In the
history of science, the
mechanical equivalent of heat was a theory, connected to the
theory of heat, developed in about 1843, that
heat Q and
mechanical work W were equivalent via a proportionality constant
A:
»
This formula or equivalency was also called theorem of the equivalence of heat and work, which was a precursory form of the
first law of thermodynamics. In 1854, by studying the works of
Sadi Carnot and
James Joule, the German physicist
Rudolf Clausius enunciated this theorem as such:
This principle, was built on the observations of many experiments, such as
Count Rumfords cannon boring experiment, and
James Joule's paddle-wheel experiment. For example, by mechanically doing the work of rubbing ice together, heat can be created owing to friction, which thus melts the ice. Conversely, heat from a coal furnace can be used to power a
steam engine, and thus used for purposeful work. In other words, heat and work can be converted into one another. This theory 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.
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'd 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 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.
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