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This block began on 15:12, 27 August 2023 and has been set to finish on: <b>15:12, 27 August 2028</b>.</td></tr> </tbody></table> <div style="text-align: center;"><big> </big><p><big><b>You are not blocked from reading pages, only from changing or creating them.</b></big><br /> If you have just clicked a <span style="color:#BA0000; text-decoration:underline;">red link</span>, you were blocked from creating a new page as no article on that topic is there yet. </p> </div> If you think you were not blocked fairly, you may make unblock requests or file appeals at <a href="https://meta.wikimedia.org/wiki/Steward_requests/Global" class="extiw" title="meta:Steward requests/Global">meta:Steward requests/Global</a>.</div></div><hr /> <p>You can view and copy the source of this page. </p><textarea readonly="" accesskey="," id="wpTextbox1" cols="80" rows="25" style="" class="mw-editfont-monospace" lang="en" dir="ltr" name="wpTextbox1">:''This article refers to the law of conservation of energy in physics. For energy resources sustainably, see: [[Energy conservation]].'' In [[physics]], the '''conservation of energy''' is that energy can not be created or destroyed, it can only be changed from one form to another, such as when electrical energy is changed into heat energy. Formally, it says that the total amount of [[energy]] in an isolated system remains constant, although it may change forms, e.g. [[friction]] turns [[kinetic energy]] into [[thermal energy]]. In [[thermodynamics]], the '''[[first law of thermodynamics]]''' is a statement of the conservation of energy for thermodynamic systems. From a mathematical point of view, the energy conservation law is a consequence of the shift symmetry of [[time]]; energy conservation is a result of 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 (time itself)". == Historical information == Ancient [[philosopher]]s as far back as [[Thales|Thales of Miletus]] had the idea that there is some underlying substance of which everything is made. But that is not the same as our concept of "mass-energy" today (for example, Thales thought the underlying substance was water). In 1638, [[Galileo]] published his analysis of several situations. This included the famous "interrupted pendulum". This can be described (in modernized language) as conservatively converting potential energy to kinetic energy and back again. However, Galileo did not explain the process in modern terms and had not understood the modern concept either. The [[Germany|German]] [[Gottfried Wilhelm Leibniz]] during 1676-1689 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>'' ), :<math>\sum_{i} m_i v_i^2</math> 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. [[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 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 approximately equal to the thermal energy ([[heat]]) gained by the water by [[friction]] with the paddle. Over the period 1840-1843, similar work was carried out by engineer [[Ludwig A. Colding]] though it was little-known outside his native [[Denmark]]. ==Proof== It is easy to see that <math>E=KE+PE</math> which is also <math>E=\frac{1}{2}mv^2 + V</math> <math>E=\frac{1}{2}mx'^2+V(x)</math> Assuming that <math>x'(t)</math> and that <math>x(t)</math>, then <math>\frac{dE}{dt}=\frac{\partial E}{\partial x'}\frac{dx'}{dt}+\frac{\partial E}{\partial x}\frac{dx}{dt}</math> <math>\frac{dE}{dt}=(mx')(x'')-Fx'</math> (Since <math>V'(x)=-F</math>) <math>\frac{dE}{dt}=Fx'-Fx'=0</math> Therefore, energy does not vary with time. ==Related pages== * [[Conservation law]] * [[Energy]] * [[Thermodynamics]] == Sources == === Modern accounts === *Goldstein, Martin, and Inge F., 1993. ''The Refrigerator and the Universe''. Harvard Univ. Press. A gentle introduction. * {{cite book | author=Kroemer, Herbert; Kittel, Charles | title=Thermal Physics (2nd ed.) | publisher=W. H. Freeman Company | year=1980 }} {{ISBN|0-7167-1088-9}} * {{cite book | author=Nolan, Peter J. | title=Fundamentals of College Physics, 2nd ed. | publisher=William C. Brown Publishers | year=1996 }} * {{cite book | author=Oxtoby & Nachtrieb | title=Principles of Modern Chemistry, 3rd ed. | publisher=Saunders College Publishing | year=1996 }} * {{cite book | author=Papineau, D. | title=Thinking about Consciousness | url=https://archive.org/details/thinkingaboutcon0000papi | location=Oxford | publisher=Oxford University Press | year=2002 }} * {{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}} *Stenger, Victor J. (2000). ''Timeless Reality''. Prometheus Books. Especially chpt. 12. Nontechnical. * {{cite book | author=Tipler, Paul | title=Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.) | url=https://archive.org/details/physicsforscient0002tipl | publisher=W. H. Freeman | year=2004 }} ISBN 0-534-40842-7 *{{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}} ===Classic accounts=== * {{cite journal | author=Colding, L.A. | title=On the history of the principle of the conservation of energy | journal=London, Edinburgh and Dublin Philosophical Magazine and Journal of Science | volume=27 | year=1864 | issue=179 | pages=56–64 | doi=10.1080/14786446408643620 }} * {{cite book | author=Mach, E. | title=History and Root of the Principles of the Conservation of Energy | publisher=Open Court Pub. Co., IL | year=1872 }} * {{cite book | author=Poincaré, H. | title=Science and Hypothesis | url=https://archive.org/details/scienceandhypoth00poinuoft | publisher=Walter Scott Publishing Co. Ltd; Dover reprint, 1952 | year=1905 }}, {{ISBN|0-486-60221-4}} Chapter 8, "Energy and Thermo-dynamics" == Other websites == * [http://35.9.69.219/home/modules/pdf_modules/m158.pdf <small>MISN-0-158</small> ''The First Law of Thermodynamics''] {{Webarchive|url=https://web.archive.org/web/20051023005506/http://35.9.69.219/home/modules/pdf_modules/m158.pdf |date=2005-10-23 }} (PDF file) by Jerzy Borysowicz for [http://www.physnet.org Project PHYSNET].  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