Basic definition of work, the product of a force moving an object through a distance; in its original conceptual form, a weight lifted through a height, as in the lifting of water out of a flooded coal mine. |

Force and distance

In the 1687 publication

Motive Power

In the 1824 publication

Motive power = weight∙height

The units of the term weight, later explicitly defined as mass of the object times the force of gravity

Travail

The actual term “work” as the product of force and distance, was coined by French physicist Gustave Coriolis who used the French term

“The name ofworkis defined as the product of a weight carried, multiplied by the distance from transport, or in general the product of an area covered, multiplied by a force directed perpendicular to this space; it is necessary to consider only the effort is exerted in the direction of the area covered.”

Coriolis, it seems, derived his notion of work as a replacement of German mathematician Gottfried Leibniz's 1686 theory of vis viva (living force, i.e. kinetic energy or

“The integral ∫ PdS, PdSthe product of the tangential component of the forceFby the infinitesimal arcdsdescribed by its point of application, is called the amount ofworkdue to this forceF. The PdSproduct is the element of work at the same strength.”

Nearly word-for-word, this seems to be the basis of the opening "Mathematical Introduction" section of Rudolf Clausius' textbook

W = F∙d

In this work, Coriolis promoted the technical term “work” (travail) to cover a wide variety of equivalent terms used by practitioners. He states:

“All of the practitioners today understand by the vis viva (living force) theworkwhich the velocity acquired by a body is capable of doing.”

French mathematician Jean-Victor Poncelet, the commandant general of the École Polytechnique, acknowledged that the word “work” was brought in by Coriolis. [4] Poncelet was Coriolis’ teacher and source of stimulus of many of his ideas. Poncelet, who in 1824 had become professor of 'mechanics applied to machines', later built on the logic of Coriolis and lectured successfully on the topic of work done by machines, wherein he used the word 'travail' to signify work. [6] Poncelet expanded the concepts of agents of work far beyond vis viva, so that it became a unifying concept of physical, chemical, and biological processes. [7]

Coriolis, a former student (1808) and later tutor (1816) at the École Polytechnique, may have adopted parts of his logic on that outlined earlier by the Carnot the younger, but this is unlikely. Coriolis does, however, devote a section to the "theorem of Carnot", but in what seems to be on the work of Lazare Carnot. [9]

Clapeyron's pressure-volume work

The graphical measure of work was identified in 1834 by French mining engineer Émile Clapeyron who used the phrase “mechanical action” as “the integral of the product of the pressure times the differential of the volume” during either the expansion or contraction of the gas and the resultant piston movement. [5] Specifically, in 1796, Scottish instrument maker James Watt and his employee John Southern developed a work measurement tool called an "indicator diagram", used to exactly quantify the work produced by a steam engine, which made a chart of the pressure of the steam in a cylinder plotted out against the steam's volume.

From this, as was determined by Clapeyron, the work of the steam can be determined using calculus:

Mechanical work

Beginning in 1850, Clausius built on these foundations (Carnot, Coriolis, and Clapeyron) by digging into the nature of atomic work, in the working substance, using the logic that: "[whenever a] body moves under the influence of [a] force, work is performed." [1] Clausius used the terms "motive power", "work", and "mechanical work" somewhat interchangeably; although tending towards the latter terminology in his later papers. In his work, the equation view was used such that the product of the force

Units of work

In circa 1830s, Coriolis proposed a unit of work, namely the 'dynamode'. The unit represents 1000 kilogram-metres and was proposed by Coriolis as a measure which could provide a sensible unit with which to measure the work which a person might do, a horse, or a steam engine. Although his term 'work' has become standard, the dynamode did not prove popular in the long run as the unit of work. [4]

In 1875, Clausius was defining the "unit of work" as the kilogram-meter, based on the standard force of gravity, as "that which must be performed in order to lift a unit of weight [kilogram] through a unit of length [meter]". [1] The differentiation between mass [kilograms] and weight [kilograms

In particular, the joule was adopted as the unit for electrical work, heat, mechanical work and energy in 1948 at the 9th General Conference on Weights and Measures, avoiding the calorie as far as possible. This unit was also formally approved in 1960 in the International System of Units (SI). [10]

Human molecular work

In human molecular interaction terms, i.e. with reference to human occupational work, the definition is the same, namely any activity energetically equivalent to lifting a weight. The exact quantification of this measurement, e.g. when trying, for instance, to measure "household work" or "child raising work" as compared the work spent in lifting buckets of water up a well, is a major area of research in human thermodynamics. This is where the development of human indicator diagrams are needed.

References

1. (a) Clausius, Rudolf. (1879).

(b) Bennett, Joseph. (1858).

2. (a) Quote: "we use here motive power (work) to express the useful effect that a motor is capable of producing. This effect can always be likened to the elevation of a weight to a certain height. It has, as we know, as a measure, the product of the weight multiplied by the height to which it is raised."

(b) Carnot, Sadi. (1824). “Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power.” Paris: Chez Bachelier, Libraire, Quai Des Augustins, No. 55.

(c) Stoner, Clinton D. (2000). "Inquiries into the Nature of Free Energy and Entropy in Respect to Biochemical Thermodynamics."

3. (a) Jammer, Max (1957).

(b) Holtzapple, Mark, T. and Reece, Dan W. (2002).

4. (a) Coriolis Biography – MacTutor History of Mathematics Archive.

(b) O I Franksen, “The virtual work principle - a unifying systems concept”, in

(c) The contribution of Coriolis, Poncelet, and Navier to the the concept of “work” is examined in detail in: Grattan-Guinness, I. (1984). “Work for the workers : advances in engineering mechanics and instruction in France, 1800-1830,

5. Clapeyron, Émile. (1834). “Memoir on the Motive Power of Heat”,

6. Laider, Keith J. (1993).

7. Roche, John J. (1998).

8. Coriolis, Gustave. (1844).

9. ibid, Coriolis (1844). Section: “Theoreme de Carnot”, pg. 110.

10. Anon. (1971). “The Adoption of Joules as Units of Energy”, Food and Agriculture Organization of the United Nations.

Further reading

● Mortimer, Robert G. (2000).