# Work

 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.
In science, work quantifies the measure of the "dynamic effect" of a motor or the action of the movement of a body under the influence of a force. [1] The term was first described as "motive power" in 1824 by French physicist Sadi Carnot to quantify the "effect that a motor is capable of producing", including such effects as to lift water or ore out of mines, impel ships, excavate ports and rivers, forge iron, fashion wood, grind grains, spin and weave cloth, or transport heavy burdens, etc.; each of which can be likened to the measure of the energy associated with the lifting of a weight through a gravitational height. [2]

Force and distance
In the 1687 publication The Mathematical Principles of Natural Philosophy (The Principia), English physicist Isaac Newton outlined the laws governing the relationship between the motions of bodies and force. In simplified form, Newton’s three laws of motion state that one: a body will stay at rest or continue at constant motion unless acted on by an external force; two: the force acting on an object is equal to the product of the mass of the object and its acceleration; three: every action has an equal and opposite reaction.

Motive Power
In the 1824 publication Reflections on the Motive Power of Fire, French physicist Sadi Carnot, a former student (1812-14) of the École Polytechnique, defined the term "motive power", what we now understand as work, as: "the effect that a motor is capable of producing", which can be likened to "the elevation of a weight to a certain height", having a measure of "the product of the weight multiplied by the height to which it is raised". [2] In equation form:

Motive power = weight height

The units of the term weight, later explicitly defined as mass of the object times the force of gravity mg, however, were not clarified at this point by Carnot.

Travail
The actual term “work” as the product of force and distance, was coined by French physicist Gustave Coriolis who used the French term travail in his 1829 textbook Calculation of the Effect of Machines. [3] In the preface to this work, the English translation reads:

“The name of work is 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 mv²), namely in via the useful effect that a moving mass (e.g. a piston) is capable of doing. [7] To cite an example of Coriolis' terminology, in his 1844 second edition, Coriolis outlined a section on what he called the "principle of the transmission of work in the movement of a material point". Defining P as sum of the moving forces, he states: [8]

“The integral ∫ PdS, PdS the product of the tangential component of the force F by the infinitesimal arc ds described by its point of application, is called the amount of work due to this force F . The PdS product 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 The Mechanical Theory of Heat (1865, 1875). In modern equation form:

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) the work which 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:

$W=\int_{V_i}^{V_f} P\,dV$

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 F and the distance d through which the force moves a body is the "work" done:

$W = F d \,$

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 [kilogramsm/s²], and the subsequent SI unit of work, Joule [kilogramsm²/s²] came in later years.

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). The Mechanical Theory of Heat, (pg. 1), (2nd ed). London: Macmillan & Co.
(b) Bennett, Joseph. (1858). A Treatise on Hydraulics, (pg. 316). London: D. Van nostrand.
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." Entropy 2 (3) pgs. 106-141.
3. (a) Jammer, Max (1957). Concepts of Force, (pg. 167). Dover Publications, Inc.
(b) Holtzapple, Mark, T. and Reece, Dan W. (2002). Foundations of Engineering, (pg. 312). McGraw-Hill.
4. (a) Coriolis Biography – MacTutor History of Mathematics Archive.
(b) O I Franksen, “The virtual work principle - a unifying systems concept”, in Structures and operations in engineering and management systems, Trondheim, 1980 (Trondheim, 1981), 17-152.
(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, Ann. of Sci. 41 (1), 1-33.
5. Clapeyron, Émile. (1834). “Memoir on the Motive Power of Heat”, Journal de l’Ecole Polytechnique. XIV, 153 (and Poggendorff's Annalender Physick, LIX, [1843] 446, 566).
6. Laider, Keith J. (1993). The World of Physical Chemistry, (pg. 77). Oxford University Press.
7. Roche, John J. (1998). The Mathematics of Measurement (pg. 159). Springer.
8. Coriolis, Gustave. (1844). Treatise on the Mechanics of Solid Bodies and Calculation of the Effect on Machines (Traité de la Mécanique des Corps Solides et du Calcul de l'effet des Machines) (section: Principle of the Transmission of Work in the Movement of a Material Point, pgs. 35-40). 2nd. Ed. Paris.
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.