text:
Conservation of energy
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article is about the law of Conservation of Energy in physics. For sustainable energy resources, see Energy conservation.
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (February 2013) (Learn how and when to remove this template message)
In physics, 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.[1] This law means that energy can neither be created nor destroyed; rather, it can only be transformed 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 the forms of energy that were released in the explosion, such as the kinetic 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, conservation of energy was distinct from conservation of mass; however, special relativity showed that mass could be converted to energy and vice versa by E = mc2, and science now takes the view that mass–energy is conserved.
Scientifically speaking, conservation of energy can be rigorously proven by the Noether 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.[2] For systems which do not have time translation symmetry, it may not be possible to define conservation of energy. Examples include curved spacetimes in general relativity[3] or time crystals in condensed matter physics.[4][5][6][7]
Contents
[hide]
1 History
1.1 Mechanical equivalent of heat
1.2 Mass–energy equivalence
1.3 Conservation of energy in beta decay
2 First law of thermodynamics
3 Noether's theorem
4 Relativity
5 Quantum theory
6 See also
7 References
8 Bibliography
8.1 Modern accounts
8.2 History of ideas
9 External links
History[edit]
This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (November 2015) (Learn how and when to remove this template message)
Gottfried Leibniz
Ancient philosophers as far back as Thales of Miletus c. 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 this universal system, composed of four roots (earth, air, water, fire), "nothing comes to be or perishes";[8] instead, these elements suffer continual rearrangement.
In 1605, Simon Stevinus was able to solve a number of problems in statics based on the principle that perpetual motion was impossible.
In 1638, 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. 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, Christian Huygens published 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 momentums 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, he gave a much clearer statement regarding the height of ascent of a moving body, and connected this idea with the impossibility of a perpetual motion. Huygens' study of the dynamics of pendulum motion was based on a single principle: that the center of gravity of a heavy object cannot lift itself.
The fact that kinetic energy is scalar, unlike linear momentum which is a vector, and hence easier to work with did not escape the attention of Gottfried Wilhelm Leibniz. It was Leibniz during 1676–1689 who first attempted a mathematical formulation of the kind of energy which is connected with motion (kinetic energy). Using Huygens' work on collision, Leibniz noticed that in many mechanical systems (of several masses, mi each with velocity vi),
∑ i m i v i 2 {\displaystyle \sum _{i}m_{i}v_{i}^{2}}
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, such as Newton, held that the conservation of momentum, which holds even in systems with friction, as defined by the momentum:
∑ i m i v i {\displaystyle \,\!\sum _{i}m_{i}v_{i}}
was the conserved vis viva. It was later shown that both quantities are conserved simultaneously, given the proper conditions such as an elastic collision.
In 1687, Isaac Newton published his Principia, which 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.
Daniel Bernoulli
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 conservation principle. Daniel's study of loss of vis viva of flowing water led him to formulate the Bernoulli's principle, which relates 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 (1706 – 1749) 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 the balls were dropped from, equal to the initial potential energy. Earlier workers, including Newton and Voltaire, had all believed that "energy" (so far as they understood the concept at all) 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 from. In classical physics the correct formula is E k = 1 2 m v 2 {\displaystyle E_{k}={\frac {1}{2}}mv^{2}} , where E k {\displaystyle E_{k}} is the kinetic energy of an object, m {\displaystyle m} its mass and v {\displaystyle v} its speed. On this basis, Châtelet proposed that energy must always have the same dimensions in any form, which is necessary to be able to relate it in different forms (kinetic, potential, heat…).[9][10]
Engineers such as John Smeaton, Peter Ewart, Carl Holtzmann, 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.[11] 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 (as importantly) that the conversion was quantitative and could be predicted (allowing for a universal conversion constant between kinetic energy and heat). Vis viva then started to be known as energy, after the term was first used in that sense by Thomas Young in 1807.
Gaspard-Gustave Coriolis
The recalibration of vis viva to
1 2 ∑ i m i v i 2 {\displaystyle {\frac {1}{2}}\sum _{i}m_{i}v_{i}^{2}}
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 (quantity of work) and the latter, travail mécanique (mechanical work), and both championed its use in engineering calculation.
In a paper Über die Natur der Wärme(German "On the Nature of Heat/Warmth"), 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."
Mechanical equivalent of heat[edit]
This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (November 2015) (Learn how and when to remove this template message)
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, whereas conservation of energy entails the contrary principle that heat and mechanical work are interchangeable.
In the middle of the eighteenth century, Mikhail Lomonosov, a Russian scientist, postulated his corpusculo-kinetic theory of heat, which rejected the idea of a caloric. Through the results of empirical studies, Lomonosov came to the conclusion that heat was not transferred through the particles of the caloric fluid.
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.
James Prescott Joule
The mechanical equivalence principle was first stated in its modern form by the German surgeon Julius Robert von Mayer in 1842.[12] 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.[13]
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.
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 internal energy gained by the water through friction with the paddle.
Over the period 1840–1843, similar work was carried out by engineer Ludwig A. Colding, although it was little known outside his native Denmark.
Both Joule's and Mayer's work suffered from resistance and neglect but it was Joule's that eventually drew the wider recognition.
For the dispute between Joule and Mayer over priority, see Mechanical equivalent of heat: Priority.
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 1846, Grove published his theories in his book The Correlation of Physical Forces.[14] In 1847, drawing on the earlier work of Joule, 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).[15] The general modern acceptance of the principle stems from this publication.
In 1850, William Rankine first used the phrase the law of the conservation of energy for the principle.[16]
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.[17]
Mass–energy equivalence[edit]
This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (November 2015) (Learn how and when to remove this template message)
Main article: Mass–energy equivalence
Matter is composed of such things as atoms, electrons, neutrons, and protons. It has intrinsic or rest mass. In the limited range of recognized experience of the nineteenth century it was found that such rest mass is conserved. Einstein's 1905 theory of special relativity showed that it corresponds to 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 total mass or total energy. All forms of energy contribute to the total mass and total energy.
For example, an electron and a positron each have rest mass. They can perish together, converting their combined rest energy into photons 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. Likewise, non-material forms of energy can perish into matter, which has rest mass.
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 18th century these had appeared as two seemingly-distinct laws.
Conservation of energy in beta decay[edit]
Main article: Beta decay § Neutrinos in beta decay
The discovery in 1911 that electrons emitted in beta decay have a continuous rather than a discrete spectrum appeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus.[18][19] This problem was eventually resolved in 1933 by Enrico Fermi who proposed the correct description of beta-decay as the emission of both an electron and an antineutrino, which carries away the apparently missing energy.[20][21]
First law of thermodynamics[edit]
Main article: First law of thermodynamics
For a closed thermodynamic system, the first law of thermodynamics may be stated as:
δ Q = d U + δ W {\displaystyle \delta Q=\mathrm {d} U+\delta W} , or equivalently, d U = δ Q − δ W , {\displaystyle \mathrm {d} U=\delta Q-\delta W,}
where δ Q {\displaystyle \delta Q} is the quantity of energy added to the system by a heating process, δ W {\displaystyle \delta W} is the quantity of energy lost by the system due to work done by the system on its surroundings and d U {\displaystyle \mathrm {d} U} is the change in the internal energy of the system.
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 d U {\displaystyle \mathrm {d} U} 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 U {\displaystyle U} is a property of a particular state of the system when it is in unchanging thermodynamic equilibrium. Thus the term "heat energy" for δ Q {\displaystyle \delta Q} 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 δ W {\displaystyle \delta W} 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.
Entropy is a function of the state of a system which tells of limitations of the possibility of conversion of heat into work.
For a simple compressible system, the work performed by the system may be written:
δ W = P d V , {\displaystyle \delta W=P\,\mathrm {d} V,}
where P {\displaystyle P} is the pressure and d V {\displaystyle dV} is a small change in the volume of the system, each of which are system variables. In the fictive case in which the process is idealized and infinitely slow, so as to be called quasi-static, and regarded as reversible, the heat being transferred from a source with temperature infinitesimally above the system temperature, then the heat energy may be written
δ Q = T d S , {\displaystyle \delta Q=T\,\mathrm {d} S,}
where T {\displaystyle T} is the temperature and d S {\displaystyle \mathrm {d} S} is a small change in the entropy of the system. Temperature and entropy are variables of state of a system.
If an open system (in which mass may be exchanged with the environment) has several walls such that the mass transfer is through rigid walls separate from the heat and work transfers, then the first law may be written:[22]
d U = δ Q − δ W + u ′ d M , {\displaystyle \mathrm {d} U=\delta Q-\delta W+u'\,dM,\,}
where d M {\displaystyle dM} is the added mass and u ′ {\displaystyle u'} is the internal energy per unit mass of the added mass, measured in the surroundings before the process.
Noether's theorem[edit]
Main article: Noether's theorem
Emmy Noether (1882-1935) was an influential mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics.
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, developed by Emmy Noether in 1915 and first published in 1918. The theorem 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 of time; energy conservation is implied by the empirical fact that the laws of physics do not change with time itself. Philosophically this can be stated as "nothing depends on time per se". 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. Conservation of energy for finite systems is valid in such physical theories as special relativity and quantum theory (including QED) in the flat space-time.
Relativity[edit]
With the discovery of special relativity by Henri Poincaré and Albert Einstein, energy was proposed to be one component of an 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 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).
The relativistic energy of a single massive 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 E = m c 2 {\displaystyle E=mc^{2}} .
Thus, the rule of conservation of energy over time in special relativity continues to hold, so long as the 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.
In general relativity, energy–momentum conservation is not well-defined except in certain special cases. Energy-momentum is typically expressed with the aid of a stress–energy–momentum pseudotensor. However, since pseudotensors are not tensors, they do not transform cleanly between reference frames. If the metric under consideration is static (that is, does not change with time) or asymptotically flat (that is, at an infinite distance away spacetime looks empty), then energy conservation holds without major pitfalls. In practice, some metrics such as the Friedmann–Lemaître–Robertson–Walker metric do not satisfy these constraints and energy conservation is not well defined.[23] The theory of general relativity leaves open the question of whether there is a conservation of energy for the entire universe.
Quantum theory[edit]
In quantum mechanics, energy of a quantum system is described by a self-adjoint (or Hermitian) operator called the 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 in principle be exactly measured without any trade-off in precision forced by the time-energy uncertainty relations. Thus the conservation of energy in time is a well defined concept even in quantum mechanics.
See also[edit]
Energy quality
Energy transformation
Eternity of the world
Laws of thermodynamics
Lagrangian
Principles of energetics
References[edit]
Jump up ^ Richard Feynman (1970). The Feynman Lectures on Physics Vol I. Addison Wesley. ISBN 978-0 -201-02115-8.
Jump up ^ 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.
Jump up ^ Witten, Edward (1981). "A new proof of the positive energy theorem" (PDF). Communications in Mathematical Physics. 80 (3): 381–402. Bibcode:1981CMaPh..80..381W. doi:10.1007/BF01208277. ISSN 0010-3616.
Jump up ^ Grossman, Lisa (18 January 2012). "Death-defying time crystal could outlast the universe". newscientist.com. New Scientist. Archived from the original on 2017-02-02.
Jump up ^ Cowen, Ron (27 February 2012). ""Time Crystals" Could Be a Legitimate Form of Perpetual Motion". scientificamerican.com. Scientific American. Archived from the original on 2017-02-02.
Jump up ^ Powell, Devin (2013). "Can matter cycle through shapes eternally?". Nature. doi:10.1038/nature.2013.13657. ISSN 1476-4687. Archived from the original on 2017-02-03.
Jump up ^ Gibney, Elizabeth (2017). "The quest to crystallize time". Nature. 543 (7644): 164–166. Bibcode:2017Natur.543..164G. doi:10.1038/543164a. ISSN 0028-0836. Archived from the original on 2017-03-13.
Jump up ^ Janko, Richard (2004). "Empedocles, "On Nature"" (PDF). Zeitschrift für Papyrologie und Epigraphik. 150: 1–26.
Jump up ^ Hagengruber, Ruth, editor (2011) Émilie du Chatelet between Leibniz and Newton. Springer. ISBN 978-94-007-2074-9.
Jump up ^ Arianrhod, Robyn (2012). Seduced by logic : Émilie du Châtelet, Mary Somerville, and the Newtonian revolution (US ed.). New York: Oxford University Press. ISBN 978-0-19-993161-3.
Jump up ^ Lavoisier, A.L. & Laplace, P.S. (1780) "Memoir on Heat", Académie Royale des Sciences pp. 4–355
Jump up ^ von Mayer, J.R. (1842) "Remarks on the forces of inorganic nature" in Annalen der Chemie und Pharmacie, 43, 233
Jump up ^ Mayer, J.R. (1845). Die organische Bewegung in ihrem Zusammenhange mit dem Stoffwechsel. Ein Beitrag zur Naturkunde, Dechsler, Heilbronn.
Jump up ^ Grove, W. R. (1874). The Correlation of Physical Forces (6th ed.). London: Longmans, Green.
Jump up ^ "On the Conservation of Force". Bartleby. Retrieved April 6, 2014.
Jump up ^ William John Macquorn Rankine (1853) "On the General Law of the Transformation of Energy," Proceedings of the Philosophical Society of Glasgow, vol. 3, no. 5, pages 276-280; reprinted in: (1) Philosophical Magazine, series 4, vol. 5, no. 30, pages 106-117 (February 1853); and (2) W. J. Millar, ed., Miscellaneous Scientific Papers: by W. J. Macquorn Rankine, ... (London, England: Charles Griffin and Co., 1881), part II, pages 203-208: "The law of the Conservation of Energy is already known—viz. that the sum of all the energies of the universe, actual and potential, is unchangeable."
Jump up ^ Hadden, Richard W. (1994). On the shoulders of merchants: exchange and the mathematical conception of nature in early modern Europe. SUNY Press. p. 13. ISBN 0-7914-2011-6. , Chapter 1, p. 13
Jump up ^ Jensen, Carsten (2000). Controversy and Consensus: Nuclear Beta Decay 1911-1934. Birkhäuser Verlag. ISBN 3-7643-5313-9.
Jump up ^ Brown, Laurie M. (1978). "The idea of the neutrino". Physics Today. 31 (9): 23–8. Bibcode:1978PhT....31i..23B. doi:10.1063/1.2995181.
Jump up ^ Wilson, F. L. (1968). "Fermi's Theory of Beta Decay". American Journal of Physics. 36 (12): 1150. Bibcode:1968AmJPh..36.1150W. doi:10.1119/1.1974382.
Jump up ^ Griffiths, D. (2009). Introduction to Elementary Particles (2nd ed.). pp. 314–315. ISBN 978-3-527-40601-2.
Jump up ^ Born, M. (1949). Natural Philosophy of Cause and Chance, Oxford University Press, London, pp. 146–147.
Jump up ^ Michael Weiss and John Baez. "Is Energy Conserved in General Relativity?". Retrieved 5 Jan 2017. CS1 maint: Uses authors parameter (link)
Bibliography[edit]
Modern accounts[edit]
Goldstein, Martin, and Inge F., (1993). The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction.
Kroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. ISBN 0-7167-1088-9.
Nolan, Peter J. (1996). Fundamentals of College Physics, 2nd ed. William C. Brown Publishers.
Oxtoby & Nachtrieb (1996). Principles of Modern Chemistry, 3rd ed. Saunders College Publishing.
Papineau, D. (2002). Thinking about Consciousness. Oxford: Oxford University Press.
Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks/Cole. ISBN 0-534-40842-7.
Stenger, Victor J. (2000). Timeless Reality. Prometheus Books. Especially chpt. 12. Nontechnical.
Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.). W. H. Freeman. ISBN 0-7167-0809-4.
Lanczos, Cornelius (1970). The Variational Principles of Mechanics. Toronto: University of Toronto Press. ISBN 0-8020-1743-6.
History of ideas[edit]
Brown, T.M. (1965). "Resource letter EEC-1 on the evolution of energy concepts from Galileo to Helmholtz". American Journal of Physics. 33 (10): 759–765. Bibcode:1965AmJPh..33..759B. doi:10.1119/1.1970980.
Cardwell, D.S.L. (1971). From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age. London: Heinemann. ISBN 0-435-54150-1.
Guillen, M. (1999). Five Equations That Changed the World. New York: Abacus. ISBN 0-349-11064-6.
Hiebert, E.N. (1981). Historical Roots of the Principle of Conservation of Energy. Madison, Wis.: Ayer Co Pub. ISBN 0-405-13880-6.
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
Sarton, G.; Joule, J. P.; Carnot, Sadi (1929). "The discovery of the law of conservation of energy". Isis. 13: 18–49. doi:10.1086/346430.
Smith, C. (1998). The Science of Energy: Cultural History of Energy Physics in Victorian Britain. London: Heinemann. ISBN 0-485-11431-3.
Mach, E. (1872). History and Root of the Principles of the Conservation of Energy. Open Court Pub. Co., Illinois.
Poincaré, H. (1905). Science and Hypothesis. Walter Scott Publishing Co. Ltd; Dover reprint, 1952. ISBN 0-486-60221-4. , Chapter 8, "Energy and Thermo-dynamics"
External links[edit]
MISN-0-158 The First Law of Thermodynamics (PDF file) by Jerzy Borysowicz for Project PHYSNET.
Authority control
GND: 4152219-9
Retrieved from "https://en.wikipedia.org/w/index.php?title=Conservation_of_energy&oldid=840149362"
Categories:
Energy (physics)
Laws of thermodynamics
Conservation laws
History of physics
History of ideas
Hidden categories:
CS1 maint: Uses authors parameter
Articles needing additional references from February 2013
All articles needing additional references
Articles needing additional references from November 2015
Wikipedia articles with GND identifiers
Articles containing video clips
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
Languages
Afrikaans
Alemannisch
العربية
Aragonés
অসমীয়া
Asturianu
Azərbaycanca
تۆرکجه
বাংলা
Башҡортса
Беларуская
Беларуская (тарашкевіца)
Български
Bosanski
Català
Čeština
Cymraeg
Deutsch
Eesti
Ελληνικά
Español
Esperanto
Euskara
فارسی
Fiji Hindi
Français
Gaeilge
Galego
한국어
Հայերեն
हिन्दी
Hrvatski
Bahasa Indonesia
Interlingua
Íslenska
Italiano
עברית
Къарачай-малкъар
ქართული
Қазақша
Kreyòl ayisyen
Latina
Latviešu
Lietuvių
Magyar
Македонски
മലയാളം
Монгол
မြန်မာဘာသာ
Nederlands
日本語
Norsk
Norsk nynorsk
Occitan
Oʻzbekcha/ўзбекча
ਪੰਜਾਬੀ
پنجابی
Piemontèis
Polski
Português
Română
Русиньскый
Русский
Scots
Simple English
Slovenčina
Slovenščina
کوردی
Српски / srpski
Srpskohrvatski / српскохрватски
Suomi
Svenska
தமிழ்
Татарча/tatarça
ไทย
Türkçe
Українська
اردو
Tiếng Việt
Winaray
ייִדיש
粵語
中文
74 more
Edit links
This page was last edited on 8 May 2018, at 01:37.
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

values: mw-page-base noprint

values: mw-head-base noprint

values: firstHeading firstHeading en

values: siteSub noprint

values: jump-to-nav mw-jump

attrs: role class

values:
note
hatnote navigation-not-searchable

value: td

value: b

values: Help:Introduction to referencing with Wiki Markup/1

value: i

value: small

values: plainlinks metadata ambox ambox-content ambox-Refimprove

values:
/wiki/Energy_conversion
mw-redirect
Energy conversion

values:
/wiki/Noether_theorem
mw-redirect
Noether theorem

values:
/wiki/Time_crystals
mw-redirect
Time crystals

attrs: alt src width height class srcset data-file-width data-file-height

values:
/wiki/Gottfried_Leibniz
mw-redirect
Gottfried Leibniz

values:
/wiki/Simon_Stevinus
mw-redirect
Simon Stevinus

values:
/wiki/Christian_Huygens
mw-redirect
Christian Huygens

values: vertical-align: -3.005ex; width:8.764ex; height:5.509ex;

values:
/wiki/Conservation_of_momentum
mw-redirect
Conservation of momentum

values: vertical-align: -3.005ex; width:8.509ex; height:5.509ex;

values: Philosophiæ Naturalis Principia Mathematica

values: vertical-align: -1.838ex; width:12.123ex; height:5.176ex;

values: vertical-align: -0.671ex; width:2.804ex; height:2.509ex;

values: vertical-align: -0.338ex; width:2.04ex; height:1.676ex;

values: vertical-align: -0.338ex; width:1.128ex; height:1.676ex;

values:
/wiki/Gaspard-Gustave_Coriolis
mw-redirect
Gaspard-Gustave Coriolis

values: vertical-align: -3.005ex; width:11.15ex; height:6.343ex;

values: Edit section: Mechanical equivalent of heat

values:
/wiki/Julius_Robert_von_Mayer
mw-redirect
Julius Robert von Mayer

values:
/wiki/Mechanical_work
mw-redirect
Mechanical work

values:
/wiki/%C3%89mile_Clapeyron
mw-redirect
Émile Clapeyron

values:
/wiki/William_Rankine
mw-redirect
William Rankine

values:
/wiki/Peter_Guthrie_Tait
mw-redirect
Peter Guthrie Tait

values: Philosophiae Naturalis Principia Mathematica

values: Edit section: Conservation of energy in beta decay

values: Edit section: First law of thermodynamics

values: {\displaystyle \delta Q=\mathrm {d} U+\delta W}

values: vertical-align: -0.671ex; width:15.385ex; height:2.676ex;

values: {\displaystyle \mathrm {d} U=\delta Q-\delta W,}

values: vertical-align: -0.671ex; width:16.032ex; height:2.676ex;

values: vertical-align: -0.671ex; width:2.887ex; height:2.676ex;

values: vertical-align: -0.338ex; width:3.484ex; height:2.343ex;

values: vertical-align: -0.338ex; width:3.075ex; height:2.176ex;

values: vertical-align: -0.338ex; width:1.783ex; height:2.176ex;

values: {\displaystyle \delta W=P\,\mathrm {d} V,}

values: vertical-align: -0.671ex; width:12.441ex; height:2.676ex;

values: vertical-align: -0.338ex; width:1.745ex; height:2.176ex;

values: vertical-align: -0.338ex; width:3.003ex; height:2.176ex;

values: {\displaystyle \delta Q=T\,\mathrm {d} S,}

values: vertical-align: -0.671ex; width:11.447ex; height:2.676ex;

values: vertical-align: -0.338ex; width:1.636ex; height:2.176ex;

values: vertical-align: -0.338ex; width:2.792ex; height:2.176ex;

values: vertical-align: -0.671ex; width:25.319ex; height:2.843ex;

values: \mathrm {d} U=\delta Q-\delta W+u'\,dM,\,

values: vertical-align: -0.338ex; width:3.658ex; height:2.176ex;

values: vertical-align: -0.338ex; width:2.014ex; height:2.509ex;

values:
/wiki/Symmetry_in_physics
mw-redirect
Symmetry in physics

values:
/wiki/Time_translation
mw-redirect
Time translation

values:
/wiki/Canonical_conjugate
mw-redirect
Canonical conjugate

values:
/wiki/Inertial_reference_frame
mw-redirect
Inertial reference frame

values:
/wiki/Center_of_momentum_frame
mw-redirect
Center of momentum frame

values:
/wiki/Total_energy
mw-redirect
Total energy

values: vertical-align: -0.338ex; width:8.976ex; height:2.676ex;

values:
/wiki/Wave_functions
mw-redirect
Wave functions

values:
/wiki/Principles_of_energetics
mw-redirect
Principles of energetics

values:
nofollow
external text
//doi.org/10.1007%2FBF01208277

values:
nofollow
external text
//www.worldcat.org/issn/0010-3616

values:
nofollow
external text
//doi.org/10.1038%2Fnature.2013.13657

values:
nofollow
external text
//www.worldcat.org/issn/1476-4687

values:
nofollow
external text
//doi.org/10.1038%2F543164a

values:
nofollow
external text
//www.worldcat.org/issn/0028-0836

values:
nofollow
external text
http://www.bartleby.com/30/125.html

values:
nofollow
external text
//doi.org/10.1063%2F1.2995181

values:
nofollow
external text
//doi.org/10.1119%2F1.1974382

values: Category:CS1 maint: Uses authors parameter

values: -moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;

values:
nofollow
external text
//doi.org/10.1119%2F1.1970980

values:
nofollow
external text
//doi.org/10.1086%2F346430

values:
/wiki/Portable_Document_Format
mw-redirect
Portable Document Format

values:
nofollow
external text
http://www.physnet.org

values:
nofollow
external text
https://d-nb.info/gnd/4152219-9

values: Category:Articles needing additional references from February 2013

values: Category:All articles needing additional references

values: Category:Articles needing additional references from November 2015

values: Category:Wikipedia articles with GND identifiers

values: Category:Articles containing video clips

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Conservation_of_energy
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values: p-namespaces navigation vectorTabs p-namespaces-label

values:
p-variants
navigation
vectorMenu emptyPortlet
p-variants-label

values: Past revisions of this page [ctrl-alt-h]

values: p-views navigation vectorTabs p-views-label

values:
p-cactions
navigation
vectorMenu emptyPortlet
p-cactions-label

values:
mw-wiki-logo
/wiki/Main_Page
Visit the main page

values:
/wiki/Main_Page
Visit the main page [ctrl-alt-z]
z

values: Featured content – the best of Wikipedia

values: Find background information on current events

values:
/wiki/Special:Random
Load a random article [ctrl-alt-x]
x

values: portal navigation p-navigation p-navigation-label

values: Guidance on how to use and edit Wikipedia

values: About the project, what you can do, where to find things

values: A list of recent changes in the wiki [ctrl-alt-r]

values: portal navigation p-interaction p-interaction-label

values: List of all English Wikipedia pages containing links to this page [ctrl-alt-j]

values: Recent changes in pages linked from this page [ctrl-alt-k]

values:
/wiki/Wikipedia:File_Upload_Wizard
Upload files [ctrl-alt-u]
u

values: A list of all special pages [ctrl-alt-q]

values: Permanent link to this revision of the page

values: Link to connected data repository item [ctrl-alt-g]

values: Printable version of this page [ctrl-alt-p]

values:
interlanguage-link interwiki-af
display: none;

values:
interlanguage-link interwiki-als
display: none;

values: حفظ الطاقة (فيزياء) – Arabic

values:
interlanguage-link interwiki-an
display: none;

values: শক্তিৰ সংৰক্ষণশীলতা – Assamese

values:
interlanguage-link interwiki-as
display: none;

values:
interlanguage-link interwiki-ast
display: none;

values: Enerjinin saxlanması qanunu – Azerbaijani

values:
interlanguage-link interwiki-az
display: none;

values: انرژی‌نین ساخلانماسی قانونو – South Azerbaijani

values:
interlanguage-link interwiki-azb
display: none;

values: শক্তির নিত্যতা – Bangla

values:
interlanguage-link interwiki-bn
display: none;

values: Энергия һаҡланыу законы – Bashkir

values:
interlanguage-link interwiki-ba
display: none;

values: Закон захавання энергіі – Belarusian

values:
interlanguage-link interwiki-be
display: none;

values: Закон захаваньня энэргіі – Belarusian (Taraškievica orthography)

values:
interlanguage-link interwiki-be-x-old
display: none;

values: Закон за запазване на енергията – Bulgarian

values:
interlanguage-link interwiki-bg
display: none;

values:
interlanguage-link interwiki-bs
display: none;

values:
interlanguage-link interwiki-ca
display: none;

values:
interlanguage-link interwiki-cs
display: none;

values:
interlanguage-link interwiki-cy
display: none;

values:
interlanguage-link interwiki-de
display: none;

values:
interlanguage-link interwiki-et
display: none;

values: Αρχή διατήρησης της ενέργειας – Greek

values:
interlanguage-link interwiki-el
display: none;

values: Principo de konservado de energio – Esperanto

values:
interlanguage-link interwiki-eo
display: none;

values: Energiaren kontserbazioaren printzipioa – Basque

values:
interlanguage-link interwiki-eu
display: none;

values: پایستگی انرژی – Persian

values:
interlanguage-link interwiki-fa
display: none;

values:
interlanguage-link interwiki-hif
display: none;

values:
interlanguage-link interwiki-ga
display: none;

values:
interlanguage-link interwiki-gl
display: none;

values: 에너지 보존 법칙 – Korean

values:
interlanguage-link interwiki-ko
display: none;

values: Էներգիայի պահպանման օրենք – Armenian

values:
interlanguage-link interwiki-hy
display: none;

values: ऊर्जा संरक्षण का नियम – Hindi

values:
interlanguage-link interwiki-hr
display: none;

values:
interlanguage-link interwiki-ia
display: none;

values:
interlanguage-link interwiki-is
display: none;

values: Legge di conservazione dell'energia – Italian

values:
interlanguage-link interwiki-it
display: none;

values: חוק שימור האנרגיה – Hebrew

values:
interlanguage-link interwiki-he
display: none;

values: Энергия сакълауну закону – Karachay-Balkar

values:
interlanguage-link interwiki-krc
display: none;

values: ენერგიის შენახვის კანონი – Georgian

values:
interlanguage-link interwiki-ka
display: none;

values: Энергияның сақталу заңы – Kazakh

values:
interlanguage-link interwiki-kk
display: none;

values:
interlanguage-link interwiki-ht
display: none;

values:
interlanguage-link interwiki-la
display: none;

values:
interlanguage-link interwiki-lv
display: none;

values:
interlanguage-link interwiki-lt
display: none;

values:
interlanguage-link interwiki-hu
display: none;

values: Закон за зачувување на енергијата – Macedonian

values:
interlanguage-link interwiki-mk
display: none;

values: ഊർജ്ജ സം‌രക്ഷണ നിയമം – Malayalam

values:
interlanguage-link interwiki-ml
display: none;

values: Энерги хадгалагдах хууль – Mongolian

values:
interlanguage-link interwiki-mn
display: none;

values: စွမ်းအင် တည်မြဲမှု နိယာမ – Burmese

values:
interlanguage-link interwiki-my
display: none;

values:
interlanguage-link interwiki-nl
display: none;

values: エネルギー保存の法則 – Japanese

values:
interlanguage-link interwiki-ja
display: none;

values:
interlanguage-link interwiki-oc
display: none;

values: Energiyaning saqlanish va aylanish qonuni – Uzbek

values:
interlanguage-link interwiki-uz
display: none;

values: ਊਰਜਾ ਦੀ ਸੰਭਾਲ – Punjabi

values:
interlanguage-link interwiki-pa
display: none;

values: انرجی بچت دا قنون – Western Punjabi

values:
interlanguage-link interwiki-pnb
display: none;

values: Prinsipi ëd conservassion ëd l'energìa – Piedmontese

values:
interlanguage-link interwiki-pms
display: none;

values: Lei da conservação da energia – Portuguese

values: Закон всокочіня енерґії – Rusyn

values:
interlanguage-link interwiki-rue
display: none;

values: Закон сохранения энергии – Russian

values:
interlanguage-link interwiki-sco
display: none;

values:
interlanguage-link interwiki-sk
display: none;

values:
interlanguage-link interwiki-sl
display: none;

values:
interlanguage-link interwiki-ckb
display: none;

values: Закон очувања енергије – Serbian

values:
interlanguage-link interwiki-sr
display: none;

values: Zakon očuvanja energije – Serbo-Croatian

values:
interlanguage-link interwiki-sh
display: none;

values:
interlanguage-link interwiki-sv
display: none;

values: ஆற்றல் காப்பு – Tamil

values:
interlanguage-link interwiki-ta
display: none;

values: Энергия саклану кануны – Tatar

values:
interlanguage-link interwiki-tt
display: none;

values: กฎทรงพลังงาน – Thai

values: Закон збереження енергії – Ukrainian

values:
interlanguage-link interwiki-uk
display: none;

values: قانون بقائے توانائی – Urdu

values:
interlanguage-link interwiki-war
display: none;

values: קאנסערווירונג פון ענערגיע – Yiddish

values:
interlanguage-link interwiki-yi
display: none;

values: 能量守恒定律 – Chinese

values: /static/images/wikimedia-button-1.5x.png 1.5x, /static/images/wikimedia-button-2x.png 2x

values: /static/images/poweredby_mediawiki_132x47.png 1.5x, /static/images/poweredby_mediawiki_176x62.png 2x

values:
suggestions
display: none; font-size: 13px;

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Conservation_of_energy rootpage-Conservation_of_energy skin-vector action-view