Energy

Energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units is the joule.
Forms of energy include the kinetic energy of a moving object, the potential energy stored by an object, the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, the internal energy contained within a thermodynamic system, and rest energy associated with an object's rest mass. These are not mutually exclusive.
All living organisms constantly take in and release energy. The Earth's climate and ecosystems processes are driven primarily by radiant energy from the Sun.

Forms

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 object's components – while potential energy reflects the potential of an object to have motion, generally being based upon the object's position within a field or what is stored within 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, the sum of translational and rotational kinetic and potential energy within a system is referred to as mechanical energy, whereas nuclear energy refers to the combined potentials within an atomic nucleus from either the nuclear force or the weak force, among other examples.

Type of energy	Description
Chemical	potential energy due to chemical bonds
Chromodynamic	potential energy that binds quarks to form hadrons
Elastic	potential energy due to the deformation of a material exhibiting a restorative force as it returns to its original shape
Electric	potential energy due to or stored in electric fields
Gravitational	potential energy due to or stored in gravitational fields
Ionization	potential energy that binds an electron to its atom or molecule
Magnetic	potential energy due to or stored in magnetic fields
Mechanical	the sum of macroscopic translational and rotational kinetic and potential energies
Mechanical wave	kinetic and potential energy in an elastic material due to a propagating oscillation of matter
Nuclear	potential energy that binds nucleons to form the atomic nucleus
Radiant	potential energy stored in the fields of waves propagated by electromagnetic radiation, including light
Rest	potential energy due to an object's rest mass
Rotational	kinetic energy due to the rotation of an object
Sound wave	kinetic and potential energy in a material due to a sound propagated wave
Thermal	kinetic energy of the microscopic motion of particles, a kind of disordered equivalent of mechanical energy

History

The word energy derives from the, which possibly appears for the first time in the work of Aristotle in the 4th century BC. 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, 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 motions 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. Writing in the early 18th century, Émilie du Châtelet proposed the concept of conservation of energy in the marginalia of her French language translation of Newton's Principia Mathematica, which represented the first formulation of a conserved measurable quantity that was distinct from momentum, and which would later be called "energy".
In 1807, Thomas Young was possibly the first to use the term "energy" instead of vis viva, in its modern sense. Gustave-Gaspard Coriolis described "kinetic energy" in 1829 in its modern sense, and in 1853, William Rankine coined the term "potential energy". 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 1845 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 as the field of thermodynamics. Thermodynamics aided the rapid development of explanations of chemical processes by Rudolf Clausius, Josiah Willard Gibbs, Walther Nernst, and others. It also led to a mathematical formulation of the concept of entropy by Clausius and to the introduction of laws of radiant energy by Jožef Stefan. 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. Thus, since 1918, theorists have understood that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time.
Albert Einstein's 1905 theory of special relativity showed that rest mass corresponds to an equivalent amount of rest energy. This means that rest mass can be converted to or from equivalent amounts of forms of energy, for example, kinetic energy, potential energy, and electromagnetic radiant energy. When this happens, rest mass is not conserved, unlike the total mass or total energy. All forms of energy contribute to the total mass and total energy. Thus, conservation of energy and conservation of mass are one law. In the 18th century, these had appeared as two seemingly-distinct laws.
The first evidence of quantization in atoms was the observation of spectral lines in light from the sun in the early 1800s by Joseph von Fraunhofer and William Hyde Wollaston. The notion of quantized energy levels was proposed in 1913 by Danish physicist Niels Bohr in the Bohr theory of the atom. The modern quantum mechanical theory giving an explanation of these energy levels in terms of the Schrödinger equation was advanced by Erwin Schrödinger and Werner Heisenberg in 1926. Noether's theorem shows that the symmetry of this equation is equivalent to a conservation of probability. At the quantum level, mass-energy interactions are all subject to this principle. During wave function collapse, the conservation of energy does not hold at the local level, although statistically the principle holds on average for sufficiently large numbers of collapses. Conservation of energy does apply during wave function collapse in H. Everett's many-worlds interpretation of quantum mechanics.

Units of measure

In dimensional analysis, the base units of energy are given by: Work = Force × Distance = M L² T⁻², with the fundamental dimensions of Mass M, Length L, and time T. In the International System of Units, the unit of energy is the joule. It is a derived unit that is equal to the energy expended, or work done, in applying a force of one newton through a distance of one metre.
The SI unit of power, defined as energy per unit of time, is the watt, which is one joule per second. Thus, a kilowatt-hour, which can be realized as the energy delivered by one kilowatt of power for an hour, is equal to 3.6 million joules. The CGS energy unit is the erg and the imperial and US customary unit is the foot-pound.
Other energy units such as the electronvolt, food calorie, thermodynamic kilocalorie and BTU are used in specific areas of science and commerce.

Scientific use

Classical mechanics

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.
This says that the work is equal to the line integral of the force F along a path C; for details see the mechanical work article. 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 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.
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, 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.