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In physics, the law of conservation of energy states that the total amount of energy in any isolated system remains constant but cannot be recreated, 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, and is the more encompassing version of the conservation of energy. In short, the law of conservation of energy states that energy can not be created or destroyed, it can only be changed from one form to another. For the physical concepts, see conservation of energy and energy efficiency. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 151 languages. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... Thermodynamics (from the Greek Î¸ÎµÏÎ¼Î·, therme, meaning heat and Î´Ï…Î½Î±Î¼Î¹Ï‚, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ...

Ancient philosophers as far back as Thales of Miletus 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). 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. However, Galileo did not state the process in modern terms and again cannot be credited with the crucial insight. 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 masses, mi each with velocity vi ), For the span of recorded history starting roughly 5,000-5,500 years ago, see Ancient history. ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... For the Defense and Security Company, see Thales Group. ... Events March 29 - Swedish colonists establish first settlement in Delaware, called New Sweden. ... Galileo can refer to: Galileo Galilei, astronomer, philosopher, and physicist (1564 - 1642) the Galileo spacecraft, a NASA space probe that visited Jupiter and its moons the Galileo positioning system Life of Galileo, a play by Bertolt Brecht Galileo (1975) - screen adaptation of the play Life of Galileo by Bertolt Brecht... Gottfried Leibniz Gottfried Wilhelm von Leibniz (July 1, 1646 in Leipzig - November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorb descent. ... Events January 29 - Feodor III becomes Tsar of Russia First measurement of the speed of light, by Ole RÃ¸mer Bacons Rebellion Russo-Turkish Wars commence. ... Year 1689 (MDCLXXXIX) was a common year starting on Saturday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Tuesday of the 10-day slower Julian calendar). ... For other uses, see Mass (disambiguation). ... This article is about velocity in physics. ...

$sum_{i} m_i v_i^2$

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 held that the conservation of momentum, which holds even in systems with friction, as defined by the momentum: Vis Viva is the principle that the difference between the aggregate work of the accelerating forces of a system and that of the retarding forces is equal to one half the vis viva accumulated or lost in the system while the work is being done. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... Not to be confused with physician, a person who practices medicine. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... This article is about momentum in physics. ...

$,!sum_{i} m_i v_i$

was the conserved vis viva. It was later shown that, under the proper conditions, both quantities are conserved simultaneously such as in elastic collisions. As long as black-body radiation (not shown) doesnâ€™t escape a system, atoms in thermal agitation undergo essentially elastic collisions. ...

The recalibration of vis viva to

$frac {1} {2}sum_{i} m_i v_i^2$

which can be understood as finding the exact value for the kinetic energy to 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. In thermodynamics, work is the quantity of energy transferred from one system to another without an accompanying transfer of entropy. ... Gaspard-Gustave de Coriolis or Gustave Coriolis (May 21, 1792â€“September 19, 1843), mathematician, mechanical engineer and scientist born in Paris, France. ... Jean-Victor Poncelet (July 1, 1788 – December 22, 1867) was a mathematician and engineer who did much to revive projective geometry. ... Year 1819 (MDCCCXIX) was a common year starting on Friday (link will display the full calendar) in the [[Grhttp://en. ... 1839 (MDCCCXXXIX) was a common year starting on Tuesday (see link for calendar). ...

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." The Zeitschrift fÃ¼r Physik (Journal of Physics) was published from 1920 until 1997. ... Queen Victoria, Queen of the United Kingdom (1837 - 1901) 1837 (MDCCCXXXVII) was a common year starting on Sunday (see link for calendar). ... Karl Friedrich Mohr (November 4, 1806 - September 28, 1879) was a German pharmacist famous for his early statement of the principle of conservation of energy. ...

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. Conservation of energy also known as the first law of thermodynamics is possibly the most important, and certainly the most practically useful, of several conservation laws in physics. ...

The mechanical equivalence principle was first stated in its modern form by the German surgeon Julius Robert von Mayer.[2] 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 had discovered that heat and mechanical work were both forms of energy, and later, after improving his knowledge of physics, he calculated a quantitative relationship between them. Julius Robert von Mayer. ... This article does not cite any references or sources. ... For other uses, see Blood (disambiguation). ... For other uses, see Red (disambiguation). ... This article is about the chemical element and its most stable form, or dioxygen. ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ... In physics, mechanical work is the amount of energy transferred by a force. ...

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.

Over the period 1840-1843, similar work was carried out by engineer Ludwig A. Colding though it was little known outside his native Denmark. 1840 is a leap year starting on Wednesday (link will take you to calendar). ... Ludwig A. Colding (1815 - 1888) was a Danish engineer who played a key role in formulating the principle of the conservation of energy. ...

Both Joule's and Mayer's work suffered from resistance and neglect but it was Joule's that, perhaps unjustly, 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). Grove published his theories in his book The Correlation of Physical Forces.[3] 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). The general modern acceptance of the principle stems from this publication. Conservation of energy also known as the first law of thermodynamics is possibly the most important, and certainly the most practically useful, of several conservation laws in physics. ... Jan. ... Sir William Robert Grove (1811 â€“ 1896) was a British chemist born in Swansea in Wales. ... For other uses, see Light (disambiguation). ... Electricity (from New Latin Ä“lectricus, amberlike) is a general term for a variety of phenomena resulting from the presence and flow of electric charge. ... For other senses of this word, see magnetism (disambiguation). ... 1847 was a common year starting on Friday (see link for calendar). ... Sadi Carnot in the dress uniform of a student of the Ã‰cole polytechnique Nicolas LÃ©onard Sadi Carnot (June 1, 1796 - August 24, 1832) was a French physicist and military engineer who gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the... Emile_Clapeyron Benoit Paul Ã‰mile Clapeyron (February 26, 1799 - January 28, 1864) was an French engineer and physicist, considered as one of the founders of thermodynamics. ... Hermann Ludwig Ferdinand von Helmholtz (August 31, 1821 â€“ September 8, 1894) was a German physician and physicist. ...

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 generally regarded as nothing more than an example of Whig history. 1877 (MDCCCLXXVII) was a common year starting on Monday (see link for calendar). ... Peter Tait Peter Guthrie Tait (April 28, 1831 - July 4, 1901) was a Scottish mathematical physicist. ... Newtons own copy of his Principia, with handwritten corrections for the second edition. ... Whig history is a pejorative name given to a view of history that is shared by a number of eighteenth and nineteenth century British writers on historical subjects. ...

## The first law of thermodynamics

For a thermodynamic system with a fixed number of particles, the first law of thermodynamics may be stated as: The laws of thermodynamics, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. ... The zeroth law of thermodynamics may be succintly stated as: If two thermodynamic systems A and B are in thermal equilibrium, and B and C are also in thermal equilibrium, then A and C are in thermal equilibrium. ... In thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the conservation of energy. ... The second law of thermodynamics is an expression of the universal law of increasing entropy. ... The third law of thermodynamics (hereinafter Third Law) states that as a system approaches the zero absolute temperature (hereinafter ZAT), all processes cease and the entropy of the system approaches a minimum value. ... In thermodynamics, the combined law of thermodynamics is simply a mathemtical summation of the first law of thermodynamics and the second law of thermodynamics subsumed into a single concise mathematical statement as shown below: Here, U is internal energy, T is temperature, S is entropy, P is pressure, and V... In thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the conservation of energy. ...

$delta Q = mathrm{d}U + delta W,$, or equivalently, $mathrm{d}U = delta Q - delta W,$,

where δQ is the amount of energy added to the system by a heating process, δW is the amount of energy lost by the system due to work done by the system on its surroundings and dU is the increase 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 dU increment of internal energy. Work and heat are processes which add or subtract energy, while the internal energy U is a particular form of energy associated with the system. Thus the term "heat energy" for δQ 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 δW means "that amount of energy lost as the result of work". The most significant result of this distinction is the fact that one can clearly state the amount of internal energy possessed by a thermodynamic system, but one cannot tell how much energy has 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. In English, this means that energy cannot be created or destroyed, only converted from one form to another.

For a simple compressible system, the work performed by the system may be written

$delta W = P,mathrm{d}V$,

where P is the pressure and dV is a small change in the volume of the system, each of which are system variables. The heat energy may be written This article is about pressure in the physical sciences. ... For other uses, see Volume (disambiguation). ...

$delta Q = T,mathrm{d}S$,

where T is the temperature and dS is a small change in the entropy of the system. Temperature and entropy are also system variables. For other uses, see Temperature (disambiguation). ... For other uses, see: information entropy (in information theory) and entropy (disambiguation). ...

## Mechanics

In mechanics, conservation of energy is usually stated as

E = T + V.

Actually this is the particular case of the more general conservation law

$sum_{i=1}^N p_i dot{q}_i - L=const$ and $p_i=frac{partial L}{partial dot{q}_i}$

where L is the Lagrangian function. For this particular form to be valid, the following must be true:

• The system is scleronomous (neither kinetic nor potential energy are explicit functions of time)
• The kinetic energy is a quadratic form with regard to velocities.
• The potential energy doesn't depend on velocities.

Mechanical system is scleronomous if the equations of constraints do not contain the time as an explicit variable. ...

### Noether's Theorem

Main article: Noether's Theorem

The conservation of energy is a common feature in many physical theories. It is understood as a consequence of Noether's theorem, which states every 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". In other words, if the theory is invariant under the continuous symmetry of time translation then its energy (which is canonical conjugate quantity to time) is conserved. Conversely, theories which are not invariant under shifts in time (for 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 theory can be embedded within a time-invariant meta-theory energy conservation can always be recovered by a suitable re-definition of what energy is. Thus conservation of energy is valid in all modern physical theories, such as special and general relativity and quantum theory (including QED). Noethers theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. ... Noethers theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. ... In mathematics, continuous symmetry is an intuitive idea corresponding to the concept of viewing some symmetries as motions, as opposed to e. ... This article is about the concept of time. ... A pair of variables mathematically defined in such a way that they become Fourier transform duals of one-another, or more generally are related through Pontryagin duality. ... QED can mean several different things: Q.E.D. Latin Quod erat demonstrandum, used at the end of mathematical proofs The QED project intended to construct a formalized database of all mathematical knowledge The QED text editor program Quantum electrodynamics, a field of physics Quantum Effect Devices, a maker of...

### Relativity

With the discovery of special relativity by Albert Einstein, energy was found 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 in any given inertial reference frame. Also conserved is the vector length (Minkowski norm), which is the rest 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 the massive particle, or the center-of-momentum frame for objects or systems), the total energy of particle or object (including internal kinetic energy in systems) is related to its rest mass via the famous equation E = mc2. Thus, the rule of conservation of energy in special relativity was shown to be a special case of a more general rule, alternatively called the conservation of mass and energy, the conservation of mass-energy, the conservation of energy-momentum, the conservation of invariant mass or now usually just referred to as conservation of energy. For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... â€œEinsteinâ€ redirects here. ... It has been suggested that this article or section be merged with Momentum#Momentum_in_relativistic_mechanics. ... In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... For other uses, see Mass (disambiguation). ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... In special relativity the rest frame of a particle is the coordinate system (frame of reference) in which the particle is at rest. ... The center of mass frame (also called the center of momentum frame, CM frame, or COM frame) is defined as being the particular inertial frame in which the center of mass of a system of interest, is at rest (has zero velocity). ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... The term mass in special relativity can be used in different ways, occasionally leading to confusion. ...

In general relativity conservation of energy-momentum is expressed with the aid of a stress-energy-momentum pseudotensor. For a less technical and generally accessible introduction to the topic, see Introduction to general relativity. ... In the theory of general relativity, the stress-energy-momentum pseudotensor or Landau-Lifshitz pseudotensor allows the energy-momentum of a system of gravitating matter to be defined; in particular it allows the total matter plus the gravitating energy-momentum to be conserved within the framework of general relativity, so...

### Quantum theory

In quantum mechanics, energy is defined as proportional to the time derivative of the wave function. Lack of commutation of the time derivative operator with the time operator itself mathematically results in an uncertainty principle for time and energy: the longer the period of time, the more precisely energy can be defined (energy and time become a conjugate Fourier pair). However, quantum theory in general, and the uncertainty principle specifically, do not violate energy conservation. For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... A time derivative is a derivative of a function with respect to time, t. ... A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. ... Commutation may mean: In Mathematics, commutation refers to a Commutative operation, where a x b = b x a In Law, commutation refers to a reduction in sentence for a criminal act. ... In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution, and the larger the associated standard deviation is, the more uncertain we might say that that characteristic is for the system. ... Conjugate can be: in mathematics in terms of complex numbers, the complex conjugate; more generally see conjugate element (field theory). ... A Fourier pair is two quantities which are Fourier transforms of each other. ...

## Mathematical viewpoint

From a mathematical point of view, 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 (see: Noether's theorem). Philosophically this can be stated as "nothing depends on time per se". This article or section does not cite its references or sources. ... This article is about the concept of time. ... For a list of set rules, see Laws of science. ... Noethers theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. ...

## Notes

1. ^ Lavoisier, A.L. & Laplace, P.S. (1780) "Memoir on Heat", Académie Royal des Sciences pp4-355
2. ^ von Mayer, J.R. (1842) "Remarks on the forces of inorganic nature" in Annalen der Chemie und Pharmacie, 43, 233
3. ^ Grove, W. R. (1874). The Correlation of Physical Forces, 6th ed., London: Longmans, Green.

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov-Lavoisier law), states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ... The Principles of Energetics can be thought of as a broad overarching expression of the many different laws uncovered in all branches of science; mechanics, biology, kinetics, electronics and theromodynamics are examples. ... The laws of thermodynamics, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. ... Noethers theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. ... In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution, and the larger the associated standard deviation is, the more uncertain we might say that that characteristic is for the system. ... For other uses, see Chaos Theory (disambiguation). ...

## References

### Modern accounts

• 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.

Cornelius Lanczos (LÃ¡nczos KornÃ©l), born KornÃ©l LÃ¶wy (February 2, 1893â€“June 25, 1974), was a Hungarian mathematician and physicist. ...

### History of ideas

• Brown, T.M. (1965). "Resource letter EEC-1 on the evolution of energy concepts from Galileo to Helmholtz". American Journal of Physics 33: 759-765.
• 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. 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. (1929). "The discovery of the law of conservation of energy". Isis 13: 18-49.
• Smith, C. (1998). The Science of Energy: Cultural History of Energy Physics in Victorian Britain. London: Heinemann. ISBN 0-485-11431-3.

Thomas Samuel Kuhn (July 18, 1922 – June 17, 1996) was an American intellectual who wrote extensively on the history of science and developed several important notions in the philosophy of science. ...

### Classic accounts

• Colding, L.A. (1864). "On the history of the principle of the conservation of energy". London, Edinburgh and Dublin Philosophical Magazine and Journal of Science 27: 56-64.
• Mach, E. (1872). History and Root of the Principles of the Conservation of Energy. Open Court Pub. Co., IL.
• 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"

Ludwig A. Colding (1815 - 1888) was a Danish engineer who played a key role in formulating the principle of the conservation of energy. ... Ernst Mach Ernst Mach (February 18, 1838 â€“ February 19, 1916) was an Austrian-Czech physicist and philosopher and is the namesake for the Mach number and the optical illusion known as Mach bands. ... Jules Henri PoincarÃ© (April 29, 1854 â€“ July 17, 1912) (IPA: [1]) was one of Frances greatest mathematicians and theoretical physicists, and a philosopher of science. ...

Results from FactBites:

 generic document for building HyperPhysics (0 words) The conservation of energy principle is one of the foundation principles of all science disciplines. Conservation of Energy: the total energy of the system is constant. Conservation of Momentum: the mass times the velocity of the center of mass is constant.
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