• Czech: úsilí
• Dutch: inspanning
• Finnish: ponnistus
• German: Anstrengung , Aufwand
• Hebrew:
• Italian: sforzo
• Kurdish:
• Polish: wysiłek
• Portuguese: esforço
• Spanish: esfuerzo
• Swedish: Ansträngning, Insats

• Czech: snaha
• Dutch: inspanning, moeite
• Finnish: yritys
• German: Bemühung , Bestrebung , Anstrengung
• Hebrew:
• Polish: staranie
• Portuguese: esforço , empenho
• Spanish: esfuerzo
• Swedish: Bemödande, Prestation

• ttbc Spanish: ahínco

main Elastic potential energy Elastic potential energy is defined as a work needed to compress (or expand) a spring. The force, F, in a spring or any other system which obeys Hooke's law is proportional to the extension or compression, x,

F = -kx

where k is the force constant of the particular spring (or system). In this case, the calculated work becomes

E_ = kx^2.

Hooke's law is a good approximation for behaviour of chemical bonds under normal conditions, i.e. when they are not being broken or formed.

Kinetic energy

Kinetic energy, symbols Ek, T or K, is the work required to accelerate an object to a given speed. Indeed, calculating this work one easily obtains the following:

E_ = \int \mathbf \cdot d \mathbf = \int \mathbf \cdot d \mathbf= mv^2

At speeds approaching the speed of light, c, this work must be calculated using Lorentz transformations, which results in the following:

E_ = m c^2\left(\frac - 1\right)

This equation reduces to the one above it, at small (compared to c) speed. A mathematical by-product of this work (which is immediately seen in the last equation) is that even at rest a mass has the amount of energy equal to:

E_ = mc^2

This energy is thus called rest mass energy.

Thermal energy

Thermal energy (of some media - gas, plasma, solid, etc) is the energy associated with the microscopical random motion of particles constituting the media. For example, in case of monoatomic gas it is just a kinetic energy of motion of atoms of gas as measured in the reference frame of the center of mass of gas. In case of many-atomic gas rotational and vibrational energy is involved. In the case of liquids and solids there is also potential energy (of interaction of atoms) involved, and so on.

A heat is defined as a transfer (flow) of thermal energy across certain boundary (for example, from a hot body to cold via the area of their contact. A practical definition for small transfers of heat is

\Delta q = \int C_T

where Cv is the heat capacity of the system. This definition will fail if the system undergoes a phase transition—e.g. if ice is melting to water—as in these cases the system can absorb heat without increasing its temperature. In more complex systems, it is preferable to use the concept of internal energy rather than that of thermal energy (see Chemical energy below).

Despite the theoretical problems, the above definition is useful in the experimental measurement of energy changes. In a wide variety of situations, it is possible to use the energy released by a system to raise the temperature of another object, e.g. a bath of water. It is also possible to measure the amount of electric energy required to raise the temperature of the object by the same amount. The calorie was originally defined as the amount of energy required to raise the temperature of one gram of water by 1 °C (approximately 4.1855 J, although the definition later changed), and the British thermal unit was defined as the energy required to heat one pound of water by 1 °F (later fixed as 1055.06 J).

Electric energy

The electric potential energy of given configuration of charges is defined as the work which must be done against the Coulomb force to rearrange charges from infinite separation to this configuration (or the work done by the Coulomb force separating the charges from this configuration to infinity). For two point-like charges Q1 and Q2 at a distance r this work, and hence electric potential energy is equal to:

E_ =

where ε0 is the electric constant of a vacuum, 107/4πc0² or 8.854188…×10−12 F/m. Conservation of energy is the mathematical consequence of translational symmetry of time (that is, the indistinguishability of time intervals taken at different time) - see Noether's theorem.

According to energy conservation law 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 a fundamental principle of physics. It follows from the translational symmetry of time, 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.

Thus 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.

In quantum mechanics energy is expressed using the Hamiltonian operator. On any time scales, the uncertainty in the energy is by

\Delta E \Delta t \ge \frac

which is similar in form to the Heisenberg uncertainty principle (but not really mathematically equivalent thereto, since H and t are not dynamically conjugate variables, neither in classical nor in quantum mechanics).

In particle physics, this inequality permits a qualitative understanding of virtual particles which carry momentum, exchange by which and with real particles, is responsible for the creation of all known fundamental forces (more accurately known as fundamental interactions). Virtual photons (which are simply lowest quantum mechanical energy state of photons) are also responsible for electrostatic interaction between electric charges (which results in Coulomb law), for spontaneous radiative decay of exited atomic and nuclear states, for the Casimir force, for van der Waals bond forces and some other observable phenomena.

Energy and life

Any living organism relies on an external source of energy—radiation from the Sun in the case of green plants; chemical energy in some form in the case of animals—to be able to grow and reproduce. The daily 1500–2000 Calories (6–8 MJ) recommended for a human adult are taken as a combination of oxygen and food molecules, the latter mostly carbohydrates and fats, of which glucose (C6H12O6) and stearin (C57H110O6) are convenient examples. The food molecules are oxidised to carbon dioxide and water in the mitochondria

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 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 when split and reacted with water, is used for other metabolism (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:

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: 3kJ

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 energy or radiation), and it is true that most real machines manage higher efficiencies. However, 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"). 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, i.e. reconverted into carbon dioxide and heat.

See also

• Activation energy
• American Museum of Science and Energy (AMSE)
• Americans for Balanced Energy Choices (ABEC)
• Enthalpy
• Energy conservation
• Entropy
• Interaction energy
• Internal energy
• List of books about energy issues
• List of energy topics
• Orders of magnitude (energy)
• Power (physics)
• Renewable energy
• Solar radiation
• Thermodynamic free energy
• Thermodynamics
• Units of energy
• Negative energy
• World energy resources and consumption

Notes and references

Further reading

• Energy and Entropy
• New Century Senior Physics

External links

sisterlinks Energy

• Compact description of various energy sources. Energy sources and ecology.
• Conservation of Energy - a chapter from an online textbook
• Energy for kids
• Energy Source Comparisons by Energy Literacy Advocates
• Glossary of Energy Terms
• Middle East Energy & Power News — ArabianBusiness.com
• What does energy really mean? From Physics World
• on Project Physnet
• EnergyWiki

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