Joule’s equivalent

Ill 1847 Joule published a paper that contained an overwhelming amount of experimental data. All his results averaged out to a value of 4.15 J/cal (in modern units), with a spread about this mean of only five percent. The best modern value of Joule s Equivalent IS 4.184 J/cal, and so his results were accurate to better than one percent. This was truly amazing, for the heat measurements Joule performed were the most difficult in all of physics at that time. 

Joule obtained a much improved estimate of the Joule s equivalent of heat (Jjq = 4.15 J cal-1, within 1% of the modem value) and demonstrated its quantitative consistency for all these effects. Thus, Joule s name is rightly attached to the SI unit of energy, and he deserves to be considered the scientist most responsible for quantitative establishment of the first law of thermodynamics. 

Thomson, W. "On the dynamical theory of heat with numerical results deduced from Mr. Joule s Equivalent of a thermal unit and M. Regnault s Observations on steam ", Trans. Roy. Soc. Edin., 1853, 261-288. 

Having met Joule for the first time at the 1847 meeting of the British Association for the Advancement of Science in Oxford, Thomson initially accepted that Joule s experiments had shown that work converted into heat. Committed to Carnot s theory of the production of work from a fall of heat, however, he could not accept the converse proposition that work had been converted into heat could simply be recovered as useful work. Therefore, he could not agree to Joule s claim for mutual convertibility. By 1848 he had appropriated from the lectures of the late Thomas Young (reprinted in the mid-1840s) the term energy as a synonym for vis viva (the term in use at the time, traditionally measured as mtc) and its equivalent terms such as work, but as yet the term appeared only in a footnote. 

The correctness of this statement is to be inferred from the exact agreement between the values of the mechanical equivalent of heat obtained by different methods. Thus, in Joule s second series of experiments, mechanical work is directly converted into heat in the first and third series, it is indirectly transformed through the medium of electro-magnetic energy in the fourth series, the energy of an electric current is converted into heat the identity of the values of J so obtained implies a complete conversion of the initial forms of energy into heat energy. 

The calculation of Mayer was thrown into a different form by Rankine (1850), who showed that, instead of estimating the mechanical equivalent of heat from the difference of the specific heats of air, one could take Joule s value of the mechanical equivalent and the known ratio of the specific heats, and thence determine the specific heats themselves. 

He is remembered for Joule s Law lhat describes the rale at which heal is produced by an electric current. Joule s work showed there were different kinds or energy, which can be changed into each other. He established the mechanical equivalence of heat. His work led to the law of conservation of energy. Alsu, he collaborated with William Thomson (Lord Kelvin) and verified experimentally the Joule-Thomson refrigeration effect. 

One of the most intriguing achievements of the 19th century was James Joule s (1818-1889) determination of the mechanical equivalent of heat and, therefore, the first law of thermodynamics. There is a study of the background to this paper, through the analysis of Joule s work in electrochemistry.88... 

In Rayleigh s treatment of the Boussinesq s problem, we realized that Joule s heat equivalent had to be cancelled, because in this problem the liquid was supposed to be an ideal one. This is - of course - as with many problems arising in the areas of... 

Heat transfer processes are described by physical properties and process-related parameters, the dimensions of which not only include the base dimensions of Mass, Length and Time but also Temperature, , as the fourth one. In the discussion of the heat transfer characteristic of a mixing vessel (Example 20) it was shown that, in the dimensional analysis of thermal problems, it is advantageous to expand the dimensional system to include the amount of heat, H [kcal], as the fifth base dimension. Joule s mechanical equivalent of heat, J, must then be introduced as the corresponding dimensional constant in the relevance list. Although this procedure does not change the pi-space, a dimensionless number is formed which contains J and, as such, frequently proves to be irrelevant. As a result, the pi-set is finally reduced by one dimensionless number. 

Joule spoke to the Greenock Philosophical Society in the Watt Institution on 19January 1865, On Some Facts in the Science of Heat Developed Since the Time of Watt .8 The bulk of the lecture was given over to a description of Joule s own, already famous, experimental demonstration of the mechanical equivalent of heat... 

The question at once arises as to how much work must be done to produce this much heat. This question was answered by experiments carried out in Manchester, England, between 1840 and 1878 by James Prescott Joule (1818-1889), after Count Rumford (Benjamin Thompson, 1753-1814, an American Tory) had shown in 1798 that the friction of a blunt borer in a cannon caused an increase in temperature of the cannon. Joule s work led to essentially the value now accepted for the mechanical equivalent of heat, that is, the relation between heat and work ... 

In the boring experiment, work is done by the surroundings on the system (the brass cannon), the energy of the system rises and heat is also released to the surroundings (water bath). The First Law of Thermodynamics and the mechanical equivalent of heat (1 calorie = 4.184 joule) were established in 1843 by James Prescott Joule (1818-89). In order to raise the temperature of 1 gram of water by 1 °C (1 calorie), 4.184 joule of mechanical work, such as spinning paddles in water (Joule s experiment), is required. 

We quote Joule s report on the experiment literally. It is delivered that Joule did his experiments on the mechanical equivalent of heat by measuring the temperature increase of water, when the energy of a falling weight was dissipated into the water. However, from his original paper it becomes clear that he performed also several other experiments of this type. 

Fig. 2.9 Joule s apparatus for demonstrating the equivalency of energy and heat (from Abbott (1869) The new theory of heat. Harper s New Monthly Magazine 39 322-329).

Experiments analogous to those just described were first performed by Joule in the 1840s [5]. Those experiments accomplished several things they fully discredited the old caloric theory of heat (a theory that considered heat to be transported by movement of a substance called caloric), they demonstrated that a temperature change can occur without heat transfer, and they provided a numerical conversion factor between equivalent amounts of heat and work. However for us. Joule s most important result leads to (2.1.27). 

In the context of resistive circuits and in light of conservation of energy and electrical potential. Joule s first law and Ohm s law are equivalent and derivable from each other, although they were discovered... 

A long memoir communicated by Joule in 1846 to the Paris Academy, too late for a prize, was printed in English in 1852. It gives many references to publications by others, repeats his fundamental law, speaks now of the resistance occasioned by polarisation , and describes new experiments on the evolution of heat by currents in wires. Joule repeats his proposition that the resistance to electrolysis presented by water does not occasion the evolution of heat in the decomposing cell , but diminishes the heat evolved in the whole circuit on account of the decreased electromotive force of the current , and it is reasonable to infer that this diminution of the heat evolved by the circuit is occasioned by the absorption of heat in the decomposing cell . This assumption of the exact equivalence of heat of reaction and electrical work is not really correct, but it was also made simultaneously by Helmholtz, who refers to Joule s publications. 

For the Daniell cell Thomson calculated from Joule s results for heats of reaction an electromotive force equivalent to 1 074 volts, practically the same as the measured value. From Joule s figures he calculated the equivalent of 1 416 volts for the electrolysis of water, and remarks that one Daniell cell would not be sufficient for this, but two would. The agreement of the calculated and observed results with the Daniell cell is accidental, and the general conclusion of Helmholtz and Thomson is incorrect (see p. 698). 

By examining both Joule s published work and his apparatus, part of which survives in the Joule Collection of the Greater Manchester Museum of Science and Industry, the considerable experimental skill involved in determining the equivalent values becomes clear. We are also able to chart the changing style of his scientific work, and can begin to relate his method of work to his developing theories about natural phenomena. 

He went on to calculate from the expansion of air a further set of values for the mechanical equivalent of heat which broadly agreed with the electromagnetic experiments. These experiments and, in particular. Joule s concern for very sensitive measuring instruments suggest that he was, to some extent at least, using experiments to prove his theory of the nature of heat. This experimental style contrasts with his earlier, more open-ended approach. 

Figure 3.13 Joule s apparatus for measuring the mechanical equivalent of heat (redrawn from a figure in Ref. [83]).

This problem guides you through a calculation of the mechanical equivalent of heat using data from one of James Joule s experiments with a paddle wheel apparatus (see Sec. 3.7.2). The experimental data are collected in Table 3.2. 

Beginning in 1844, Clapeyron taught the course on steam engines at the Ecole Nationale des Fonts et Chaussees near Paris, the oldest French engineering school. In this course, surprisingly, he seldom mentioned his theory of heat engines based on Carnot s work." He eventually embraced the equivalence of heat and work established by Joule s experiments." ... 

Work and Heat. In classical mechanics, when a force F displaces a body by an amount Js, the work done dW = ds. Work is measured in joules. Dissipative forces, such as friction between solids in contact, or viscous forces in liquids, can generate heat from work. Joule s experiments demonstrated that a certain amount of work, regardless of the manner in which it is performed, always produces the same amount of heat. Thus, the following equivalence between work and heat is established ... 

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