Walter J. Homer
National Bureau of Standards Washington, D.C. 20234
A Joule
In 1867 James Prescott Joule reported on a task assigned to him earlier by the British Association for the Advancement of Science (I). He stated that the experiments he was about to report on, as well as the request to carry them out, could have been made earlier hut that both the experiments and the request had been necessarily delayed pending the development of an accurate method of measuring resistance in cgs mechanical units. He stated that since such a method had been described by Sir William Thomson (Lord Kelvin) in 18.51 ( 2 ) and used successsfully by Professor J. Clerk Maxwell and associates in 1863 (3) he had been able to complete his assigned task within the past two years. He had been asked by the Association to undertake an evaluation of the mechanical equivalent of heat by electrical means involving cgs mechanical units. Joule had become prominent as a result of his studies on the relations between work and heat, had previously determined the mechanical equivalent of heat by purely mechanical means, and was considered by the Association as the logical one to undertake what was considered a crncial and most important experimental task. The year 1967 marked the centennial of Joule's report to the British Association, and although his experiments may he well known and fully appreciated, it seems appropriate, a t this time, to again pay tribute to his experimental ingenuity and contributions to thermodynamics. Furthermore, his experiments reported in 1867 ultimately had a profound influence on the establishment of the international electrical units, adopted by the International Electrical Congress which met in Chicago in 1893 and legalized in this country in 1894 by Public Law No. 105passed by the 53rdU.S. Congress. Some eighteen years prior to his electrical experiments Jonle (4) had determined the mechanical equivalent of heat by the agitation of water. In commenting on the results obtained from his first two series of electrical experiments Joule ( I ) wrote "The equivalents obtained in the two foregoing series of experiments are as much as one-fiftieth in excess of the equivalent I obtained in 1849 by agitating water." Thinking that the discrepancy he had found between the mechanical equivalents of heat determined mechanically and electrically arose from the inherent difficulties in the latter Joule strove to remove the uncertainties in the latter in a third series of electrical measurements (1). I n this method a current of known magnitude is passed through a coil of known resistance and the temMentioned in a discussion on September 12, 1967, at the Chicago Meeting of the American Chemical Society and dso in an
introduction to a paper on the "History of the National Stmdard of Electromotive Force." Dresented before the Instrument Society of America on the sakedate
perature rise produced by the heat generated in the coil measured with a suitable thermometer. In his third series of electrical experiments Joule provided for better stirring of the water in the calorimeter, used better insulation around his calorimeter, and coated his resistance coil with non-corrosive varnish. Even so, the results of his third series of experiments exceeded that obtained from the agitation of water by more than 1% (see below). I n each series of electrical experiments Jonle determined the magnitude of the current in cgs mechanical units using a tangent galvanometer and a "current weigher" of his own design. The resistance of his Ag-Pt coil was known in cgs units in terms of the British Association for Advancement of Science (B.A.) unit of resistance. As a source of electric power he used a series of Daniel1 cells. He used a mercury-in-glass thermometer calibrated in degrees Fahrenheit to measure the change in temperature of the water in his calorimeter (12.951 divisions of the thermometer were equivalent to I0F). The results of his three electrical experiments, given in foot-grain-second units of work for a grain of water raised l ° F (heat capacity of water) were as follows: Series 1, average of 10 experiments-25,335 Series 2, average of 15 experiments-25,366 Series 3, average of 30 experiments-25,217
Owing to the refinements in the third series of experiments Joule recommended that the third value be accepted as "the result of the inquiry." When reduced to weighings in vacua this value became 25,187. The average temperature of the water in the calorimeter in the last experiment was 65.53'F. When converted to cgs units and degrees Celsius, Joule's value becomes: 4.2119 X 10' cgs units (or ergs) at 18.63T
a value which, in spite of the experimental refinements, still exceeded the value he obtained by the agitation of water (see below). Historically, the above value based on the heat capacity of water has been designated in a variety of ways as the "mechanical equivalent of heat," or the "mechanical equivalent of the unit of heat," or the "electrical equivalent of heat," or "Joule's Equivalent" denoted by the symbol J . This symbol is now used in the Syst&neInternational d'UnitBs (SI), adopted in a resolution, 11th General Conference on Weights and Measures, Paris, October, 1960, for the unit of energy (in the former cgs system the erg was the unit of energy). I n 1888 the British Association for the Advancement of Science (6) adopted the name "therm" for t.he gramwater-degree Centigrade (now Celsius) unit of heat and Volume 45, Number 2, February 1968 / 123
In earlier experiments Joule (4) had determined the mechanical equivalent of heat mechanically by agitating water with a metallic paddle made to rotate by the dropping of known weights a known distance. The mean of 40 such experiments gave 772.692 ft-lb for the work required to raise the temperature of 1 lb of water 1°F a t about 50°F. On conversion to cgs units and degrees Celsius, using 981.3 em s e r Zfor the acceleration of gravity a t llanchester, England, where Joule conducted his experiments, the above value becomes:
showed that the resistance of the B.A. standard coil was 1% smaller than the cas theoretical ao~roximatelv value. This~esultattested to the excellency of Joule's measurements, for if the B.A. unit was, say 1% too small, ~~~l~would then have over-estimated the total enercv &en to his calorimeter bv" 1%. ,", and. as a result. he would have calculated a value for the'mechanical equivalent of heat which would be 1% larger than the true value, a result in close agreement with what Joule actually had found. The average of the ohm determinations carried out by Lorenz (8), Rowland (Q),and Rayleigh and Schuster (10) lead to the relation: 1 B.A. ohm = 0.9867 ohm, which was confirmed in 1882 by Rayleigh (11) who obtained a ratio of 0.9865 and in 1883 by Rayleigh and Sidgwick ( I t ) who obtained a ratio of 0.9867. A value of 0.9866 was finally agreed upon. Joule's experiments, therefore, had a profound effect on the establishment of the "international" cgs electrical units adopted by the Chicago International Electrical Congress of 1893.% His experiments made possible an agreement among the various countries between the ratio of the B.A., Siemens, and the British legal ohms and the absolute ohm and in an assignment of an emf (1.434 int. v) to Clark's cell at 1 5 T . If the above ratio mere applied to Joule's electrical experiments of 1867 his mechanical equivalent of heat, determined electricallv. would have been:
4.1600 X 10' cgs units (or ergs) at 10°C
4.1555 X 10' cgs units (or e r e ) at 18.63T
honored the memory of Joule by adopting the name ".ioulen for 10' cas units of work (or enerav), -". . thus: A O T - , I,...-... =.> 0
&
""C.".
(The Association rounded Joule's value of 4.2119 X lo7 cgs units to 4.2.) Eight years later the Association (6) adopted the name "calorie" as a replacement for "therm," hence: 4.2 .I
=
I ~d
Today, since energy is usually measured in terms of electrical units based on the mksa (or "absolute") units for the ohm, ampere, and volt, the joule is usually defined as the work done in one second when a current of 1 amp io, maintained by an emf of 1 v. The expression "mechanical equivalent of heat" in modern usage is merely a conversion factor between two energy units (?).I
Neglecting the difference in temperature it may be seen that Joule's electrical result for the mechanical equivalent of heat exceeded his older mechanical value by 1.25%. (The 2% maximum difference Joule referred to and given in quotes in the second paragraph of this article came from his comparison of his mechanical value and the average of his first two series of electrical experiments.) At that time Joule offered no explanation for the difference he found between his mechanical and electrical determinations of the mechanical equivalent of heat. If he suspected that the value of the B.A. unit of resistance was in error he refrained from saying so. However, redeterminations of the ohm carried out by Lorenz (8) in 1873, Rowland (9) in 1878, and Rayleigh and Schuster (10) in 1881 by widely different methods
' The thermaehemieal calorie is now defined as eaual to 4.1840 of the heat capacity of a substance. The ~elalion: 1 international ohm = 1.000495 sbsbsolute ohm, adopted in 1948 (I$), had an inconsequential effect, when applied, in comparison with the effect of appliorttion of the ratio fomld between the B.A. and cgs units following Joule's experiments. a The difference of 0.0045 between Joule's values at 10" and 18.63"C may be compared with 0.0094 obtained by Stimson (14) for the same temperature interval. In 1878 Joule (15), using a modification of his "agitation-of-water" method obtained 772.55 ft-lb for 60.5"F at seeilevel and the latitude of Greenwich; in cgn units and for degrees Celsius and using 981.17 cm sear2 for the acceleration of gravity at Greenwich this value becomes 4.1587 X 10' cgs units at 15.83'C. The difference of 0.0012 between his new mechanical value (at 15.83T) and the electrical value of 1867 (corrected to "absolute ohm") at 18.63"C may be compared with 0.0022 obtained 77 yeam later by Stimson (14). ' T h e largest change may be traced to a difference between the mercury-in-glass thermometers and the perfect gas (air) thermometer, see Rowland (16).
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in close agreement &h his "agitation-of-water" resuk3 The fact that Joule's value for the mechanical equivalent of heat was lat,er altered by himself3 and others4 by refinements in techniques does not detract from his contributions. The pioneer nature and the classical refinement of Joule's experiments set them apart from others of his day and from strict numerical appraisal. Although tribute to his work has been perpetuated in the use of his name to designate the unit of work, the centennial of one of his most famous experiments, which later influenced so many scientific disciplines,should not, pass without notice. Literature Cited (1) JOULE,J. P., Reports of the Electrical Standards Committee of the British Association, Fifth Report, Dundee, App. VI, 256 (1867). (2) THOMSON, SIR WILLIIM (LORDKELVIN),Phil. Mag.,[4], 2, 551 (1851). (3) MAXWELL,J. CLERK,STEWART,B. and JENKIN, F., "Reports of the Electrical Standard Committee of the British Association," Second Report, Newcastle-on-Tyne, 1863, App. D, 140. J. P., Phil. Mag., 131, 35, 533 (1849). (4) JOULE, (5) "Reports of the Electricd Standards Committee of the British Association." Fifteenth ReDort. Bath 1888. D. 341. (6) "Reports of the Electrical ~ t a n d k d scornmittel bf the British Association," Twenty-third Report, Liverpool, 1896, p. 539. E. F., Mech. Eng., 52, No. 2, 139 (1930). (7) MUELLER, (8) LORENZ, L., Ann. Physik., 149,251 (1873). ( 9 ) &WAND, H. A,, Am. J. Sci., 115,430 (1878). (10) RAYLEIOH,LORD, AND SCWSTER, A., Proc. Roy. SOC. (London), 32, 104 (1881). (11) RAYLEIOH,LORD, Pmc. Royal SOC.(London), 33, 398 iIRR21. \----,-
(12) RAYLEIOH, LORD,AND SIDGWICK, MRS. H.,Proc. Roy. Soc. (London), 34, 438 (1883). (13) "Announcement of Changes in Electrical and Photometric Units," Nat. Bur. Standards Circ. 459, 1947.
(14) STIMSON,R. F., An. J . Physics 23, 614 (1955). (15) JOULE,J. P., Pmc. RAY. Sac. (London), 27, 38 (1878), abstrrtot only; complete paper appears in "The Scientific Papers of James Prescott Joule," Taylor and Francis,
London, 1884, Vol. 1, p. 632. (16) ROWLAND, H. A,, Proc. Am. A d . Arts Sci., 15, 75 (1879). (17) C k . Bc Eng. News 41, 43 (Nov. 18, 1963); Nat. Bur. Standa~dsTech. News, 47, 175 (1963).
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