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Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field gravitational , electric or magnetic , the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns , the radiant energy carried by light, and the thermal energy due to an object's temperature.
Mass and energy are closely related. Due to mass—energy equivalence , any object that has mass when stationary called rest mass also has an equivalent amount of energy whose form is called rest energy , and any additional energy of any form acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy.
For example, after heating an object, its increase in energy could be measured as a small increase in mass, with a sensitive enough scale.
Living organisms require energy to stay alive, such as the energy humans get from food. Human civilization requires energy to function, which it gets from energy resources such as fossil fuels , nuclear fuel , or renewable energy.
The processes of Earth's climate and ecosystem are driven by the radiant energy Earth receives from the sun and the geothermal energy contained within the earth.
The total energy of a system can be subdivided and classified into potential energy, kinetic energy, or combinations of the two in various ways.
Kinetic energy is determined by the movement of an object — or the composite motion of the components of an object — and potential energy reflects the potential of an object to have motion, and generally is a function of the position of an object within a field or may be stored in the field itself.
While these two categories are sufficient to describe all forms of energy, it is often convenient to refer to particular combinations of potential and kinetic energy as its own form.
For example, macroscopic mechanical energy is the sum of translational and rotational kinetic and potential energy in a system neglects the kinetic energy due to temperature, and nuclear energy which combines utilize potentials from the nuclear force and the weak force , among others.
In contrast to the modern definition, energeia was a qualitative philosophical concept, broad enough to include ideas such as happiness and pleasure.
In the late 17th century, Gottfried Leibniz proposed the idea of the Latin : vis viva , or living force, which defined as the product of the mass of an object and its velocity squared; he believed that total vis viva was conserved.
To account for slowing due to friction, Leibniz theorized that thermal energy consisted of the random motion of the constituent parts of matter, although it would be more than a century until this was generally accepted.
The modern analog of this property, kinetic energy , differs from vis viva only by a factor of two.
In , Thomas Young was possibly the first to use the term "energy" instead of vis viva , in its modern sense. The law of conservation of energy was also first postulated in the early 19th century, and applies to any isolated system.
It was argued for some years whether heat was a physical substance, dubbed the caloric , or merely a physical quantity, such as momentum.
In James Prescott Joule discovered the link between mechanical work and the generation of heat. These developments led to the theory of conservation of energy, formalized largely by William Thomson Lord Kelvin as the field of thermodynamics.
Thermodynamics aided the rapid development of explanations of chemical processes by Rudolf Clausius , Josiah Willard Gibbs , and Walther Nernst.
According to Noether's theorem , the conservation of energy is a consequence of the fact that the laws of physics do not change over time.
In , Joule independently discovered the mechanical equivalent in a series of experiments. The most famous of them used the "Joule apparatus": a descending weight, attached to a string, caused rotation of a paddle immersed in water, practically insulated from heat transfer.
It 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.
It is a derived unit. It is equal to the energy expended or work done in applying a force of one newton through a distance of one metre.
However energy is also expressed in many other units not part of the SI, such as ergs , calories , British Thermal Units , kilowatt-hours and kilocalories , which require a conversion factor when expressed in SI units.
The SI unit of energy rate energy per unit time is the watt , which is a joule per second. Thus, one joule is one watt-second, and joules equal one watt-hour.
Other energy units such as the electronvolt , food calorie or thermodynamic kcal based on the temperature change of water in a heating process , and BTU are used in specific areas of science and commerce.
In classical mechanics, energy is a conceptually and mathematically useful property, as it is a conserved quantity. Several formulations of mechanics have been developed using energy as a core concept.
Work , a function of energy, is force times distance. Work and thus energy is frame dependent. For example, consider a ball being hit by a bat.
In the center-of-mass reference frame, the bat does no work on the ball. But, in the reference frame of the person swinging the bat, considerable work is done on the ball.
The total energy of a system is sometimes called the Hamiltonian , after William Rowan Hamilton. The classical equations of motion can be written in terms of the Hamiltonian, even for highly complex or abstract systems.
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.
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