Energy

For information on using energy resources sustainably see Energy conservation. For an album by Operation Ivy see Energy (album).

Lightning is a highly visible form of energy transfer.

Broadly speaking, energy refers to "the potential for causing a change". There are different forms of energy. Many forms of energy refer to changes in movement of objects or their potential for causing other kinds of change. Hence, in the real world, energy can be viewed as the ability to perform an action.

The etymology of the term is from Greek ενεργεια, εν- means "in" and έργον means "work"; the -ια suffix forms an abstract noun. The compound εν-εργεια in Epic Greek meant "divine action" or "magical operation"; it is later used by Aristotle in a meaning of "activity, operation" or "vigour", and by Diodorus Siculus for "force of an engine".

Nature of Energy

The term energy, as used in physical sciences, particularly physics is a fundamental concept pertaining to the ability for action; it is the ability to do work, for example, a physical system mostly does mechanical work.^[1] 'Work' in this case is defined by the product of force and distance in relation to motion, of an object, whether macroscopic or microscopic. Energy in this sense is frame dependent and thus can only be defined relative to certain reference state of the system. This is because motion is always from a given reference state to another. For example, a speeding bullet has plenty of kinetic energy in reference system of non-moving observer, but it has zero kinetic energy in proper (co-moving) reference frame. Of course, the selection of such a reference state is completely arbitrary and usually is selected to maximally simplify the problem to be dealt with.

One such useful reference frame is called the "rest frame" for simple objects, and called the "center of momentum frame" for systems of objects. These reference inertial frames are useful because certain types of energy (including some kinetic energy) in systems cannot be arbirarily made to completely disappear by choice of reference frame. The reason for this is that choosing a frame which makes kinetic energy diappear for one particle, may make it appear for another particle in relative motion, in the same system. In general, kinetic energy appears in such systems as part of an invariant quantity, when they are viewed in the reference frame in which the total vector momentum of the system is zero. In such cases, the total energy of the system appears as an invariant, and determines the invariant mass of the system. Invariant mass and the energy associated with it are independent of the observer, and they are what determine familiar aspects of objects such as weight and gravitational field. The energy associated with the invariant mass of an object is sometimes called the rest energy of the object, even when the object is composed of moving parts (such as vibrating atoms or moving molecules of gas). + Thus, in the context of natural sciences energy is an attribute of a system that can be quantified in many interdependent forms. Note however that motion is not a requirement for energy to exist in a system, because often there is much more potential energy (and its related forms) in a system than kinetic energy.

- Some of the invariant mass of systems may be present in forms which may be easily extracted to do work (such as chemical or nuclear potential energy) or in forms that are less easily extracted and capable of work only in certain circumstances (such as heat). However, all these types of energy are associated with mass. The invariant mass of an object may thus be thought of as a certain amount of frozen energy, some of which may be available to do work, depending on circumstance.

Energy, in the context of natural sciences, is subject to conservation. Thus, energy cannot be made or destroyed, it can only be transformed. In practice, usable energy is usually lost during transfer, an effect known as entropy.

Forms of Energy

Scientific forms

Energy, in the context of natural sciences: physics, chemistry, biology etc., can be in several forms: mechanical potential—due to possible physical interactions with other objects (for example, gravitational potential energy); kinetic—contained in macroscopic motion; chemical—potential stored in chemical bonds between atoms; electrical—potential due to possible charge interactions; thermal—contained in the kinetic energy of individual molecules; nuclear—potential stored between constituents of nuclei. Light can be viewed as energy in the form of photons or waves, depending on the context. The theory of general relativity provides a framework to envision mass itself as an expression of energy.

Another form of energy, a form of energy said to permeate the universe, is called dark energy.

Non-scientific forms

To mathematicians, engineers, physicists and scientists, the word "energy" has a strict and quantifiable definition. Mixing of the non-scientific and scientific definitions of the word is deprecated and leads to confusion. Despite this, the fact remains that the word Energy is often used in contexts outside the natural sciences.

For example, in the context of economics, the term energy is used in discussions related to resources, such petroleum products and electric power generation that enable us to use machines.

In the context of psychology, sociology, politics etc., energy can be in in the form of emotional energy, embodied energy, and perhaps psychic energy.

In the context of colloquial language, that is in common speech, the word energy is used to describe the behaviour of individuals. This may be similar to the physical use of the term work (force x distance), although this form is in fact quite different. Energy can be used to describe someone with a vigorous, enterprising, hard working or ambitious drive, or to describe someone’s physical and mental capacity when applied to a particular activity, or to describe someone with an vivid imagination implying vitality and intensity of expression. Similarly, The term "energy" is widely used in a spiritual or non-scientific way that cannot be quantified or even defined. The term energy, in such contexts, is used in traditional and New age mysticism and in fields such as parapsychology, acupuncture and reiki, prana anf yoga. Paranormal researchers will often refer to "psychokinetic energy" when attempting to explain paranormal phenomena or the concept of a spirit or soul. These forms of 'so called' energy are not quantifiable and are therefore unacceptable to the scientific community.

Conservation of energy

Energy conservation law follows from translational symmetry of time. By other words, most phenomena below the cosmic scale do not depend on location on time coordinate. Yet by other words: yesterday, today, and tomorrow are physically indistinguishable. The mutual uncertainty of energy and time in quantum mechanics is related through the uncertainty principle:

$\Delta E\Delta t\geq h$

which thus shall not be considered as a violation of energy conservation law but rather as a mathematical (=logical) prohibition to define energy over an arbitrary small time interval with arbitrary high certainty.

As a consequence of energy conservation law, one form of energy can be readily transformed into another - for instance, a battery converts chemical energy into electrical energy. Similarly, gravitational potential energy is converted into the kinetic energy of moving water (and a turbine) in a dam, which in turn is transformed into electric energy by a generator.

The law of conservation of energy states that in a closed system the total amount of energy, corresponding to the sum of a system's constituent energy components, remains constant. Some works, thus some forms of energy, are not easily measured by the unaided observer.

Units

SI

Because energy is defined via work then the SI unit for energy are the same as the unit of work – the joule (J), named in honour of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to 1 newton-metre and, in terms of SI base units:

$1\ \mathrm {J} =1\ \mathrm {kg} \left({\frac {\mathrm {m} }{\mathrm {s} }}\right)^{2}=1\ {\frac {\mathrm {kg} \cdot \mathrm {m} ^{2}}{\mathrm {s} ^{2}}}$

An energy unit that is used in atomic physics, particle physics and high energy physics is the electronvolt (eV). One eV  is equivalent to 1.60217653×10⁻¹⁹ J.

When large amounts of energy are involved, often TNT equivalent unit is used. 1 ton of TNT equivalent is equal to 4.2 × 10⁹ Joules. Therefore, 1 kT TNT is 4.2 × 10¹² Joules, and 1 MT TNT is 4.2 × 10¹⁵ Joules.

In spectroscopy the unit cm^-1 = 0.0001239 eV is used to represent energy since energy is inversely proportional to wavelength from the equation $E=h\nu =hc/\lambda$.

(Note that torque, which is typically expressed in newton-metres, has the same dimension and this is not a simple coincidence: a torque of 1 newton-metre applied on 1 radian requires exactly 1 newton-metre=joule of energy.)

Other units of energy

In cgs units, one erg is 1 g cm² s⁻², equal to 1.0×10⁻⁷ J.

The imperial/US units for both energy and work include the foot-pound force (1.3558 J), the British thermal unit (Btu) which has various values in the region of 1055 J, and the horsepower-hour (2.6845 MJ).

The energy unit used for everyday electricity, particularly for utility bills, is the kilowatt-hour (kW h), and one kW h is equivalent to 3.6×10⁶ J  (3600 kJ or 3.6 MJ).

The calorie equals the amount of heat necessary to raise the temperature of one gram of water by 1 Celsius degree, at a pressure of 1 atm. It is equal to 4.1868 J. Food energy is measured in kilocalories, commonly abbreviated as Calories (= 10³ calories).

Transfer of energy

Work

Main article: Mechanical work

Because energy is defined as a work, then definition of a work is central to understand various kinds of energy.

Work is a defined as a path integral of force F over distance s:

$W=\int \mathbf {F} \cdot \mathrm {d} \mathbf {s}$

The equation above says that the work ($W$) is equal to the integral of the dot product of the force ($\mathbf {F}$) on a body and the infinitesimal of the body's translation ($\mathbf {s}$).

Depending on kind of force F involved, work of this force results in corresponding kind of energy (gravitational, electrostatic, kinetic, etc).

Heat

Main article: Heat

Heat is the common name for thermal energy of an object that is due to the motion of the constituents - usually atoms and molecules. This motion can be translational (motion of molecules or atoms as a whole); vibrational (relative motion of atoms within molecules) or rotational (motion of the atoms of a molecule about a common centre). It is the form of energy which is usually linked with a change in temperature or in a change in phase of matter. In chemistry, heat is the amount of energy which is absorbed or released when atoms are rearranged between various molecules by a chemical reaction. The relationship between heat and energy is similar to that between work and energy. Heat flows from areas of high temperature to areas of low temperature. All objects (matter) have a certain amount of internal energy that is related to the random motion of their atoms or molecules. This internal energy is directly proportional to the temperature of the object. When two bodies of different temperature come in to thermal contact, they will exchange internal energy until the temperature is equalised. The amount of energy transferred is the amount of heat exchanged. It is a common misconception to confuse heat with internal energy, but there is a difference: the change of the internal energy is the heat that flows from the surroundings into the system plus the work performed by the surroundings on the system. Heat energy is transferred in three different ways: conduction, convection and/or radiation.

Conservation of energy

The first law of thermodynamics says that the total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. This law is used in all branches of physics, but frequently violated by quantum mechanics (see off shell). Noether's theorem relates the conservation of energy to the time invariance of physical laws.

An example of the conversion and conservation of energy is a pendulum. At its highest points the kinetic energy is zero and the potential gravitational energy is at its maximum. At its lowest point the kinetic energy is at its maximum and is equal to the decrease of potential energy. If one unrealistically assumes that there is no friction, the energy will be conserved and the pendulum will continue swinging forever. (In practice, available energy is never perfectly conserved when a system changes state; otherwise, the creation of perpetual motion machines would be possible.)

Another example is a chemical explosion in which potential chemical energy is converted to kinetic energy and heat in a very short time.

Relations between different forms of energy

All forms of energy: thermal, chemical, electrical, radiant, nuclear etc. can be in fact reduced to kinetic energy or potential energy. For example thermal energy is essentially kinetic energy of atoms and molecules; chemical energy can be visualized to be the potential energy of atoms within molecules; electrical energy can be visualized to be the potential and kinetic energy of electrons; similarly radiant energy can be visualized to be the potential and kinetic energy of photons and nuclear energy as the potential energy of nucleons in atomic nuclei.

Kinetic energy

Main article: Kinetic energy

Kinetic energy is defined as the amount of work needed to accelerate a body from rest to its velocity v:

$E_{k}=W=\int \mathbf {v} \cdot \mathrm {d} \mathbf {p}$

The equation above says that the kinetic energy ($E_{k}$) is equal to the integral of the dot product of the velocity ($\mathbf {v}$) of a body and the infinitesimal of the body's momentum ($\mathbf {p}$).

For non-relativistic velocities, that is velocities much smaller than the speed of light, this mathematically results in:

$E_{k}={\begin{matrix}{\frac {1}{2}}\end{matrix}}mv^{2}$		where Ek is kinetic energy m is mass of the body v is velocity of the body

At near-light velocities, we use the correct relativistic formula:

$E_{k}=mc^{2}(\gamma -1)=\gamma mc^{2}-mc^{2}\;\!$		where m is its rest mass, $\gamma ={\frac {1}{\sqrt {1-(v/c)^{2}}}}$ $\gamma mc^{2}\,$ is the total energy of the body, $mc^{2}\,$ is again the rest mass energy, v is the velocity of the body, and c is the speed of light in a vacuum, which is approximately 300,000 kilometers per second.

See also, E=mc².

In the form of a Taylor series, the relativistic formula can be written as:

$E_{k}={\frac {1}{2}}mv^{2}-{\frac {3}{8}}{\frac {mv^{4}}{c^{2}}}+\cdots$

Hence, the Newtonian approximation for kinetic energy is simply relativistic kinetic energy at small velocities. Thus, Newtonian mechanics is the mathematical consequence of relativistic mechanics at small velocities.

Internal energy

Main article: Internal energy

Internal energy is the kinetic energy and the potential energy associated with the motion of particles. Kinetic energy includes the rotational, vibrational energy, potential - the potential electric energy of particles within system.

Internal energy is often convenient to identify with a state function of a system.

History

In the past, energy was discussed in terms of easily observable effects it has on the properties of objects or changes in state of various systems. Basically, if something changed, some sort of energy was involved in that change. As it was realized that energy could be stored in objects, the concept of energy came to embrace the idea of the potential for change as well as change itself. Such effects (both potential and realized) come in many different forms; examples are the electrical energy stored in a battery, the chemical energy stored in a piece of food, the thermal energy of a water heater, or the kinetic energy of a moving train.

The concept of energy and work are relatively new additions to the physicist’s toolbox. Neither Galileo nor Newton made any contributions to the theoretical model of energy, and it was not until the middle of the 19th century that these concepts were introduced.

The development of steam engines required engineers to develop concepts and formulas that would allow them to describe the mechanical and thermal efficiencies of their systems. Engineers such as Sadi Carnot and James Prescott Joule, mathematicians such as Émile Claperyon and Hermann von Helmholtz , and amateurs such as Julius Robert von Mayer all contributed to the notions that the ability to perform certain tasks, called work, was somehow related to the amount of energy in the system. The nature of energy was elusive, however, and it was argued for some years whether energy was a substance (the caloric) or merely a physical quantity, such as momentum.

William Thomson (Lord Kelvin) amalgamated all of these laws into his laws of thermodynamics, which aided in the rapid development of energetic descriptions of chemical processes by Rudolf Clausius, Josiah Willard Gibbs, Walther Nernst. In addition, this allowed Ludwig Boltzmann to describe entropy in mathematical terms, and to discuss, along with Jožef Stefan, the laws of radiant energy.

For further information, see the Timeline of thermodynamics.

Energy and Economy

Main article: [[:Energy development and Energy policy]]

Energy consumption per capita per country (2001). Red hues indicate increase, green hues decrease of consumption during the 1990s.

The way in which humans use energy is one of the defining characteristics of an economy. The progression from animal power to steam power, then the internal combustion engine and electricity, are key elements in the development of modern civilization. Future energy development, for example of renewable energy, may be key to avoiding the effects of global warming.

See also

• Principles of energetics
• List of energy topics
• Orders of magnitude (energy)

Energy in natural sciences

• Energy conversion
• Enthalpy
• Exergy
• Power (physics)
• Specific orbital energy
• Solar radiation
• Thermodynamics
• Thermodynamic entropy
• Internal energy
• Action potential

Energy in social context

• Energy resources
• Embodied energy
• Energy conservation
• Emergy
• Crisis
• Development
• Policy
• Renewable resources
• Energy balance
• Energy quality
• Management
• Storage
• Transmission
• EU Energy Label
• EU Intelligent Energy,
• Efficiency

Further reading

• Feynman, Richard. Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher. Helix Book. See the chapter "conservation of energy" for Feynman's explanation of what energy is and how to think about it.
• Einstein, Albert (1952). Relativity: The Special and the General Theory (Fifteenth Edition). ISBN 0-517-88441-0
• Alfred J. Lotka (1956). Elements of Mathematical Biology, forerly published as 'Elements of Physical Biology', Dover, New York.

Notes

^ This definition is one of the most common; e.g. Glossary at the NASA homepage

External links

• What does energy really mean? From Physics World
• Glossary of Energy Terms
• International Energy Agency IEA - OECD
• (pdf) - 'Actual' (First-Law) Energy in Relation to Free Energy and Entropy