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Century Measurements of the Mechanical Equivalent of Heat 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: https://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 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 meas- uring 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 cur- rent.” 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.
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