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These classical equations have remarkably direct analogs in nonrelativistic quantum mechanics. Another energy-related concept is called the Lagrangian , after Joseph-Louis Lagrange.
This formalism is as fundamental as the Hamiltonian, and both can be used to derive the equations of motion or be derived from them.
It was invented in the context of classical mechanics , but is generally useful in modern physics. The Lagrangian is defined as the kinetic energy minus the potential energy.
Usually, the Lagrange formalism is mathematically more convenient than the Hamiltonian for non-conservative systems such as systems with friction.
Noether's theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations.
A generalisation of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics and , respectively , it does not apply to systems that cannot be modeled with a Lagrangian; for example, dissipative systems with continuous symmetries need not have a corresponding conservation law.
In the context of chemistry , energy is an attribute of a substance as a consequence of its atomic, molecular or aggregate structure.
Since a chemical transformation is accompanied by a change in one or more of these kinds of structure, it is invariably accompanied by an increase or decrease of energy of the substances involved.
Some energy is transferred between the surroundings and the reactants of the reaction in the form of heat or light; thus the products of a reaction may have more or less energy than the reactants.
A reaction is said to be exothermic or exergonic if the final state is lower on the energy scale than the initial state; in the case of endothermic reactions the situation is the reverse.
Chemical reactions are almost invariably not possible unless the reactants surmount an energy barrier known as the activation energy. This exponential dependence of a reaction rate on temperature is known as the Arrhenius equation.
The activation energy necessary for a chemical reaction can be provided in the form of thermal energy.
In biology , energy is an attribute of all biological systems from the biosphere to the smallest living organism.
Within an organism it is responsible for growth and development of a biological cell or an organelle of a biological organism. Energy used in respiration is mostly stored in molecular oxygen  and can be unlocked by reactions with molecules of substances such as carbohydrates including sugars , lipids , and proteins stored by cells.
For example, if our bodies run on average at 80 watts, then a light bulb running at watts is running at 1. For a difficult task of only a few seconds' duration, a person can put out thousands of watts, many times the watts in one official horsepower.
For tasks lasting a few minutes, a fit human can generate perhaps 1, watts. For an activity that must be sustained for an hour, output drops to around ; for an activity kept up all day, watts is about the maximum.
Sunlight's radiant energy is also captured by plants as chemical potential energy in photosynthesis , when carbon dioxide and water two low-energy compounds are converted into carbohydrates, lipids, and proteins and high-energy compounds like oxygen  and ATP.
Carbohydrates, lipids, and proteins can release the energy of oxygen, which is utilized by living organisms as an electron acceptor.
Release of the energy stored during photosynthesis as heat or light may be triggered suddenly by a spark, in a forest fire, or it may be made available more slowly for animal or human metabolism, when organic molecules are ingested, and catabolism is triggered by enzyme action.
Any living organism relies on an external source of energy — radiant energy from the Sun in the case of green plants, chemical energy in some form in the case of animals — to be able to grow and reproduce.
The food molecules are oxidised to carbon dioxide and water in the mitochondria. The rest of the chemical energy in O 2  and the carbohydrate or fat is converted into heat: the ATP is used as a sort of "energy currency", and some of the chemical energy it contains is used for other metabolism when ATP reacts with OH groups and eventually splits into ADP and phosphate at each stage of a metabolic pathway , some chemical energy is converted into heat.
Only a tiny fraction of the original chemical energy is used for work: [note 2]. It would appear that living organisms are remarkably inefficient in the physical sense in their use of the energy they receive chemical or radiant energy , and it is true that most real machines manage higher efficiencies.
In growing organisms the energy that is converted to heat serves a vital purpose, as it allows the organism tissue to be highly ordered with regard to the molecules it is built from.
The second law of thermodynamics states that energy and matter tends to become more evenly spread out across the universe: to concentrate energy or matter in one specific place, it is necessary to spread out a greater amount of energy as heat across the remainder of the universe "the surroundings".
The conversion of a portion of the chemical energy to heat at each step in a metabolic pathway is the physical reason behind the pyramid of biomass observed in ecology : to take just the first step in the food chain , of the estimated In geology , continental drift , mountain ranges , volcanoes , and earthquakes are phenomena that can be explained in terms of energy transformations in the Earth's interior,  while meteorological phenomena like wind, rain, hail , snow, lightning, tornadoes and hurricanes are all a result of energy transformations brought about by solar energy on the atmosphere of the planet Earth.
Sunlight may be stored as gravitational potential energy after it strikes the Earth, as for example water evaporates from oceans and is deposited upon mountains where, after being released at a hydroelectric dam, it can be used to drive turbines or generators to produce electricity.
Sunlight also drives many weather phenomena, save those generated by volcanic events. An example of a solar-mediated weather event is a hurricane, which occurs when large unstable areas of warm ocean, heated over months, give up some of their thermal energy suddenly to power a few days of violent air movement.
In a slower process, radioactive decay of atoms in the core of the Earth releases heat. This thermal energy drives plate tectonics and may lift mountains, via orogenesis.
This slow lifting represents a kind of gravitational potential energy storage of the thermal energy, which may be later released to active kinetic energy in landslides, after a triggering event.
Earthquakes also release stored elastic potential energy in rocks, a store that has been produced ultimately from the same radioactive heat sources.
Thus, according to present understanding, familiar events such as landslides and earthquakes release energy that has been stored as potential energy in the Earth's gravitational field or elastic strain mechanical potential energy in rocks.
Prior to this, they represent release of energy that has been stored in heavy atoms since the collapse of long-destroyed supernova stars created these atoms.
In cosmology and astronomy the phenomena of stars , nova , supernova , quasars and gamma-ray bursts are the universe's highest-output energy transformations of matter.
All stellar phenomena including solar activity are driven by various kinds of energy transformations. Energy in such transformations is either from gravitational collapse of matter usually molecular hydrogen into various classes of astronomical objects stars, black holes, etc.
The nuclear fusion of hydrogen in the Sun also releases another store of potential energy which was created at the time of the Big Bang.
At that time, according to theory, space expanded and the universe cooled too rapidly for hydrogen to completely fuse into heavier elements. This meant that hydrogen represents a store of potential energy that can be released by fusion.
Such a fusion process is triggered by heat and pressure generated from gravitational collapse of hydrogen clouds when they produce stars, and some of the fusion energy is then transformed into sunlight.
In quantum mechanics , energy is defined in terms of the energy operator as a time derivative of the wave function.
The Schrödinger equation equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics.
The Schrödinger equation describes the space- and time-dependence of a slowly changing non-relativistic wave function of quantum systems.
The solution of this equation for a bound system is discrete a set of permitted states, each characterized by an energy level which results in the concept of quanta.
In the case of an electromagnetic wave these energy states are called quanta of light or photons. When calculating kinetic energy work to accelerate a massive body from zero speed to some finite speed relativistically — using Lorentz transformations instead of Newtonian mechanics — Einstein discovered an unexpected by-product of these calculations to be an energy term which does not vanish at zero speed.
He called it rest energy : energy which every massive body must possess even when being at rest. The amount of energy is directly proportional to the mass of the body:.
For example, consider electron — positron annihilation, in which the rest energy of these two individual particles equivalent to their rest mass is converted to the radiant energy of the photons produced in the process.
In this system the matter and antimatter electrons and positrons are destroyed and changed to non-matter the photons. However, the total mass and total energy do not change during this interaction.
The photons each have no rest mass but nonetheless have radiant energy which exhibits the same inertia as did the two original particles. This is a reversible process — the inverse process is called pair creation — in which the rest mass of particles is created from the radiant energy of two or more annihilating photons.
In general relativity, the stress—energy tensor serves as the source term for the gravitational field, in rough analogy to the way mass serves as the source term in the non-relativistic Newtonian approximation.
Energy and mass are manifestations of one and the same underlying physical property of a system. This property is responsible for the inertia and strength of gravitational interaction of the system "mass manifestations" , and is also responsible for the potential ability of the system to perform work or heating "energy manifestations" , subject to the limitations of other physical laws.
In classical physics , energy is a scalar quantity, the canonical conjugate to time. In special relativity energy is also a scalar although not a Lorentz scalar but a time component of the energy—momentum 4-vector.
Energy may be transformed between different forms at various efficiencies. Items that transform between these forms are called transducers.
Examples of transducers include a battery, from chemical energy to electric energy ; a dam: gravitational potential energy to kinetic energy of moving water and the blades of a turbine and ultimately to electric energy through an electric generator ; or a heat engine , from heat to work.
Examples of energy transformation include generating electric energy from heat energy via a steam turbine, or lifting an object against gravity using electrical energy driving a crane motor.
Lifting against gravity performs mechanical work on the object and stores gravitational potential energy in the object.
If the object falls to the ground, gravity does mechanical work on the object which transforms the potential energy in the gravitational field to the kinetic energy released as heat on impact with the ground.
Our Sun transforms nuclear potential energy to other forms of energy; its total mass does not decrease due to that in itself since it still contains the same total energy even if in different forms , but its mass does decrease when the energy escapes out to its surroundings, largely as radiant energy.
There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.
However, some energy transformations can be quite efficient. The direction of transformations in energy what kind of energy is transformed to what other kind is often determined by entropy equal energy spread among all available degrees of freedom considerations.
In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.
Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" transformed to more active types of energy such as kinetic or radiant energy when a triggering mechanism is available.
Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes such as uranium and thorium , by nucleosynthesis , a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae , to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth.
This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion , chemical potential energy is transformed to kinetic energy and thermal energy in a very short time.
Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum.
At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one unrealistically assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.
This is referred to as conservation of energy. In this closed system, energy cannot be created or destroyed; therefore, the initial energy and the final energy will be equal to each other.
This can be demonstrated by the following:. Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed.
It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence.
In different theoretical frameworks, similar formulas were derived by J. Part of the rest energy equivalent to rest mass of matter may be converted to other forms of energy still exhibiting mass , but neither energy nor mass can be destroyed; rather, both remain constant during any process.
Conversely, the mass equivalent of an everyday amount energy is minuscule, which is why a loss of energy loss of mass from most systems is difficult to measure on a weighing scale, unless the energy loss is very large.
Examples of large transformations between rest energy of matter and other forms of energy e. Thermodynamics divides energy transformation into two kinds: reversible processes and irreversible processes.
An irreversible process is one in which energy is dissipated spread into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms fewer quantum states , without degradation of even more energy.
A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above.
In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe such as an expansion of matter, or a randomisation in a crystal.
As the universe evolves in time, more and more of its energy becomes trapped in irreversible states i. This has been referred to as the inevitable thermodynamic heat death of the universe.
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Current collector optimizer topology to extract maximum power from non-uniform aged PV array. Call for Papers. Special Issues.Main articles: History of energy and timeline of thermodynamics, statistical mechanics, and random processes. The Schrödinger equation describes the space- and time-dependence of a slowly changing non-relativistic wave function of quantum systems. Efficient, intelligent and sustainable — this is our aim for how energy should be generated and used in future. Global Environmental Temperance Deutsch in the Ocean and on Land. This book, originally a Scientific American issue, covers Hiramasa every major concern and concept since debated Kartenspieler Ugs Energy Deutsch and energy resourcespopulation trends, and environmental degradation. In geologycontinental driftmountain rangesvolcanoesand earthquakes are phenomena that can be explained in terms of energy transformations in the Earth's interior,  while meteorological phenomena like wind, rain, hailsnow, lightning, tornadoes and hurricanes are all Energy Deutsch result of energy transformations brought about by solar energy on the atmosphere of the planet Earth. And it This property is responsible for the inertia and strength of gravitational interaction of the system "mass manifestations"and is also responsible for the potential ability of the Daniel Weinand to perform work or heating "energy manifestations"subject to the limitations of other physical laws. Lifting against gravity performs mechanical work on the object and stores gravitational potential energy in the Rider Kostenlos Spielen. Article Selections. Zeroth First Second Third. This thermal energy drives plate tectonics and may lift mountains, via orogenesis. At two points in the oscillation cycle it is entirely kinetic, and at two points it is Merkur Tipps Tricks potential. In this heat Kartenspiel Solitaire the energy of the universe does not change, but the fraction of energy which is available to do work through a heat engineor be transformed to other usable forms of energy Spielstation König öffnungszeiten the use of generators attached to heat Roulette Gratis Spielengrows less and less. Read more.