In physics, energy is the quantitative property that must be
transferred to an object in order to perform work on, or to heat, the
object.[note 1]
Contents 1 Forms 2 History 3 Units of measure 4 Scientific use 4.1 Classical mechanics
4.2 Chemistry
4.3 Biology
4.4
5 Transformation 5.1
6 Conservation of energy
7
7.1 Closed systems 7.2 Open systems 8 Thermodynamics 8.1 Internal energy 8.2 First law of thermodynamics 8.3 Equipartition of energy 9 See also 10 Notes 11 References 12 Further reading 13 External links Forms This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (September 2016) (Learn how and when to remove this template message) In a typical lightning strike, 500 megajoules of electric potential energy is converted into the same amount of energy in other forms, mostly light energy, sound energy and thermal energy.
The total energy of a system can be subdivided and classified into
potential energy, kinetic energy, or combinations of the two in
various ways.
Some forms of energy (that an object or system can have as a measurable property) Type of energy Description Mechanical the sum of macroscopic translational and rotational kinetic and potential energies Electric potential energy due to or stored in electric fields Magnetic potential energy due to or stored in magnetic fields Gravitational potential energy due to or stored in gravitational fields Chemical potential energy due to chemical bonds Ionization potential energy that binds an electron to its atom or molecule Nuclear potential energy that binds nucleons to form the atomic nucleus (and nuclear reactions) Chromodynamic potential energy that binds quarks to form hadrons Elastic potential energy due to the deformation of a material (or its container) exhibiting a restorative force Mechanical wave kinetic and potential energy in an elastic material due to a propagated deformational wave Sound wave kinetic and potential energy in a fluid due to a sound propagated wave (a particular form of mechanical wave) Radiant potential energy stored in the fields of propagated by electromagnetic radiation, including light Rest potential energy due to an object's rest mass Thermal kinetic energy of the microscopic motion of particles, a form of disordered equivalent of mechanical energy History
Main articles:
Thomas Young – the first to use the term "energy" in the modern sense. The word energy derives from the Ancient Greek: ἐνέργεια,
translit. energeia, lit. 'activity, operation',[1] which
possibly appears for the first time in the work of
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. Main article: Units of energy
In 1843, James Prescott
Part of a series of articles about Classical mechanics F → = m a → displaystyle vec F =m vec a Second law of motion History Timeline Branches Applied Celestial Continuum Dynamics Kinematics Kinetics Statics Statistical Fundamentals Acceleration Angular momentum Couple D'Alembert's principle Energy kinetic potential Force Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia Mass Mechanical power Mechanical work Moment Momentum Space Speed Time Torque Velocity Virtual work Formulations Newton's laws of motion Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Udwadia–Kalaba equation Koopman–von Neumann mechanics Core topics Damping (ratio) Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator Inertial / Non-inertial reference frame
Motion (linear) Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body dynamics Euler's equations Simple harmonic motion Vibration Rotation Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational speed Angular acceleration / displacement / frequency / velocity Scientists Galileo Huygens Newton Kepler Horrocks Halley Euler d'Alembert Clairaut Lagrange Laplace Hamilton Poisson Daniel Bernoulli Johann Bernoulli Cauchy v t e Main articles: Mechanics, Mechanical work, and Thermodynamics 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. W = ∫ C F ⋅ d s displaystyle W=int _ C mathbf F cdot mathrm d mathbf s This says that the work ( W displaystyle W ) 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 remarkably direct
analogs in nonrelativistic quantum mechanics.[4]
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).
Basic overview of energy and human life. 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.
C 6 H 12 O 6 + 6 O 2 ⟶ 6 CO 2 + 6 H 2 O displaystyle ce C6H12O6 + 6O2 -> 6CO2 + 6H2O C57H110O6 + 81.5O2 → 57CO2 + 55H2O and some of the energy is used to convert ADP into ATP. ADP + HPO42− → ATP + H2O The rest of the chemical energy in O2[7] 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] gain in kinetic energy of a sprinter during a 100 m race: 4 kJ gain in gravitational potential energy of a 150 kg weight lifted through 2 metres: 3 kJ Daily food intake of a normal adult: 6–8 MJ 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").[note 3] Simpler organisms can achieve
higher energy efficiencies than more complex ones, but the complex
organisms can occupy ecological niches that are not available to their
simpler brethren. 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 124.7 Pg/a of
carbon that is fixed by photosynthesis, 64.3 Pg/a (52%) are used
for the metabolism of green plants,[8] i.e. reconverted into carbon
dioxide and heat.
E = h ν displaystyle E=hnu (where h displaystyle h is
ν displaystyle nu the frequency). In the case of an electromagnetic wave these energy
states are called quanta of light or photons.
Relativity
When calculating kinetic energy (work to accelerate a massive body
from zero speed to some finite speed) relativistically – using
E 0 = m c 2 displaystyle E_ 0 =mc^ 2 , where m is the mass of the body, c is the speed of light in vacuum, E 0 displaystyle E_ 0 is the rest energy. 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.[10]
Some forms of transfer of energy ("energy in transit") from one object or system to another Type of transfer process Description Heat that amount of thermal energy in transit spontaneously towards a lower-temperature object Work that amount of energy in transit due to a displacement in the direction of an applied force Transfer of material that amount of energy carried by matter that is moving from one system to another A turbo generator transforms the energy of pressurised steam into electrical energy
E p displaystyle E_ p ) to kinetic energy ( E k displaystyle E_ k ) and then back to potential energy constantly. 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: E p i + E k i = E p F + E k F displaystyle E_ pi +E_ ki =E_ pF +E_ kF
(4) The equation can then be simplified further since E p = m g h displaystyle E_ p =mgh (mass times acceleration due to gravity times the height) and E k = 1 2 m v 2 displaystyle E_ k = frac 1 2 mv^ 2 (half mass times velocity squared). Then the total amount of energy can be found by adding E p + E k = E t o t a l displaystyle E_ p +E_ k =E_ total .
c 2 displaystyle c^ 2 is extremely large relative to ordinary human scales, the conversion of an everyday amount of rest mass (for example, 1 kg) from rest energy to other forms of energy (such as kinetic energy, thermal energy, or the radiant energy carried by light and other radiation) can liberate tremendous amounts of energy (~ 9 × 10 16 displaystyle 9times 10^ 16 joules = 21 megatons of TNT), as can be seen in nuclear reactors and
nuclear weapons. 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.g., kinetic
energy into particles with rest mass) are found in nuclear physics and
particle physics.
Reversible and non-reversible transformations
There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law—it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same. — The Feynman Lectures on Physics Most kinds of energy (with gravitational energy being a notable exception)[14] are subject to strict local conservation laws as well. In this case, energy can only be exchanged between adjacent regions of space, and all observers agree as to the volumetric density of energy in any given space. There is also a global law of conservation of energy, stating that the total energy of the universe cannot change; this is a corollary of the local law, but not vice versa.[12][13] This law is a fundamental principle of physics. As shown rigorously by Noether's theorem, the conservation of energy is a mathematical consequence of translational symmetry of time,[15] a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable. This is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval. The uncertainty principle should not be confused with energy conservation - rather it provides mathematical limits to which energy can in principle be defined and measured. Each of the basic forces of nature is associated with a different type of potential energy, and all types of potential energy (like all other types of energy) appears as system mass, whenever present. For example, a compressed spring will be slightly more massive than before it was compressed. Likewise, whenever energy is transferred between systems by any mechanism, an associated mass is transferred with it. In quantum mechanics energy is expressed using the Hamiltonian operator. On any time scales, the uncertainty in the energy is by Δ E Δ t ≥ ℏ 2 displaystyle Delta EDelta tgeq frac hbar 2 which is similar in form to the
Δ E = W + Q displaystyle Delta E=W+Q
(1) where E displaystyle E is the amount of energy transferred, W displaystyle W represents the work done on the system, and Q displaystyle Q represents the heat flow into the system. As a simplification, the heat term, Q displaystyle Q , is sometimes ignored, especially when the thermal efficiency of the transfer is high. Δ E = W displaystyle Delta E=W
(2) This simplified equation is the one used to define the joule, for example. Open systems Beyond the constraints of closed systems, open systems can gain or lose energy in association with matter transfer (both of these process are illustrated by fueling an auto, a system which gains in energy thereby, without addition of either work or heat). Denoting this energy by E displaystyle E , one may write Δ E = W + Q + E . displaystyle Delta E=W+Q+E.
(3) Thermodynamics
Internal energy
d E = T d S − P d V displaystyle mathrm d E=Tmathrm d S-Pmathrm d V, , where the first term on the right is the heat transferred into the system, expressed in terms of temperature T and entropy S (in which entropy increases and the change dS is positive when the system is heated), and the last term on the right hand side is identified as work done on the system, where pressure is P and volume V (the negative sign results since compression of the system requires work to be done on it and so the volume change, dV, is negative when work is done on the system). This equation is highly specific, ignoring all chemical, electrical, nuclear, and gravitational forces, effects such as advection of any form of energy other than heat and pV-work. The general formulation of the first law (i.e., conservation of energy) is valid even in situations in which the system is not homogeneous. For these cases the change in internal energy of a closed system is expressed in a general form by d E = δ Q + δ W displaystyle mathrm d E=delta Q+delta W where δ Q displaystyle delta Q is the heat supplied to the system and δ W displaystyle delta W is the work applied to the system.
Equipartition of energy
The energy of a mechanical harmonic oscillator (a mass on a spring) is
alternatively kinetic and potential. At two points in the oscillation
cycle it is entirely kinetic, and at two points it is entirely
potential. Over the whole cycle, or over many cycles, net energy is
thus equally split between kinetic and potential. This is called
equipartition principle; total energy of a system with many degrees of
freedom is equally split among all available degrees of freedom.
This principle is vitally important to understanding the behaviour of
a quantity closely related to energy, called entropy.
Book: Energy
Combustion Index of energy articles Index of wave articles Orders of magnitude (energy) Power station Transfer energy Notes ^ The second law of thermodynamics imposes limitations on the capacity
of a system to transfer energy by performing work, since some of the
system's energy might necessarily be "consumed" in the form of heat
instead. See e.g. Lehrman, Robert L. (1973). "
References ^ Harper, Douglas. "Energy". Online Etymology Dictionary. Archived
from the original on October 11, 2007. Retrieved May 1, 2007.
^ Smith, Crosbie (1998). The Science of
Further reading Alekseev, G. N. (1986).
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