Energy

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

The term Energy (from Greek Εν-εργεια, εν means one, a single particle and έργον, meaning the ability to act) refers to the ability of a physical system to do mechanical work.^[1] It is a fundamental concept pertaining to the ability for action. The energy of a system can be quantified in many interdependent forms, but the total energy of a system is subject to conservation. Energy can't be made or destroyed, but it can be transformed.

Energy is quantified relative to a reference state or level. For example, a litre of water has more thermal energy when at a higher temperature, and an automobile in motion has more kinetic energy than when at rest. It is important to realize that the selection of a reference state is arbitrary, but that an informed selection can greatly simplify one's understanding of that system.

Forms or types of energy

Energy 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.

Conservation of energy

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.

This law follows from translational symmetry of time, which states the independence of any physical process on the moment it started. As energy and time are conjugate quantities their mutual uncertainty is related through the uncertainty principle:

<math>\Delta E \Delta t \ge h </math>

which thus shall not be considered as a violation of energy conservation (but rather as a mathematical impossibility to define energy over an arbitrary small time interval).

Units

SI

The SI unit for both energy and work is 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:

<math>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}</math>

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

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

(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 metric units usually are self-consistent, and this particular one may seem arbitrary. It's not, the metric measurement for time is the second, and there are 3,600 seconds in an hour -- in other words, 1 kW second = 1 kJ, but the kW h is a more convenient unit for everyday use.

The calorie equals the amount of heat necessary to raise the temperature of one kilogram of water by 1 Celsius degree, at a pressure of 1 atm. It is equal to 4.1868 kJ. Food energy is measured in kilocalories, commonly abbreviated as 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:

<math> W = \int \mathbf{F} \cdot \mathrm{d}\mathbf{s}</math>

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

Depending on kind of force F involved, work of this force results in various kinds 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 atoms and molecules that constitute the object. 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 some non-zero velocity v:

<math>E_k = W = \int \mathbf{v} \cdot \mathrm{d}\mathbf{p}</math>

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

For non-relativistic velocities, that is velocities much smaller than the speed of light, we can use the Newtonian approximation

<math>E_k = \begin{matrix} \frac{1}{2} \end{matrix} mv^2</math>

where

E_k 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:

<math>E_k = m c^2 (\gamma - 1) = \gamma m c^2 - m c^2 \;\!</math>

<math>\gamma = \frac{1}{\sqrt{1 - (v/c)^2}} </math>

where

v is the velocity of the body

m is its rest mass

c is the speed of light in a vacuum, which is approximately 300,000 kilometers per second

<math>\gamma m c^2 \,</math> is the total energy of the body

<math>m c^2 \,</math> is again the rest mass energy.

See also, E=mc².

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

<math>E_k = \frac{1}{2} mv^2 - \frac{3}{8} \frac{mv^4} {c^2} + \cdots </math>

Hence, the second and higher terms in the series correspond with the "inaccuracy" of the Newtonian approximation for kinetic energy in relation to the relativistic formula.

However, the phrase "conservation of energy" is often confusing to a non scientist. This is so, because of the common usage of the terms "save energy" or conserve energy" used in campaigns for conservation of energy resources like electricity or fossil fuels.

Internal energy

Main article: Internal energy

Internal energy is the kinetic energy associated with the motion of molecules, and the potential energy associated with the rotational, vibrational and electric energy of atoms within molecules. Internal energy, like energy, is a quantifiable 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. To simply say energy is "change or the potential for change", however, misses many important examples of energy as it exists in the physical world.

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 articles: Energy development and Energy policy

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.

Spiritual energy

The term "energy" is widely used in a spiritual or non-scientific way that cannot be quantified or even defined.

To mathematicians, engineers and scientists, the word "energy" has a strict and quantifiable definition. Any usage of the word that violates this definition must be termed pseudoscience. They argue that the mixing of the non-scientific and scientific definitions of the word creates confusion.

Examples of pseudoscience are mysticism and parapsychology in fields such as acupuncture and reiki. Paranormal researchers will often refer to "psychokinetic energy" when attempting to explain paranormal phenomena or the concept of a spirit or soul.

See also

• Principles of energetics
• List of energy topics

Energy in natural sciences

• Energy balls
• Energy conservation
• Energy conversion
• Enthalpy
• Energy quality
• Exergy
• Power (physics)
• Specific orbital energy
• Solar radiation
• Thermodynamics
• Thermodynamic entropy

Energy resources

• List
• Embodied energy
• Emergy
• Crisis
• Development
• Policy
• Renewable
• Energy balance
• 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 Entropyar:طاقة

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