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Energy transformation; In a typical lightning strike, 500 megajoules of electric potential energy is converted into the same amount of energy in other forms, most notably light energy, sound energy and thermal energy.

In physics, energy is one of the basic quantitative properties describing a physical system or object's state. Energy can be transformed (converted) among a number of forms that may each manifest and be measurable in differing ways. The law of conservation of energy states that the (total) energy of a system can increase or decrease only by transferring it in or out of the system. The total energy of a system can be calculated by simple addition when it is composed of multiple non-interacting parts or has multiple distinct forms of energy. Common energy forms include the kinetic energy of a moving object, the radiant energy carried by light and other electromagnetic radiation, and various types of potential energy such as gravitational and elastic. Energy is measured in SI units of joules ( J ). Common types of energy transfer and transformation include processes such as heating a material, performing mechanical work on an object, generating or making use of electric energy, and many chemical reactions.

Units of measurement for energy are usually defined via a work process. The work performed by a given body on another is defined in physics as the force (SI unit: newton) applied by the given body, multiplied by the distance (SI unit: metre) of movement against the opposing force exerted by the other body. Thus, the energy unit is the newton-metre, which is called the joule. The SI unit of power (energy per unit time) is the watt, which is simply a joule per second. Thus, a joule is a watt-second, so 3600 joules equal a watt-hour. The CGS energy unit is the erg, and the imperial and US customary unit is the foot pound. Other energy units such as the electron volt, 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 and have unit conversion factors relating them to the joule.

Potential energy is energy stored by virtue of the position of an object in a force field, such as a gravitational, electric or magnetic field. For example, lifting an object against gravity performs work on the object and stores gravitational potential energy; if it falls, gravity does work on the object which transforms the potential energy to kinetic energy associated with its speed. Some specific forms of energy include elastic energy due to the stretching or deformation of solid objects, chemical energy such as is released when a fuel burns, and thermal energy, the microscopic kinetic and potential energies of the disordered motions of the particles making up matter.

Not all of the energy in a system can be transformed or transferred by a work process; the amount that can is called the available energy. In particular the second law of thermodynamics limits the amount thermal energy that can be transformed into other forms of energy. Mechanical and other forms of energy can be transformed in the other direction into thermal energy without such limitations.

Any object that has mass when stationary (thus called rest mass), equivalently has rest energy as can be calculated using Albert Einstein's equation E = mc2. Being a form of energy, rest energy can be transformed to or from other forms of energy, while the total amount of energy does not change. From this perspective, the amount of matter in the universe contributes to its total energy.

Similarly, all energy manifests as a proportionate amount of mass. For example, adding 25 kilowatt-hours (90 megajoules) of any form of energy to an object increases its mass by 1 microgram. If you had a sensitive enough mass balance or scale, this mass increase could be measured. Our Sun (or a nuclear bomb) transforms nuclear potential energy to other forms of energy; its total mass doesn't decrease due to that in itself (since it still contains the same total energy even if in different forms), but its mass does decrease when the energy escapes out to its surroundings, largely as radiant energy.

A new form of energy can't be defined arbitrarily. In order to be valid, it must be shown to be transformable to or from a predictable amount of some known form(s) of energy, thus showing how much energy it represents in the same units used for all other forms. It must obey conservation of energy, so it must never decrease or increase except via such a transformation (or transfer). Also, if an alleged new form of energy can be shown not to change the mass of a system in proportion to its energy, then it is not a form of energy.

Living organisms require available energy to stay alive; humans get such energy from food along with the oxygen needed to metabolize it. Civilization requires a supply of energy to function; energy resources such as fossil fuels are a vital topic in economics and politics. Earth's climate and ecosystem are driven by the radiant energy Earth receives from the sun (as well as the geothermal energy contained within the earth), and are sensitive to changes in the amount received.

Forms of energy

Energy exists in many forms:

In the context of physical sciences, several forms of energy have been identified. These include[need quotation to verify]:

Thermal energy is energy of microscopic constituents of matter, which may include both kinetic and potential energy.

Some entries in the above list constitute or comprise others in the list. The list is not necessarily complete. Whenever physical scientists discover that a certain phenomenon appears to violate the law of energy conservation, new forms are typically added that account for the discrepancy.

Heat and work are special cases in that they are not properties of systems, but are instead properties of processes that transfer energy. In general we cannot measure how much heat or work are present in an object, but rather only how much energy is transferred among objects in certain ways during the occurrence of a given process. Heat and work are measured as positive or negative depending on which side of the transfer we view them from.

Classical mechanics distinguishes between kinetic energy, which is determined by an object's movement through space, and potential energy, which is a function of the position of an object within a field, which may itself be related to the arrangement of other objects or particles. These include gravitational energy (which is stored in the way masses are arranged in a gravitational field), several types of nuclear energy (which utilize potentials from the nuclear force and the weak force), electric energy (from the electric field), and magnetic energy (from the magnetic field).

Other familiar types of energy are a varying mix of both potential and kinetic energy. An example is mechanical energy which is the sum of (usually macroscopic) kinetic and potential energy in a system. Elastic energy in materials is also dependent upon electrical potential energy (among atoms and molecules), as is chemical energy, which is stored and released from a reservoir of electrical potential energy between electrons, and the molecules or atomic nuclei that attract them.[need quotation to verify].

Potential energies are often measured as positive or negative depending on whether they are greater or less than the energy of a specified base state or configuration such as two interacting bodies being infinitely far apart.

Wave energies (such as radiant or sound energy), kinetic energy, and rest energy are each greater than or equal to zero because they are measured in comparison to a base state of zero energy: "no wave", "no motion", and "no inertia", respectively.

It has been attempted to categorize all forms of energy as either kinetic or potential, but as Richard Feynman points out:


Also, at relativistic speeds, defining kinetic energy is problematic because the energy due to the body's motion does not simply contribute additively to the total energy as it does at classical speeds.


History of understanding

Thomas Young – the first to use the term "energy" in the modern sense.

The word energy derives from the Greek ἐνέργεια energeia, which possibly appears for the first time in the work of Aristotle in the 4th century BCE. (Ancient Greek: ἐνέργεια energeia “activity, operation”[1])


In 1807, Thomas Young was possibly the first to use the term "energy" instead of vis viva, in its modern sense.[2] 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 first postulated in the early 19th century, and applies to any isolated system. 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.[3] Since 1918 it has been known that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time.

It was argued for some years whether energy was a substance (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. This led to the theory of conservation of energy, and development of the first law of thermodynamics.

Finally, William Thomson (Lord Kelvin) amalgamated these many discoveries into the laws of thermodynamics, which aided the rapid development of explanations of chemical processes by Rudolf Clausius, Josiah Willard Gibbs, and Walther Nernst. 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.



Units of measure


Energy in various contexts

Classical mechanics

Work, a form of energy, is force times distance.







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 is thus often said to be stored by cells in the structures of molecules of substances such as carbohydrates (including sugars), lipids, and proteins, which release energy when reacted with oxygen in respiration. In human terms, the human equivalent (H-e) (Human energy conversion) indicates, for a given amount of energy expenditure, the relative quantity of energy needed for human metabolism, assuming an average human energy expenditure of 12,500kJ per day and a basal metabolic rate of 80 watts. For example, if our bodies run (on average) at 80 watts, then a light bulb running at 100 watts is running at 1.25 human equivalents (100 ÷ 80) i.e. 1.25 H-e. For a difficult task of only a few seconds' duration, a person can put out thousands of watts, many times the 746 watts in one official horsepower. For tasks lasting a few minutes, a fit human can generate perhaps 1,000 watts. For an activity that must be sustained for an hour, output drops to around 300; for an activity kept up all day, 150 watts is about the maximum.[6] The human equivalent assists understanding of energy flows in physical and biological systems by expressing energy units in human terms: it provides a “feel” for the use of a given amount of energy[7]

Earth sciences

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.,[8] 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.



Energy and life

Basic overview of energy and human life.


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


Daily food intake of a normal adult: 6–8 MJ


Energy transformation

The concept of energy and its transformations is vital in explaining and predicting most natural phenomena. One form of energy can often be readily transformed into another; for instance, a battery, from chemical energy to electric energy; a dam: gravitational potential energy to kinetic energy of moving water (and the blades of a turbine) and ultimately to electric energy through an electric generator.

There are strict limits to how efficiently energy can be converted into other forms of energy via work, and heat as described by Carnot's theorem and the second law of thermodynamics. These limits are especially evident when an engine is used to perform work. Some energy transformations can be quite efficient.

The direction of transformations in energy (what kind of energy is transformed to what other kind) is often described by entropy (equal energy spread among all available degrees of freedom) considerations, as in practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.



Conservation of energy and mass in transformation

Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

Matter may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. However, since c^2 is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~9\times 10^{16} joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics.

Reversible and non-reversible transformations

Transformation of energy into useful work is a core topic of thermodynamics. In nature, transformations of energy can be fundamentally classed into two kinds: those that are thermodynamically reversible, and those that are thermodynamically irreversible. A reversible process in thermodynamics is one in which no energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomization in a crystal).

Transformation with the age of the universe




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. Sunlight is also captured by plants as chemical potential energy in photosynthesis, when carbon dioxide and water (two low-energy compounds) are converted into the high-energy compounds carbohydrates, lipids, and proteins. Plants also release oxygen during photosynthesis, which is utilized by living organisms as an electron acceptor, to release the energy of carbohydrates, lipids, and proteins. 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 these molecules are ingested, and catabolism is triggered by enzyme action.


Conservation of energy


Most kinds of energy (with gravitational energy being a notable exception)[12] 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.[4][13] Conservation of energy is the mathematical consequence of translational symmetry of time (that is, the indistinguishability of time intervals taken at different time)[14] - see Noether's theorem.




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.





Applications of the concept of energy


In classical physics energy is considered a scalar quantity, the canonical conjugate to time. In special relativity energy is also a scalar (although not a Lorentz scalar but a time component of the energy-momentum 4-vector).[16] In other words, energy is invariant with respect to rotations of space, but not invariant with respect to rotations of space-time (= boosts).

Energy transfer

A system can transfer energy to another system by simply transferring matter to it (since matter is equivalent to energy, in accordance with its mass). However, when energy is transferred by means other than matter-transfer, the transfer produces changes in the second system, as a result of work done on it. This work manifests itself as the effect of force(s) applied through distances within the target system.

For example, a system can emit energy to another by transferring (radiating) electromagnetic energy, but this creates forces upon the particles that absorb the radiation. Similarly, a system may transfer energy to another by physically impacting it, but in that case the energy of motion in an object, called kinetic energy, results in forces acting over distances (new energy) to appear in another object that is struck. Transfer of thermal energy by heat occurs by both of these mechanisms: heat can be transferred by electromagnetic radiation, or by physical contact in which direct particle-particle impacts transfer kinetic energy.

Because energy is strictly conserved and is also locally conserved (wherever it can be defined), it is important to remember that by the definition of energy the transfer of energy between the "system" and adjacent regions is work. A familiar example is mechanical work. In simple cases this is written as the following equation:

\Delta{}E = W








\Delta{}E = W + Q






where Q represents the heat flow into the system.


\Delta{}E = W + Q + E














The equation can then be simplified further since E_p = mgh (mass times acceleration due to gravity times the height) and 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_{total}.

Energy and the laws of motion

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, as below;

The Hamiltonian


The Lagrangian


Usually, the Lagrange formalism is mathematically more convenient than the Hamiltonian for non-conservative systems (such as systems with friction).

Noether's Theorem

Noether's (first) theorem (1918) 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 generalization of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (1788 and 1833, 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.

Energy and thermodynamics

Internal energy

Internal energy is the sum of all microscopic forms of energy of a system. It is the energy needed to create the system. It is related to the potential energy, e.g., molecular structure, crystal structure, and other geometric aspects, as well as the motion of the particles, in form of kinetic energy. Thermodynamics is chiefly concerned with changes in internal energy and not its absolute value, which is impossible to determine with thermodynamics alone.[18]

The first law of thermodynamics

The first law of thermodynamics asserts that energy (but not necessarily thermodynamic free energy) is always conserved[19] and that heat flow is a form of energy transfer. For homogeneous systems, with a well-defined temperature and pressure, a commonly used corollary of the first law is that, for a system subject only to pressure forces and heat transfer (e.g., a cylinder-full of gas), the differential change in the internal energy of the system (with a gain in energy signified by a positive quantity) is given as


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


where \delta Q is the heat supplied to the system and \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 alternatively at two other 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 behavior of a quantity closely related to energy, called entropy. Entropy is a measure of evenness of a distribution of energy between parts of a system. When an isolated system is given more degrees of freedom (i.e., given new available energy states that are the same as existing states), then total energy spreads over all available degrees equally without distinction between "new" and "old" degrees. This mathematical result is called the second law of thermodynamics.

Oscillators, phonons, and photons




Because an electric oscillator (LC circuit) is analogous to a mechanical oscillator, its energy must be, on average, equally kinetic and potential. It is entirely arbitrary whether the magnetic energy is considered kinetic and whether the electric energy is considered potential, or vice versa. That is, either the inductor is analogous to the mass while the capacitor is analogous to the spring, or vice versa.




Quantum mechanics



When calculating kinetic energy (work to accelerate a mass 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 mass energy - energy which every mass must possess even when being at rest. The amount of energy is directly proportional to the mass of body:

 E = m c^2 ,


m is the mass,
c is the speed of light in vacuum,
E is the rest mass energy.

For example, consider electron-positron annihilation, in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. This is a reversible process - the inverse process is called pair creation - in which the rest mass of particles is created from energy of two (or more) annihilating photons. In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons). However, the total system mass and energy do not change during this interaction.


It is not uncommon to hear that energy is "equivalent" to mass. It would be more accurate to state that every energy has an inertia and gravity equivalent, and because mass is a form of energy, then mass too has inertia and gravity associated with it.


A schematic diagram of a Calorimeter - An instrument used by physicists to measure energy. In this example is it is X-Rays.


Energy density



See also

Notes and references

  1. ^ Harper, Douglas. "Energy". Online Etymology Dictionary. Retrieved May 1, 2007. 
  2. ^ Smith, Crosbie (1998). The Science of Energy – a Cultural History of Energy Physics in Victorian Britain. The University of Chicago Press. ISBN 0-226-76420-6. 
  3. ^ Lofts, G; O'Keeffe D; et al. (2004). "11 — Mechanical Interactions". Jacaranda Physics 1 (2 ed.). Milton, Queensland, Australia: John Willey & Sons Australia Ltd. p. 286. ISBN 0-7016-3777-3. 
  4. ^ a b Feynman, Richard (1964). The Feynman Lectures on Physics; Volume 1. U.S.A: Addison Wesley. ISBN 0-201-02115-3. 
  5. ^ Ristinen, Robert A., and Kraushaar, Jack J. Energy and the Environment. New York: John Wiley & Sons, Inc., 2006.
  6. ^ "Retrieved on May-29-09". Retrieved 2010-12-12. 
  7. ^ Bicycle calculator - speed, weight, wattage etc. [1].
  8. ^ "Earth's Energy Budget". Retrieved 2010-12-12. 
  12. ^ "E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws". 1918-07-16. Retrieved 2010-12-12. 
  13. ^ a b The Laws of Thermodynamics including careful definitions of energy, free energy, et cetera.
  14. ^ "Time Invariance". Retrieved 2010-12-12. 
  15. ^ Berkeley Physics Course Volume 1. Charles Kittel, Walter D Knight and Malvin A Ruderman
  16. ^ a b Misner, Thorne, Wheeler (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 0-7167-0344-0. 
  17. ^ The Hamiltonian MIT OpenCourseWare website 18.013A Chapter 16.3 Accessed February 2007

Further reading

  • Crowell, Benjamin (2011) [2003]. Light and Matter. Fullerton, CA: Light and Matter. 
  • Ross, John S. (23 April 2002). "Work, Power, Kinetic Energy". Project PHYSNET. Michigan State University. 
  • Smil, Vaclav (2008). Energy in nature and society: general energetics of complex systems. Cambridge, USA: MIT Press. ISBN 0-262-19565-8. 

External links