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# Mechanical equivalent of heat

In the history of science, the mechanical equivalent of heat was a concept that played an important part in the development and acceptance of the conservation of energy and the establishment of the science of thermodynamics in the 19th century.

The idea was proposed by Julius Robert von Mayer (1842) and independently by James Prescott Joule (1843). Similar work was carried out by Ludwig A. Colding (1840-1843). Joule contended that motion and heat were mutually interchangeable and that in every case, a given amount of work would generate the same amount of heat.

## History

The idea that heat and work were equivalent was proposed by Julius Robert von Mayer (1842) and independently by James Prescott Joule (1843). Similar work was carried out by Ludwig A. Colding (1840-1843). Central to these developments, however, was Joule's famous 1843 paper, entitled "The Mechanical Equivalent of Heat", in which he published the value A for the amount of work W required to produce a unit of heat Q. Joule contended that motion and heat were mutually interchangeable and that in every case, a given amount of work would generate the same amount of heat.

Joule experimented on the amount of mechanical work needed to raise the temperature of a pound of water by one degree Fahrenheit and found a consistent value of 772.24 foot pound force (4.1550 J·cal-1).

Though a standardised value of 4.1860 J·cal-1 was established in the early 20th century, in the 1920s, it was ultimately realised that the constant is simply the specific heat of water, a quantity that varies with temperature between the values of 4.17 and 4.22 J·g-1·°C-1.

The change in unit has been the result of the demise of the calorie as a unit in physics and chemistry.

## Priority

Both Mayer and Joule met with contemporary neglect and resistance owing to the eminence of the caloric theory of heat. Colding's work was little-known outside his native Denmark. Hermann Helmholtz probably first became aware of the principle through Joule's work, on which he based his definitive 1847 declaration of the conservation of energy, but by 1862 he had come to credit both Joule and Mayer.

Also in 1847, Joule's presentation at the British Association for the Advancement of Science in Oxford was attended by the precocious and maverick William Thomson, later to become Lord Kelvin. Thomson was intrigued but initially sceptical. Over the next two years, Thomson became increasingly convinced of Joule's theory, finally admitting his conviction in print in 1851, simultaneously crediting Mayer. Thus began a fruitful, though largely epistolary, collaboration between the two men, Joule conducting experiments, Thomson analysing the results and suggesting further experiments. The collaboration lasted from 1852 to 1856. Its published results did much to bring about general acceptance of Joule's work and the kinetic theory in England.

However, in 1848, Mayer had first had sight of Joule's papers and wrote to the French Académie des Sciences to assert priority. His letter was published in the Comptes Rendus and Joule was quick to react. Thomson's close relationship with Joule allowed him to become dragged into the controversy. The pair planned that Joule would admit Mayer's priority for the idea of the mechanical equivalent but to claim that experimental verification rested with Joule. Thomson's associates, co-workers and relatives such as William John Macquorn Rankine, James Thomson, James Clerk Maxwell, and Peter Guthrie Tait joined to champion Joule's cause.

On May 18, 1850, Mayer attempted to commit suicide, possibly in part owing to distress caused by the controversy.

However, in 1862, John Tyndall, in one of his many excursions into popular science and many public disputes with Thomson and his circle, gave a lecture at the Royal Institution entitled On Force[1] in which he credited Mayer with conceiving and measuring the mechanical equivalent of heat. Thomson, and Tait were angered and an undignified and public exchange of correspondence took place in the pages of the Philosophical Magazine and, the rather more popular, Good Words. Tait even resorted to championing Colding's cause in an attempt to undermine Mayer.

Though, Tyndall again pressed Mayer's cause in Heat: A Mode of Motion (1863), with the publication of Sir Henry Enfield Roscoe's Edinburgh Review article Thermo-Dynamics in January 1864, Joule's reputation was sealed while that of Mayer entered a period of obscurity.

## Notes

1. ^ The usage of terms such as work, force, energy, power, etc. in the 18th and 19th centuries by scientific workers does not necessarily reflect the standardised modern usage.