its final volume. Again, the starting and 5. Ref. 3, p. 301 final points on the pressure-volume graph were locat- 6. G.A. Hirn, Theorie Mecanique de la Chaleur, premiere ed, and the work calculated by the area under the partie: Exposition Analytique et Experimental, 2nd ed. curve. This time Joule obtained 4.41, 4.38, and 4.09 (Gauthier-Villars, Paris, 1865). See also Thomas B. J/cal. Today we would say that the air had under- Greenslade, Jr., “A striking Joule’s constant determination,” Phys. Teach. 18, 208–209 (March 1980). gone a throttling process and use the physical principle in our refrigerators. 7. John Tyndall, Heat Considered as a Mode of Motion (D. Appleton and Company, New York, 1873), pp. 54–55. Conclusion 8. Robert Andrews Millikan and Henry Gordon Gale, A Laboratory Course in Physics (Ginn, Boston, 1906), pp. It is my hope that physics teachers will be willing 59–62. to use portions of this material in their classes to help 9. Thomas B. Greenslade, Jr., “Joule’s constant revisited,” break the cycle of problems that most students consid- Phys. Teach. 17, 530–531 (Nov. 1979). er the reason for studying physics. Since we will cer- 10. J.P. Joule, “On the changes of temperature produced by tainly continue to rely heavily on the solution of prob- the rarefaction and condensation of air,” Phil. Mag. ser lems as primary methods of teaching physics to stu- 3, xxiii, 369–383 (1845). dents and assessing their grasp of ideas and their appli- 11. Thomas B. Greenslade, Jr., “Examination questions cation, I have supplied a number of historical physical based on historical apparatus,” Phys. Teach. 37, 172–173 situations that may be used as the basis for homework (March 1999). and examination problems.11

THE PHYSICS TEACHER ◆ Vol. 40, April 2002 This article is copyrighted248 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