|A simplified sketch of the conservation of energy, by American physics cartoonist Paul Hewitt (Ѻ), showing the transformation of chemical energy into kinetic energy into potential energy into the heat and the work of explosion of impact.|
The following circa 1863 quote by German physicist Hermann Helmholtz, a co-discoverer himself with his theories on the conservation of force, expresses the gist of the conservation of energy in relation to its developers: 
“Kirchhoff’s predecessors in the field of radiation bore him much the same relation as, in the conservation of energy, Mayer, Colding, and Seguin bore to Joule and Thomson.”
Names attributed to the graduate establishment of this of the of the conservation of energy include: German pharmacist Karl Mohr (1837), French engineer Marc Seguin (1839), German physicist Robert Mayer (1841), English physicist James Joule (1843), Danish physicist Ludwig Colding (1843), Carl Holtzmann (1845), Welsh physicist William Grove (1846), German physicist Hermann Helmholtz (1847), William Thomson (1849), among others.
Early versions of the conservation of energy, often tended to employ the German word "Kraft", which can be loosely translated as force, power, or energy, depending, but most often as "force", stating to the effect that "kraft" was conserved. Force and energy, however, are not technically equivalent. Energy, in the form of work, is related to force, via the principle of the transmission of work (1829), when the force moves and object through a distance:
In modern terms, it is understood that energy, but not force, is conserved. The details of this, in respect to the German-to-English renditions of the term "kraft", however, do not seem to have solidified into the late 19th century.
In 1837, German chemist Karl Mohr gave one of the earliest statements of the conservation of kraft: 
“Besides the fifty-four known chemical elements there is in the physical world one agent only, and this is called Kraft. It may appear, according to circumstances, as motion, chemical affinity, cohesion, electricity, light and magnetism; and from any one of these forms it can be transformed into any of the others.”
In the late 1840s, using conclusions reached by Mayer and Joule, Helmholtz formulated, very clearly, the existence of the law of conservation of energy or of “force” (as energy was called at that time).  Specifically, in 1847 Helmholtz stated an equivalent version: “vital heat is the product of mechanical forces within the organism; all heat is related to ordinary forces” and that: 
“Force itself can never be destroyed.”
One of Helmholtz' more famous publications on this subject was a series of lectures delivered at Karlsruhe, in the winter of 1862, titled “On the Conservation of Force”.  Helmholtz introduced the subject by stating that “the last decades of scientific development have led us to the recognition of a new universal law of all natural phenomena”, which asserts that:
“The quantity of force which can be brought into action in the whole of nature is unchangeable, and can neither be increased nor diminished.”
Using the example of gravity, one of the fundamental forces, Helmholtz shows how gravity can be used to do work by detailing the actions of a falling weight that drives the workings of a clock. Although the weight will have lost it capability to perform work when it reaches the floor, it will not lose its force, in that gravity remains. The amount of work can then be determined by the weight times the distance travelled.
Heat can also produce work, such as in the operation of a steam engine. Here, Helmholtz recalls the point that heat must not be considered as a substance but merely as a movement of internal particles. This is in contrast to the older views in which heat was considered as a type of substance called caloric or, before that, phlogiston, whose amount was believed to be constant. The amount of heat needed to melt a piece of ice is the same, for instance, as the amount of heat that must be extracted to refreeze the water. Helmholtz explained, however, that as soon as heat is converted into work, that an equivalent amount of heat is destroyed or “consumed” using the terminology of Rudolf Clausius.
Other examples where work is generated at a cost, described by Helmholtz, include: a raised weight can do work but while doing that it must sink and no longer do work; a stretched spring can do work but will become loose; the velocity of a mass can do work but will eventually come to rest; chemical forces (energy) can do work but they will get exhausted; electrical force can do work but will consume chemical or mechanical forces. On this logic, Helmholtz concluded that all natural forces (energy) can do work but they are at the same time exhausted to the degree of work performed. He then formulated that the total quantity of all forces capable of doing work in the whole universe remains constant. He compared this with the laws of constant mass or constant chemical elements. In conclusion, he touches briefly on the topic of perpetual motion and states that force cannot be produced from nothing: something must be consumed.
The principle of the conservation of energy has a long and elaborate history, stemming from the 1670s theory of vis viva or “living force” of German mathematician Gottfried Leibniz, to debates on the caloric theory in contrast to the mechanical equivalent of heat beginning in the years 1787 to 1798, to the coining of the term “energy” in 1807 by English physician and physicist Thomas Young. Scottish physicists Peter Tait and Balfour Stewart argue that the conservation of energy has its roots in one interpretation of Newton’s third law of motion (1687); they define the conservation of energy as follows: 
“In any system of bodies whatever, to which no energy is communicated by external bodies, and which parts with no energy to external bodies, the sum of the various potential and kinetic energies remains forever unaltered.”
On this note, two principle formulators of the modern understanding of the conservation of energy were German physician Robert Mayer and German physician and physicist Hermann Helmholtz who both spoke of the “law of the conservation of force.” 
In 1841, Mayer stated the most famous version of the conservation of energy: 
“Energy can be neither created nor destroyed.”
In 1849, in a footnote to a discussion of a perfect thermo-dynamic engine (a footnote mentioning the 1843 work of Joule), Irish physicist William Thomson stated, in his famous paper “An Account of Carnot’s Theory of the Motive Power of Heat’, that: 
“Nothing can be lost in nature—no energy can be destroyed.”
In 1874, English physicist Balfour Steward published the book The Conservation of Energy, a book that went through nine-editions over following twenty-five years. 
In chemistry, the conservation of energy is a principle which states that in a chemical reaction, the total amount of energy in the system remains unchanged.  In a chemical reaction, to elaborate, for each component there may be changes in energy due to change of physical state, changes in the nature of the chemical bonds, and either an input or output of energy. In this process, there is, however, no net gain or loss of energy. The energy of a battery, for instance, which is a direct result of a chemical reaction inside the battery, can be transferred into an electrical circuit, which can then used to produce heat or light a bulb; in this process, the total amount of energy is constant.
The principle of the conservation of energy was introduced into thermodynamics, specifically via the mechanical equivalent of heat as embodied in the first and second laws of thermodynamics, principally through the writings of German physicists Rudolf Clausius, with his 1865 textbook Mechanical Theory of Heat, and Hermann Helmholtz, with his 1882 article "The Thermodynamics of Chemical Operations".  The "law of dissipation of energy" is often seen as its counterpart.
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