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| {{About|the law of conservation of energy in physics|sustainable energy resources|Energy conservation}}
| | Hello! <br>My name is Dorris and I'm a 25 years old girl from Great Britain.<br><br>my web blog :: [http://hallenturniere.tvsteinheim-fussball.de/index.php?option=com_phocaguestbook&view=phocaguestbook&id=1&Itemid=13 Fifa 15 Coin Generator] |
| {{Refimprove|date=February 2013}}
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| [[File:physicsworks.ogg|250px|thumb|Prof. [[Walter Lewin]] demonstrates the conservation of mechanical energy, touching a wrecking ball with his jaw. ([http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-11/ MIT Course 8.01])<ref>
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| {{cite video
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| | people = [[Walter Lewin]] | date = October 4, 1999
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| | title = Work, Kinetic Energy, and Universal Gravitation. MIT Course 8.01: Classical Mechanics, Lecture 11.
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| | url = http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-11/
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| | format = ogg | medium = videotape | language = English
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| | publisher = [[MIT OpenCourseWare|MIT OCW]] | location = Cambridge, MA USA
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| | accessdate = December 23, 2010 | time = 45:35–49:11 | ref = lewin
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| | quote = "150 Joules is enough to kill you."
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| }}</ref> ]]
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| In physics, the '''law of conservation of energy''' states that the total [[energy]] of an [[isolated system]] cannot change—it is said to be [[Conservation law|''conserved'']] over time. Energy can be neither created nor destroyed, but can change [[Forms of energy|form]], for instance [[chemical energy]] can be [[Energy conversion|converted]] to [[kinetic energy]] in the explosion of a stick of [[dynamite]].
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| A consequence of the [[Laws of science|law]] of conservation of energy is that a [[Perpetual motion#Basic principles#Classification|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.<ref>Planck, M. (1923/1927). ''Treatise on Thermodynamics'', third English edition translated by A. Ogg from the seventh German edition, Longmans, Green & Co., London, page 40.</ref>
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| ==History==
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| [[File:Leibniz.jpg|thumb|150px|Gottfried Leibniz]]
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| [[Ancient]] [[philosopher]]s as far back as [[Thales|Thales of Miletus]] {{circa}}~550 BCE had inklings of the conservation of some underlying substance of which everything is made. However, there is no particular reason to identify this with what we know today as "mass-energy" (for example, Thales thought it was water). [[Empedocles]] (490–430 BCE) wrote that in his universal system, composed of [[Classical element|four roots]] (earth, air, water, fire), "nothing comes to be or perishes",<ref>{{cite journal|last=Janko|first=Richard|title=Empedocles, "On Nature"|journal=Zeitschrift für Papyrologie und Epigraphik|year=2004 |volume=150 |pages=1–26|url=http://ancphil.lsa.umich.edu/-/downloads/faculty/janko/empedocles-nature.pdf }}</ref> but these elements suffer continual rearrangement.
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| In 1638, [[Galileo Galilei|Galileo]] published his analysis of several situations—including the celebrated "interrupted pendulum"—which can be described (in modern language) as conservatively converting potential energy to kinetic energy and back again. However, Galileo did not state the process in modern terms and again cannot be credited with the crucial insight.
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| It was [[Gottfried Wilhelm Leibniz]] during 1676–1689 who first attempted a mathematical formulation of the kind of energy which is connected with ''motion'' (kinetic energy). Leibniz noticed that in many mechanical systems (of several [[mass]]es, ''m<sub>i</sub>'' each with [[velocity]] ''v<sub>i</sub>'' ),
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| :<math>\sum_{i} m_i v_i^2</math>
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| 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 [[physicist]]s at that time held that the [[conservation of momentum]], which holds even in systems with friction, as defined by the [[momentum]]:
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| :<math>\,\!\sum_{i} m_i v_i</math>
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| was the conserved ''vis viva''. It was later shown that, under the proper conditions, both quantities are conserved simultaneously such as in [[elastic collision]]s.
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| It was largely [[engineer]]s such as [[John Smeaton]], [[Peter Ewart]], [[:de:Carl Holtzmann|Carl Holtzmann]], [[Gustave-Adolphe Hirn]] and [[Marc Seguin]] who objected 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 [[chemist]]s 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]].<ref>Lavoisier, A.L. & Laplace, P.S. (1780) "Memoir on Heat", ''Académie Royale des Sciences'' pp. 4–355</ref> [[Benjamin Thompson|Count Rumford]]'s 1798 observations of heat generation during the [[Boring (manufacturing)|boring]] of [[cannon]]s added more weight to the view that mechanical motion could be converted into heat, and (as importantly) that the conversion was quantitative and could be predicted (allowing for a universal conversion constant between kinetic energy and heat). ''Vis viva'' now started to be known as ''energy'', after the term was first used in that sense by [[Thomas Young (scientist)|Thomas Young]] in 1807.
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| [[File:Gustave coriolis.jpg|thumb|150px|Gaspard-Gustave Coriolis]]
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| The recalibration of ''vis viva'' to
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| :<math>\frac {1} {2}\sum_{i} m_i v_i^2</math>
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| which can be understood as finding the exact value for the kinetic energy to [[Work (thermodynamics)|work]] conversion constant, was largely the result of the work of [[Gaspard-Gustave Coriolis]] and [[Jean-Victor Poncelet]] over the period 1819–1839. The former called the quantity ''quantité de travail'' (quantity of work) and the latter, ''travail mécanique'' (mechanical work), and both championed its use in engineering calculation.
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| In a 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 in the words: "besides the 54 known chemical elements there is in the physical world one agent only, and this is called ''Kraft'' [energy or work]. 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."
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| ===Mechanical equivalent of heat===
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| A key stage in the development of the modern conservation principle was the demonstration of the ''[[mechanical equivalent of heat]]''. The [[caloric theory]] maintained that heat could neither be created nor destroyed but conservation of energy entails the contrary principle that heat and mechanical work are interchangeable.
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| In 1798 Count Rumford ([[Benjamin Thompson]]) performed measurements of the frictional heat generated in boring cannons and developed the idea that heat is a form of kinetic energy; his measurements refuted caloric theory, but were imprecise enough to leave room for doubt.
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| [[File:SS-joule.jpg|thumb|left|130px|James Prescott Joule]]
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| The mechanical equivalence principle was first stated in its modern form by the German surgeon [[Julius Robert von Mayer]] in 1842.<ref>von Mayer, J.R. (1842) "Remarks on the forces of inorganic nature" in ''Annalen der Chemie und Pharmacie'', '''43''', 233</ref> Mayer reached his conclusion on a voyage to the [[Dutch East Indies]], where he found that his patients' [[blood]] was a deeper [[red]] because they were consuming less [[oxygen]], and therefore less energy, to maintain their body temperature in the hotter climate. He discovered that [[heat]] and [[mechanical work]] were both forms of energy and in 1845, after improving his knowledge of physics, he published a monograph that stated a quantitative relationship between them.<ref>Mayer, J.R. (1845). ''Die organische Bewegung in ihrem Zusammenhange mit dem Stoffwechsel. Ein Beitrag zur Naturkunde'', Dechsler, Heilbronn.</ref>
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| [[File:Joule's Apparatus (Harper's Scan).png|thumb|right|Joule's apparatus for measuring the mechanical equivalent of heat. A descending weight attached to a string causes a paddle immersed in water to rotate.]]
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| Meanwhile, in 1843 [[James Prescott Joule]] independently discovered the mechanical equivalent in a series of experiments. In the most famous, now called the "Joule apparatus", a descending weight attached to a string caused a paddle immersed in water to rotate. He showed that the gravitational [[potential energy]] lost by the weight in descending was equal to the thermal energy ([[heat]]) gained by the water by [[friction]] with the paddle.
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| Over the period 1840–1843, similar work was carried out by engineer [[Ludwig A. Colding]] though it was little known outside his native [[Denmark]].
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| Both Joule's and Mayer's work suffered from resistance and neglect but it was Joule's that eventually drew the wider recognition.
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| :''For the dispute between Joule and Mayer over priority, see [[Mechanical equivalent of heat#History and priority dispute|Mechanical equivalent of heat: Priority]]'' | |
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| In 1844, [[William Robert Grove]] postulated a relationship between mechanics, heat, [[light]], [[electricity]] and [[magnetism]] by treating them all as manifestations of a single "force" (''energy'' in modern terms). In 1874 Grove published his theories in his book ''The Correlation of Physical Forces''.<ref>{{cite book | author=Grove, W. R. | title=The Correlation of Physical Forces | location=London | publisher=Longmans, Green | year=1874 | edition=6th }}</ref> In 1847, drawing on the earlier work of Joule, [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] and [[Émile Clapeyron]], [[Hermann von Helmholtz]] arrived at conclusions similar to Grove's and published his theories in his book ''Über die Erhaltung der Kraft'' (''On the Conservation of Force'', 1847). The general modern acceptance of the principle stems from this publication.
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| In 1877, [[Peter Guthrie Tait]] claimed that the principle originated with Sir Isaac Newton, based on a creative reading of propositions 40 and 41 of the ''[[Philosophiae Naturalis Principia Mathematica]]''. This is now regarded as an example of [[Whig history]].<ref>{{cite book
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| |title=On the shoulders of merchants: exchange and the mathematical conception of nature in early modern Europe
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| |first1=Richard W. |last1=Hadden |publisher=SUNY Press
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| |year=1994 |isbn=0-7914-2011-6 |page=13
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| |url=http://books.google.com/books?id=7IxtC4Jw1YoC}}, [http://books.google.com/books?id=7IxtC4Jw1YoC&pg=PA13 Chapter 1, p. 13]
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| </ref>
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| ===Mass–energy equivalence===
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| {{main|Mass–energy equivalence}}
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| Matter is composed of such things as atoms, electrons, neutrons, and protons. It has [[rest mass|''intrinsic'' or ''rest'' mass]]. In the limited range of recognized experience of the nineteenth century it was found that such rest mass is conserved. In the twentieth century it was discovered that it has [[Mass-energy equivalence|an equivalent amount of]] ''rest energy''. This means that it can be converted to or from equivalent amounts of ''other'' (non-material) forms of energy, for example kinetic energy, potential energy, and electromagnetic radiant energy. When this happens, as recognized in twentieth century experience, rest mass is not conserved, unlike the [[mass in special relativity|''total'' mass]] or ''total'' energy. All forms of energy contribute to the total mass and total energy.
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| For example an [[electron]] and a [[positron]] each have rest mass. They can perish together, converting their combined rest energy into [[photon]]s having electromagnetic radiant energy, but no rest mass. If this occurs within an isolated system that does not release the photons or their energy into the external surroundings, then neither the total ''mass'' nor the total ''energy'' of the system will change. The produced electromagnetic radiant energy contributes just as much to the inertia (and to any weight) of the system as did the rest mass of the electron and positron before their demise. Conversely, non-material forms of energy can perish into matter, which has rest mass.
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| Thus, conservation of energy (''total'', including material or ''rest'' energy), and [[conservation of mass]] (''total'', not just ''rest''), each still holds as an (equivalent) law. In the nineteenth century these had appeared as two seemingly-distinct laws.
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| ==First law of thermodynamics==
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| {{main|First law of thermodynamics}}
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| For a [[Closed system#In thermodynamics|closed thermodynamic system]], the first law of thermodynamics may be stated as:
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| :<math>\delta Q = \mathrm{d}U + \delta W</math>, or equivalently, <math>\mathrm{d}U = \delta Q - \delta W,</math>
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| where <math>\delta Q</math> is the amount of [[energy]] added to the system by a heating process, <math>\delta W</math> is the amount of energy lost by the system due to [[Work (thermodynamics)|work]] done by the system on its surroundings and <math>\mathrm{d}U</math> is the change in the [[internal energy]] of the system.
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| The δ's before the heat and work terms are used to indicate that they describe an increment of energy which is to be interpreted somewhat differently than the <math>\mathrm{d}U</math> increment of internal energy (see [[Inexact differential]]). Work and heat refer to kinds of process which add or subtract energy to or from a system, while the internal energy <math>U</math> is a property of a particular state of the system when it is in unchanging thermodynamic equilibrium. Thus the term "heat energy" for <math>\delta Q</math> means "that amount of energy added as the result of heating" rather than referring to a particular form of energy. Likewise, the term "work energy" for <math>\delta W</math> means "that amount of energy lost as the result of work". Thus one can state the amount of internal energy possessed by a thermodynamic system that one knows is presently in a given state, but one cannot tell, just from knowledge of the given present state, how much energy has in the past flowed into or out of the system as a result of its being heated or cooled, nor as the result of work being performed on or by the system.
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| [[Entropy (classical thermodynamics)|Entropy]] is a function of the state of a system which tells of the possibility of conversion of heat into work.
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| For a simple compressible system, the work performed by the system may be written:
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| :<math>\delta W = P\,\mathrm{d}V,</math>
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| where <math>P</math> is the [[pressure]] and <math>dV</math> is a small change in the [[volume]] of the system, each of which are system variables. The heat energy may be written
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| :<math>\delta Q = T\,\mathrm{d}S,</math>
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| where <math>T</math> is the [[temperature]] and <math>\mathrm{d}S</math> is a small change in the [[entropy]] of the system. Temperature and entropy are variables of state of a system.
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| For a simple open system (in which mass may be exchanged with the environment), containing a single type of particle, the first law is written:<ref name="Smith1980">{{cite journal |last1=Smith |first1=D. A. |year=1980 |title=Definition of Heat in Open SYstems |journal=Aust. J. Phys |volume=33 |pages=95–105 |url=http://www.publish.csiro.au/paper/PH800095.htm |accessdate=8 March 2013}}</ref>
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| :<math>\mathrm{d}U = \delta Q - \delta W + u'\,dM,\,</math>
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| where <math>dM</math> is the added mass and <math>u'</math> is the internal energy per unit mass of the added mass. The addition of mass may be accompanied by a volume change which is not associated with work (e.g. for a liquid-vapor system, the volume of the vapor system may increase due to volume lost by the evaporating liquid). In the reversible case, the work will be given by <math>\delta W=-P(dV-v\,dM)</math> where v is the specific volume of the added mass.
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| ==Noether's theorem==
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| {{main|Noether's theorem}}
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| The conservation of energy is a common feature in many physical theories. From a mathematical point of view it is understood as a consequence of [[Noether's theorem]], which states every continuous symmetry of a physical theory has an associated conserved quantity; if the theory's symmetry is time invariance then the conserved quantity is called "energy". The energy conservation law is a consequence of the shift [[Symmetry in physics|symmetry]] of [[time]]; energy conservation is implied by the empirical fact that the [[Physical law|laws of physics]] do not change with time itself. Philosophically this can be stated as "nothing depends on time per se".
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| In other words, if the physical system is invariant under the [[continuous symmetry]] of [[time]] translation then its energy (which is [[canonical conjugate]] quantity to time) is conserved. Conversely, systems which are not invariant under shifts in time (an example, systems with time dependent potential energy) do not exhibit conservation of energy – unless we consider them to exchange energy with another, external system so that the theory of the enlarged system becomes time invariant again. Since any time-varying system can be embedded within a larger time-invariant system (with the exception of the universe), conservation can always be recovered by a suitable re-definition of what energy is and extending the scope of your system. Conservation of energy for finite systems is valid in such physical theories as special relativity or and quantum theory (including [[Quantum electrodynamics|QED]]) in the flat [[space-time]].
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| ==Relativity==
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| With the discovery of [[special relativity]] by [[Albert Einstein]], energy was proposed to be one component of an [[four-momentum|energy-momentum 4-vector]]. Each of the four components (one of energy and three of momentum) of this vector is separately conserved across time, in any closed system, as seen from any given [[inertial reference frame]]. Also conserved is the vector length ([[Minkowski space|Minkowski norm]]), which is the [[rest mass]] for single particles, and the [[invariant mass]] for systems of particles (where momenta and energy are separately summed before the length is calculated—see the article on [[invariant mass]]).
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| The relativistic energy of a single [[mass]]ive particle contains a term related to its [[rest mass]] in addition to its kinetic energy of motion. In the limit of zero kinetic energy (or equivalently in the [[rest frame]]) of a massive particle; or else in the [[center of momentum frame]] for objects or systems which retain kinetic energy, the [[total energy]] of particle or object (including internal kinetic energy in systems) is related to its [[rest mass]] or its [[invariant mass]] via the famous equation <math>E=mc^2</math>.
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| Thus, the rule of [[Mass in special relativity|''conservation of energy'' over time in special relativity]] continues to hold, so long as the [[frame of reference|reference frame]] of the observer is unchanged. This applies to the total energy of systems, although different observers disagree as to the energy value. Also conserved, and invariant to all observers, is the [[invariant mass]], which is the minimal system mass and energy that can be seen by any observer, and which is defined by the [[energy–momentum relation]].
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| In [[general relativity]] conservation of energy-momentum is expressed with the aid of a [[stress-energy-momentum pseudotensor]]. The theory of general relativity leaves open the question of whether there is a conservation of energy for the entire universe.
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| ==Quantum theory==
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| In [[quantum mechanics]], energy of a quantum system is described by a self-adjoint (Hermite) operator called Hamiltonian, which acts on the Hilbert space (or a space of [[wave functions]] ) of the system. If the Hamiltonian is a time independent operator, emergence probability of the measurement result does not change in time over the evolution of the system. Thus the expectation value of energy is also time independent. The local energy conservation in quantum field theory is ensured by the quantum [[Noether's theorem]] for energy-momentum tensor operator. Note that due to the lack of the (universal) time operator in quantum theory, the uncertainty relations for time and energy are not fundamental in contrast to the position momentum uncertainty principle, and merely holds in specific cases (See [[Uncertainty principle]]). Energy at each fixed time can be precisely measured in principle without any problem caused by the time energy uncertainty relations. Thus the conservation of energy in time is a well defined concept even in quantum mechanics.
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| ==See also==
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| * [[Energy quality]]
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| * [[Energy transformation]]
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| * [[Eternity of the world]]
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| * [[Laws of thermodynamics]]
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| * [[Lagrangian]]
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| * [[Principles of energetics]]
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| ==Footnotes==
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| {{reflist|30em}}
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| ==References==
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| ===Modern accounts===
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| * Goldstein, Martin, and Inge F., 1993. ''The Refrigerator and the Universe''. Harvard Univ. Press. A gentle introduction.
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| * {{cite book | author=Kroemer, Herbert; Kittel, Charles | title=Thermal Physics (2nd ed.) | publisher=W. H. Freeman Company | year=1980 | isbn=0-7167-1088-9 }}
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| * {{cite book | author=Nolan, Peter J. | title=Fundamentals of College Physics, 2nd ed. | publisher=William C. Brown Publishers | year=1996 | id=}}
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| * {{cite book | author=Oxtoby & Nachtrieb | title=Principles of Modern Chemistry,'' 3rd ed. | publisher=Saunders College Publishing | year=1996 | id=}}
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| * {{cite book | author=Papineau, D. | title=Thinking about Consciousness | location=Oxford | publisher=Oxford University Press | year=2002 | id=}}
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| * {{cite book | author=Serway, Raymond A.; Jewett, John W. | title=Physics for Scientists and Engineers (6th ed.) | publisher=Brooks/Cole | year=2004 | isbn=0-534-40842-7 }}
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| * Stenger, Victor J. (2000). ''Timeless Reality''. Prometheus Books. Especially chpt. 12. Nontechnical.
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| * {{cite book | author=Tipler, Paul | title=Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.) | publisher=W. H. Freeman | year=2004 | isbn=0-7167-0809-4}}
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| *{{cite book | author=[[Lanczos]], Cornelius | title=The Variational Principles of Mechanics | location= Toronto | publisher=University of Toronto Press | year=1970 | isbn=0-8020-1743-6}}
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| ===History of ideas===
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| * {{cite journal | author=Brown, T.M. | title=Resource letter EEC-1 on the evolution of energy concepts from Galileo to Helmholtz | journal=American Journal of Physics | year=1965 | volume=33 | pages=759–765 | doi = 10.1119/1.1970980|bibcode = 1965AmJPh..33..759B | issue=10 }}
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| * {{cite book | author=Cardwell, D.S.L. | title=From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age | location=London | publisher=Heinemann | year=1971 | isbn=0-435-54150-1 }}
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| * {{cite book | author=Guillen, M. | title=Five Equations That Changed the World | publisher= Abacus| year=1999 | isbn=0-349-11064-6 | location=New York }}
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| * {{cite book | author=Hiebert, E.N. | title=Historical Roots of the Principle of Conservation of Energy | publisher=Ayer Co Pub | location=Madison, Wis. | year=1981 | isbn=0-405-13880-6 }}
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| * [[Thomas Kuhn|Kuhn, T.S.]] (1957) “Energy conservation as an example of simultaneous discovery”, in M. Clagett (ed.) ''Critical Problems in the History of Science'' ''pp.''321–56
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| * {{cite journal | author=Sarton, G. | title=The discovery of the law of conservation of energy | journal=Isis | year=1929 | volume=13 | pages=18–49 | doi=10.1086/346430 | last2=Joule | first2=J. P. | last3=Carnot | first3=Sadi }}
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| * {{cite book | author=Smith, C. | title=The Science of Energy: Cultural History of Energy Physics in Victorian Britain | location=London | publisher=Heinemann | year=1998 | isbn=0-485-11431-3 }}
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| * {{cite book | author=[[Ernst Mach|Mach, E.]] | title=History and Root of the Principles of the Conservation of Energy | publisher=Open Court Pub. Co., IL | year=1872 | id=}}
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| * {{cite book | author=[[Henri Poincaré|Poincaré, H.]] | title=Science and Hypothesis | publisher=Walter Scott Publishing Co. Ltd; Dover reprint, 1952 | year=1905 | isbn=0-486-60221-4 }}, Chapter 8, "Energy and Thermo-dynamics"
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| ==External links==
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| * [http://www.physnet.org/modules/pdf_modules/m158.pdf <small>MISN-0-158</small> ''The First Law of Thermodynamics''] ([[Portable Document Format|PDF file]]) by Jerzy Borysowicz for [http://www.physnet.org Project PHYSNET].
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| {{DEFAULTSORT:Conservation Of Energy}}
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| <!--Categories-->
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| [[Category:Energy (physics)]]
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| [[Category:Laws of thermodynamics]]
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| [[Category:Conservation laws]]
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| [[Category:History of physics]]
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| [[Category:History of ideas]]
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