Conservation of energy
The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. In the case of a closed system, the principle says that the total amount of energy within the system can only be changed through energy entering or leaving the system. Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite.
Classically, the conservation of energy was distinct from the conservation of mass. However, special relativity shows that mass is related to energy and vice versa by, the equation representing mass–energy equivalence, and science now takes the view that mass-energy as a whole is conserved. This implies that mass can be converted to energy, and vice versa. This is observed in the nuclear binding energy of atomic nuclei, where a mass defect is measured. It is believed that mass-energy equivalence becomes important in extreme physical conditions, such as those that likely existed in the universe very shortly after the Big Bang or when black holes emit Hawking radiation.
Given the stationary-action principle, the conservation of energy can be rigorously proven by Noether's theorem as a consequence of continuous time translation symmetry; that is, from the fact that the laws of physics do not change over time.
A consequence of the law of conservation of energy is that a perpetual motion machine of the first kind cannot exist; that is to say, no system without an external energy supply can deliver an unlimited amount of energy to its surroundings. Depending on the definition of energy, the conservation of energy can arguably be violated by general relativity on the cosmological scale. In quantum mechanics, Noether's theorem is known to apply to the expected value, making any consistent conservation violation provably impossible, but whether individual conservation-violating events could ever exist or be observed is subject to some debate.
History
as far back as Thales of Miletus 550 BCE had inklings of the conservation of some underlying substance of which everything is made. However, there is no particular reason to identify their theories with what we know today as "mass-energy". Empedocles wrote that in his universal system, composed of four roots, "nothing comes to be or perishes"; instead, these elements suffer continual rearrangement. Epicurus on the other hand believed everything in the universe to be composed of indivisible units of matter—the ancient precursor to 'atoms'—and he too had some idea of the necessity of conservation, stating that "the sum total of things was always such as it is now, and such it will ever remain."In 1605, the Flemish scientist Simon Stevin was able to solve a number of problems in statics based on the principle that perpetual motion was impossible.
In 1639, Galileo published his analysis of several situations—including the celebrated "interrupted pendulum"—which can be described as conservatively converting potential energy to kinetic energy and back again. Essentially, he pointed out that the height a moving body rises is equal to the height from which it falls, and used this observation to infer the idea of inertia. The remarkable aspect of this observation is that the height to which a moving body ascends on a frictionless surface does not depend on the shape of the surface.
In 1669, Christiaan Huygens published a brief account on his laws of collision. Among the quantities he listed as being invariant before and after the collision of bodies were both the sum of their linear momenta as well as the sum of their kinetic energies. However, the difference between elastic and inelastic collision was not understood at the time. This led to the dispute among later researchers as to which of these conserved quantities was the more fundamental. In his Horologium Oscillatorium, Huygens gave a much clearer statement regarding the height of ascent of a moving body, and connected this idea with the impossibility of perpetual motion. His study of the dynamics of pendulum motion was based on a single principle, known as Torricelli's Principle: that the center of gravity of a heavy object, or collection of objects, cannot lift itself. Using this principle, Huygens was able to derive the formula for the center of oscillation by an "energy" method, without dealing with forces or torques.
Between 1676 and 1689, Gottfried Leibniz first attempted a mathematical formulation of the kind of energy that is associated with motion. Using Huygens's work on collision, Leibniz noticed that in many mechanical systems,
was conserved so long as the masses did not interact. He called this quantity the vis viva or living force of the system. The principle represents an accurate statement of the approximate conservation of kinetic energy in situations where there is no friction. Many physicists at that time, including Isaac Newton, held that the conservation of momentum, which holds even in systems with friction, as defined by the momentum:
was the conserved vis viva. It was later shown that both quantities are conserved simultaneously given the proper conditions, such as in an elastic collision.
In 1687, Isaac Newton published his Principia, which set out his laws of motion. It was organized around the concept of force and momentum. However, the researchers were quick to recognize that the principles set out in the book, while fine for point masses, were not sufficient to tackle the motions of rigid and fluid bodies. Some other principles were also required.
By the 1690s, Leibniz was arguing that conservation of vis viva and conservation of momentum undermined the then-popular philosophical doctrine of interactionist dualism.
The law of conservation of vis viva was championed by the father and son duo, Johann and Daniel Bernoulli. The former enunciated the principle of virtual work as used in statics in its full generality in 1715, while the latter based his Hydrodynamica, published in 1738, on this single vis viva conservation principle. Daniel's study of loss of vis viva of flowing water led him to formulate Bernoulli's principle, which asserts the loss to be proportional to the change in hydrodynamic pressure. Daniel also formulated the notion of work and efficiency for hydraulic machines; and he gave a kinetic theory of gases, and linked the kinetic energy of gas molecules with the temperature of the gas.
This focus on the vis viva by the continental physicists eventually led to the discovery of stationarity principles governing mechanics, such as the D'Alembert's principle, Lagrangian, and Hamiltonian formulations of mechanics.
Émilie du Châtelet proposed and tested the hypothesis of the conservation of total energy, as distinct from momentum. Inspired by the theories of Gottfried Leibniz, she repeated and publicized an experiment originally devised by Willem 's Gravesande in 1722 in which balls were dropped from different heights into a sheet of soft clay. Each ball's kinetic energy—as indicated by the quantity of material displaced—was shown to be proportional to the square of the velocity. The deformation of the clay was found to be directly proportional to the height from which the balls were dropped, equal to the initial potential energy. Some earlier workers, including Newton and Voltaire, had believed that "energy" was not distinct from momentum and therefore proportional to velocity. According to this understanding, the deformation of the clay should have been proportional to the square root of the height from which the balls were dropped. In classical physics, the correct formula is, where is the kinetic energy of an object, its mass and its speed. On this basis, du Châtelet proposed that energy must always have the same dimensions in any form, which is necessary to be able to consider it in different forms.
Engineers such as John Smeaton, Peter Ewart,, Gustave-Adolphe Hirn, and Marc Seguin recognized that conservation of momentum alone was not adequate for practical calculation and made use of Leibniz's principle. The principle was also championed by some chemists such as William Hyde Wollaston. Academics such as John Playfair were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on the second law of thermodynamics, but in the 18th and 19th centuries, the fate of the lost energy was still unknown.
Gradually it came to be suspected that the heat inevitably generated by motion under friction was another form of vis viva. In 1783, Antoine Lavoisier and Pierre-Simon Laplace reviewed the two competing theories of vis viva and caloric theory. Count Rumford's 1798 observations of heat generation during the boring of cannons added more weight to the view that mechanical motion could be converted into heat and that the conversion was quantitative and could be predicted. Vis viva then started to be known as energy, after the term was first used in that sense by Thomas Young in 1807.
The recalibration of vis viva to
which can be understood as converting kinetic energy to work, was largely the result of Gaspard-Gustave Coriolis and Jean-Victor Poncelet over the period 1819–1839. The former called the quantity quantité de travail and the latter, travail mécanique, and both championed its use in engineering calculations.
In the paper Über die Natur der Wärme, published in the Zeitschrift für Physik in 1837, Karl Friedrich Mohr gave one of the earliest general statements of the doctrine of the conservation of energy: "besides the 54 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."