On the Mechanical Equivalent of Heat

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. 

By James P. Joule [Brit. Assoc. Rep. 1845, trans. Chemical Sect. p. 31. Read before the British Association at Cambridge, Jun. 1845.] 

On the Existence of an Equivalent Relation Between Heat and the Ordinary Forms of Mechanical Power 

By James P. Joule, Esq. [In the letter to the Editors of the Philosophical Magazine. ] series 3, vol. xxvii, p. 205 Gentlemen, 

3 Nicolas Leonard Sadi Carnot, bom Jun. 1,1796, in Paris, died Aug. 24,1832, in Paris 

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From this example, it is clear that both conservation laws broke down at once. In a process involving friction, energy is not conserved, but rather disappears continually. At the same time, however, heat is not conserved, but appears continually. Rumford essentially suggested that the heat which appeared was really simply the energy which had disappeared, observable in a different form. This hypothesis was not really proved for a good many years, however, until Joule made his experiments on the mechanical equivalent of heat, showing that when a certain amount of work or mechanical energy disappears, the amount of heat... 

J. P. Joule, On the mechanical equivalent of heat, originally presented to the Royal Society,... 

J. R. Mayer (1842) made the first calculation of the mechanical equivalent of heat by comparing the work done on expansion of air with the heat absorbed. 

The entire agreement between the values of the mechanical equivalent of heat obtained by many different methods establishes the proposition that it is independent of the process in which the conversion of work into heat occurs, and depends solely on the choice of the units of these two magnitudes. This result was first established by Joule. 

Credit for the first recognizable statement of the principle of conservation of energy (heat plus work) apparently belongs to J. Robert Mayer (Sidebar 3.2), who published such a statement in 1842. Mayer also obtained a (slightly) improved estimate, approximately 3.56 J cal-1, for the mechanical equivalent of heat. Mayer had actually submitted his first paper on the energy-conservation principle two years earlier, but his treatment of the concepts of force, momentum, work, and energy was so confused that the paper was rejected. By 1842, Mayer had sufficiently straightened out his ideas to win publication,... 

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... 

Value of the mechanical equivalent of heat.—Depending on this principle and on the results of various experiments whose description is beyond the scope of this work, Robert Mayer, Joule, and a great number of other physicists have occupied themselves with the determination of the value of the mechanical equivalent of heat E they found that approximately... 

Mayer s calculation of the mechanical equivalent of heat is based on the difference between the specific heats Cp and c for air. Consider unit mass of air (1 g.) enclosed in a cylindrical vessel by means of a movable piston (Fig. 13). An amount of heat will be required to raise the temperature of the gas 1° if the piston be prevented from moving. On the other hand, if the piston is free to move so that only the pressure of the atmosphere jp is exerted on it, a greater amount of heat Cp will be required to raise the temperature of the gas 1°, and,... 

Of late years a number of very careful measurements of the mechanical equivalent of heat have been undertaken for this purpose. The methods employed in these measurements are the same in principle as those of Joule, and differ only in the greater refinement of the apparatus. The methods which have been employed hitherto are all based on the production of heat by friction or by the electric current. The results are tabulated below. In column 3 is given the number of ergs which is equivalent to a small 15° calorie. 

Entrojiy and probability. The recognition of the universal applicability of the law of the conservation of energy is partly based on the mechanical conception of heat as motion of the ultimate particles of matter. If heat, energy, and kinetic energy of the molecules are essentially of the same nature, and are differentiated from one another only by the units in which we measure them, the validity of the law of the equivalence of heat and work is explained. At first sight, however, it is not easy to understand why heat cannot be converted completely into work, or, in other words, why the conversion of heat into work is an irreversible process (second law of thermodynamics). In pure mechanics we deal only with perfectly reversible processes. By the principles of mechanics the complete conversion of heat into work should be just as possible as the conversion... 

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. 

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. 

A typical experiment performed by Joule is described in Prob. 3.10 on page 99. His results for the mechanical equivalent of heat, based on 40 such experiments at average temperatures in the range 13 °C-16 °C and expressed as the work needed to increase the temperature of one gram of water by one kelvin, was 4.165J. This value is close to the modern value of 4.1855 J for the 15 °C calorie, the energy needed to raise the temperature... 

Though Sadi Carnot used the caloric theory of heat to reach his conclusions, his later scientific notes reveal his realization that the caloric theory was not supported by experiments. In fact, Camot understood the mechanical equivalence of heat and even estimated the conversion factor to be approximately 3.7 joules per calorie (the more accurate value being 4.18 J/cal) [1-3]. Unfortunately, Sadi Carnot s brother, Hippolyte Camot, who was in possession of Sadi s scientific notes from the time of his death in 1832, did not make them known to the scientific community until 1878 [3]. That was the year in which Joule published his last paper. By then the equivalence between heat and work and the law of conservation of energy were well known through the work of Joule, Helmholtz, Mayer and others. (It was also in 1878 that Gibbs published his famous work On the Equilibrium of Heterogeneous Substances). 

Carl Friedrich Mohr (Coblenz, 4 November 1806-Bonn, 28 September 1879), at first an apothecary in Coblenz then associate professor of pharmacy in Bonn, published many papers and a book on pharmacy, describing new apparatus. Mohr was one of the pioneers of volumetric analysis. He also wrote on the mechanical theory of heat and chemical afimity. He sa rs in (i) heat is no longer a substance, but is rather an oscillatory motion of the smallest parts (rather like Davy s theory) he used (like Mayer in 1842) the name E aft for energy, and said heat is a form of it. He pointed out the relation of the difference of the specific heats of air at constant volume and pressure to this nature of heat, but did not (as Mayer did) calculate the mechanical Equivalent of heat from it. He is an obscure writer and his later claims to have anticipated Clausius are unfounded, but he anticipated some of Mayer s ideas. He acted... 

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