Energy is defined as a measurement of the ability to do work or to heat an object. Energy plays an essential role both in everyday events and in scientific phenomena (is one of the most quantitative properties of physics in nature).

The term energy was introduced by Aristotle in philosophy to distinguish the “power” (δύναμις, dýnamis) proper to the shapeless matter, from the real capacity (Ancient Greek ἐνέργεια, enérgeia); the word is composed of “en” intensive particle, and “ergon” ability to act. After, the term “energy” was used for the first time to indicate a physical quantity by Kepler in his Harmonice Mundi of 1619. However, the term “energy” was introduced systematically in scientific literature only since the late nineteenth century.

A precise definition of energy is not simple to provide; energy is not a concrete reality but rather an abstract mathematical concept that expresses a link between the possible processes and a temporal symmetry of physical laws. There is, therefore, no substance or fluid corresponding to pure energy. As Feynman wrote: it is important to realize that in physics today, we have no knowledge of what energy is [Richard Feynman, The Feynman Lectures on Physics, Vol I, p. 4-1].

Energy is an extensive physical quantity (the energy of two bodies is simply the sum of the energies of the bodies taken individually), which has a central importance in the formulation of many theories, from classical mechanics to thermodynamics, from the theory of relativity to quantum mechanics.

A body can increase or decrease its energy as a result of an interaction with other bodies: the variation of energy then reflects the changes that have occurred in its microscopic properties.

How to measure energy?

The SI unit of energy is the joule [J], which is the energy transferred to an object by the work of moving it a distance of 1 meter against a force of 1 newton.


The law of conservation of energy

In physics, the law of conservation of energy is one of the most important conservation laws observed in nature. The conservation principle has guided the discovery of new forms of energy and has allowed us to discover new types of physical processes and even new particles.

The principle of conservation of energy reflects the temporal symmetry of the physical laws with respect to time translations; that is, that these do not change over time.

The law of conservation of energy states that the total energy of an isolated system remains constant, it is said to be conserved over time.

This law means that energy cannot be created or destroyed, but is merely changed from one form into another or transferred from one object to another at different stages. So we can conclude that in the entire system, the total energy remains the same, but only the transformation takes place.

For example, the electricity available in an electric oven is converted to a thermal form that goes into the object in the oven.

At the beginning of the 20th century, some nuclear decays were discovered with the emission of electrons that did not seem to satisfy the principle of energy conservation. To solve the problem in 1924, Niels Bohr put forward the idea that at the atomic level energy was not strictly conserved, proposing a theory that turned out to be wrong. Wolfgang Pauli in 1930 and Enrico Fermi in 1934 postulated the existence of new interactions and a new particle never observed before, which was able to transport energy and which was missing in the experiments. In this way, guided by the principle of conservation of energy, they were able to discover the neutrino, a particle with no electric charge, actually observed experimentally in 1959.

Classically, conservation of energy was distinct from conservation of mass; however, special relativity showed that mass could be converted to energy and vice versa by E = mc2, and science now takes the view that mass-energy is conserved.

Energy sources

The Sun’s energy warms the planet’s surface, powering titanic transfers of heat and pressure in weather patterns and ocean currents. The resulting air currents drive wind turbines. Solar energy also evaporates water that falls as rain and builds up behind dams, where its motion is used to generate electricity via hydropower.

World energy resources are the estimated maximum capacity for energy production given all available resources on Earth. Energy sources can be categorized as renewable and non-renewable.

renewable resource is a resource that can be used repeatedly and replaced naturally (that can replenish itself at a similar rate to its use by people). Renewable and non-renewable energy sources can be used as primary energy sources to produce useful energy such as heat or used to produce secondary energy sources such as electricity.

non-renewable resource is a natural resource that is used up faster than it can be made by nature. It cannot be produced, grown, or generated on a scale which can sustain how quickly it is being consumed. Once it is used up, there is no more available for the future. Fossil fuels (such as coal, petroleum, and natural gas), types of nuclear power (uranium), and certain examples. Resources such as timber (when harvested sustainably) or metals (which can be recycled) are considered renewable resources. Non-renewable resources are also called exhaustible resources.

Renewable energy

Renewable energy is a kind of energy from sources that are naturally replenishing but flow-limited, such as sunlight, wind, rain, tides, waves, and geothermal heat. They are virtually inexhaustible in duration but limited in the amount of energy that is available per unit of time. Renewable energy often supplies energy in four important areas: electricity production, air/water heating/cooling, transport, and rural energy services (off-network).

Some are considered “inexhaustible,” in the sense that they regenerate at least at the same speed with which they are consumed or are not “exhaustible” in the scale of “geological eras times.” Exceptions are some energy resources which, although renewable, are exhaustible; for example, forests are considered renewable but can be depleted due to excessive exploitation by humans.

Renewable resources, whether they are material or energy, are natural resources which, due to natural characteristics or due to the production of man, are renewed over time (at a higher, or equal, renewal rate than the rate of consumption/use) and can be considered inexhaustible, or may be available for use by humans almost indefinitely. A renewable resource is also said to be “sustainable” if its rate of regeneration is equal to or higher than the rate of use.

There are many forms of renewable energy. Wind and hydroelectric power are the direct results of differential heating of the Earth’s surface which leads to air moving about (wind) and precipitation forming as the air is lifted. Solar energy is the direct conversion of sunlight using panels or collectors. Biomass energy is stored sunlight contained in plants. Other renewable energies that do not depend on sunlight are geothermal energy, which is a result of radioactive decay in the crust combined with the original heat of accreting the Earth, and tidal energy, which is a conversion of gravitational energy. It is useful to highlight how the forms of energy present on our planet (except nuclear energy, geothermal energy, and tidal energy) almost all originate from solar radiation, in fact:

  • without the Sun there would be no wind, which is caused by the irregular heating of air masses, and with it wind energy;
  • biomass energy can be considered chemically stored solar energy, through the process of chlorophyll photosynthesis;
  • hydroelectric energy, which uses waterfalls, would not exist without the water cycle from evaporation to rain, triggered by the Sun;
  • fossil fuels (coal, oil, and natural gas) derive from the sun’s energy stored in the biomass millions of years ago through the process of chlorophyll photosynthesis.

Non-renewable energy

Non-renewable energies are energy sources that tend to run out over time and therefore the environmental impact associated with their exploitation is generally more significant than that of renewable energy sources, which are instead reintegrated naturally in a relatively short period.

Non-renewable energy sources are often exploited by humanity because they can produce the highest amounts of energy with technologically simple and tested systems. Often, the use of such sources is associated with environmental pollution problems such as the production of greenhouse gases or radioactive waste. The four major nonrenewable energy sources are:

  1. Crude oil (petroleum)
  2. Natural gas
  3. Coal
  4. Uranium or plutonium (nuclear energy)

All fossil fuels are nonrenewable, but not all nonrenewable energy sources are fossil fuels; coal, crude oil, and natural gas are all considered fossil fuels because they were formed from the buried remains of plants and animals that lived millions of years ago. Uranium ore, a solid, is mined and converted to a fuel used at nuclear power plants. Uranium is not a fossil fuel, but it is classified as a nonrenewable fuel.

Types and forms of energy

Essentially the total energy of a system can be subdivided into potential (stored) energy or kinetic (working) energy, or combinations of the two in various ways. While these two categories are sufficient to describe all forms of energy, it is often convenient to refer to particular combinations of potential and kinetic energy as its form.

  • Chemical energy
  • Elastic energy
  • Electric energy
  • Gravitational energy
  • Internal energy
  • Magnetic energy
  • Mechanical energy
  • Mechanical wave energy
  • Nuclear potential energy
  • Kinetic energy
  • Potential energy
  • Quantum chromodynamics binding energy
  • Radiant energy
  • Rest energy
  • Soundwave energy
  • Thermal energy
  • Wind wave energy

Chemical energy

Chemical energy is the potential energy stored in the bonds of chemical compounds to undergo a transformation through a chemical reaction to transform other chemical substances. It varies due to the formation or breaking of chemical bonds of any kind in the chemical elements involved in chemical reactions. An example of chemical potential energy is the energy stored in fossil fuels.

Since the strength of chemical bonds is correlated with the distance between chemical species (in fact stronger chemical bonds keep the chemical species involved in the bond closer), the chemical energy depends on the mutual position of the particles that constitute a substance.

In other words, it is the work of the Coulomb force during the rearrangement of mutual positions of electrons and nuclei in atoms and molecules. It is, therefore, the energy stored in the chemical bonds, substantially attributable to the sum of the potential energy (of the electrostatic interactions of the charges present in the matter) and the kinetic energy of electrons.

Elastic energy

Elastic energy is potential energy related to elastic force, stored in the deformation of a material (compression or stretching) or a physical system (distortion of volume or shape) exhibiting a restorative force. This also means that elastic potential energy is zero in objects that have not been stretched or compressed. The elastic potential energy equation is used in calculations of positions of mechanical equilibrium. The energy is potential as it will be converted into the second form of energy, such as kinetic.

\[U=\dfrac{1}{2}k\Delta x^2\]

where \(k\) is the elastic constant of the spring while \(\Delta x\) is the distance of stretching/compression. Since this is a particular type of energy, elastic potential energy is measured in joules (J).

Properties of elastic potential energy

The elastic potential energy is directly proportional to both the elastic constant \(k\) and the square of the spring stretching \(x\); so the potential elastic energy cannot be negative. The energy stored in a spring depends on the:

  • the shape of the spring;
  • how much the spring is deformed (stretched or compressed);
  • material’s elasticity of the spring;
  • the value of the spring constant, which defines the amount of force required to deform a spring by a certain length (the work done on the spring).

Electric energy

Electric energy is the energy newly derived from electric potential energy or kinetic energy due to or stored in charged particles within an electric field. When loosely used to describe energy absorbed or delivered by an electrical circuit (for example, one provided by an electric power utility) “electrical energy” talks about energy which has been converted from electric potential energy. This energy is supplied by the combination of electric current and electric potential that is delivered by the circuit.

At the point that this electric potential energy has been converted to another type of energy, it ceases to be electric potential energy. Thus, all electrical energy is potential energy before it is delivered to the end-user. Once converted from potential energy, electrical energy can always be called another type of energy (heat, light, motion, etc.).

Gravitational energy

Gravitational energy is the potential energy a body with mass has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field. Gravitational energy is dependent on the masses of two bodies, their distance apart, and the gravitational constant \(G\).

\[U=-G\dfrac{m\cdot M}{R}\]

The general expression for gravitational potential energy arises from the law of gravity and is equal to the work done against gravity to bring a mass to a given point in space. Because of the inverse square nature of the gravity force, the force approaches zero for large distances, and it makes sense to choose the zero of gravitational potential energy at an infinite distance away.

The gravitational potential energy near a planet is then negative since gravity does positive work as the mass approaches. This negative potential is indicative of a “bound state”; once a mass is near a large body, it is trapped until something can provide enough energy to allow it to escape.

Internal energy

Internal energy is a property of a thermodynamic system. In an ideal gas, the internal energy is the statistical mean of the gas particles’ kinetic energy, and it is this kinetic motion that is the source and the effect of the transfer of heat across a system’s boundary. For this reason, the term “thermal energy” is sometimes used synonymously with internal energy.

Magnetic energy

Magnetic energy is the potential energy due to or stored in magnetic fields. Magnetic energy and electric energy are related to Maxwell’s equations. In fact, thanks to Maxwell’s work, magnetic and electric energy are more appropriately considered as a single force. Together, they are what is known as electromagnetic energy (a form of energy that has both electrical and magnetic components).

It is created when one runs a magnetic current through a wire or any other conductive material, creating a magnetic field. The magnetic energy generated can be used to attract other metal parts (as in the case in many modern machines that have moving parts) or can be used to generate electricity and store power (hydroelectric dams and batteries).

Mechanical energy

Mechanical energy is the sum of macroscopic translational and rotational kinetic and potential energies. Mechanical energy is the energy that is possessed by an object due to its motion or due to its position; can be either kinetic energy (energy of motion) or potential energy (stored energy of position).


Objects have mechanical energy if they are in motion and/or if they are at some position relative to a zero potential energy position.

The principle of the conservation of mechanical energy

The principle of the conservation of mechanical energy states that the total mechanical energy of an isolated system remains constant in time, as long as the system is free of friction and other non-conservative forces. In other words a conservative force as a force which does not change the total mechanical energy, which is true, but might shed much light on what it means.

In any real situation, frictional forces and other non-conservative forces are present, but in many cases, their effects on the system are so small that the principle of conservation of mechanical energy can be used as a fair approximation. Though energy cannot be created or destroyed in an isolated system, it can be converted to another form of energy.

Mechanical wave energy

Mechanical wave energy is kinetic and potential energy in an elastic material (medium) due to a propagated deformational wave (oscillation of matter). Mechanical waves transport energy. This energy propagates in the same direction as the wave. Examples: ocean wind-generated waves, sound waves, seismic waves.

Any kind of wave (mechanical or electromagnetic) has a certain energy. Mechanical waves can be produced only in media which possess elasticity and inertia. A mechanical wave requires initial energy input. Once this initial energy is added, the wave travels through the medium until all its energy is transferred. In contrast, electromagnetic waves require no medium, but can still travel through one. One important property of mechanical waves is that their amplitudes are measured unusually, displacement divided by (reduced) wavelength.

When this gets comparable to unity, significant nonlinear effects such as harmonic generation may occur, and, if large enough, may result in chaotic effects. For example, waves on the surface of a body of water break when this dimensionless amplitude exceeds 1, resulting in foam on the surface and turbulent mixing. Some of the most common examples of mechanical waves are water waves, sound waves, and seismic waves. There are three types of mechanical waves: transverse waves, longitudinal waves, and surface waves.

  1. Transverse waves cause the medium to vibrate at a right angle to the direction of the wave, or energy being carried by the medium. In other words: a transverse wave is a moving wave that consists of oscillations occurring perpendicular (right angled) to the direction of energy transfer (or the propagation of the wave). Transverse waves have two parts—the crest and the trough. The crest is the highest point of the wave, and the trough is the lowest. The distance between a subsequent crest and a trough is half of the wavelength. The wavelength is the distance from crest to crest or from trough to trough.
  2. Longitudinal waves cause the medium to vibrate parallel to the direction of the wave. It consists of multiple compressions and rarefactions. The rarefaction is the farthest distance apart in the longitudinal wave, and the compression is the closest distance together. In other words: longitudinal waves are waves in which the displacement of the medium is in the same direction as, or the opposite direction to, the direction of propagation of the wave. Mechanical longitudinal waves are also called compressional or compression waves, because they produce compression and rarefaction when traveling through a medium, and pressure waves, because they produce increases and decreases in pressure. The speed of the longitudinal wave is increased in the higher index of refraction, due to the closer proximity of the atoms in the medium that is being compressed. The sound is considered a longitudinal wave.
  3. Surface waves travel along a surface that is between two media. An example of a surface wave would be waved in a pool, or in an ocean, lake, or any other type of water body. In seismology, several types of surface waves are encountered. Surface waves, in this mechanical sense, are commonly known as either Love waves (L waves) or Rayleigh waves.

Nuclear potential energy

Nuclear potential energy is the potential energy of the particles inside an atomic nucleus.

Kinetic energy

Kinetic energy is the energy of motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.

Potential energy

An object can store energy as the result of its position relative to other objects, stresses within itself, its electric charge, or other factors. Potential energy is associated with forces that act on a body in a way that the total work done by these forces depends only on the initial and final positions of the body in space. These forces, which are called conservative forces, can be represented at every point in space by vectors expressed as gradients of a certain scalar function called potential.

To determine the gravitational potential energy of an object, a zero height position must first be arbitrarily assigned. Typically, the ground is considered to be a position of zero height. But this is merely an arbitrarily assigned position that most people agree upon. Since many of our labs are done on tabletops, it is often customary to assign the tabletop to be the zero height position. Again this is merely arbitrary. If the tabletop is the zero position, then the potential energy of an object is based upon its height relative to the tabletop.

Nuclear potential energy

Nuclear potential energy is the potential energy of the particles inside an atomic nucleus. The nuclear particles are bound together by the strong nuclear force. Weak nuclear forces provide the potential energy for certain kinds of radioactive decay, such as beta decay.

Nuclear particles like protons and neutrons are not destroyed in fission and fusion processes, but collections of them can have less mass than if they were individually free, in which case this mass difference can be liberated as heat and radiation in nuclear reactions (the heat and radiation have the missing mass, but it often escapes from the system, where it is not measured).

The energy from the Sun is an example of this form of energy conversion. In the Sun, the process of hydrogen fusion converts about 4 million tonnes of solar matter per second into electromagnetic energy, which is radiated into space.

Quantum chromodynamics binding energy

Quantum chromodynamics binding energy (QCD binding energy), gluon binding energy or chromodynamic binding energy is the energy binding quarks together into hadrons. It is the energy of the field of the strong force, which is mediated by gluons.

QCD binding energy contributes most of the hadron’s mass. Most of the mass of hadrons is actually QCD binding energy, through mass-energy equivalence. This phenomenon is related to chiral symmetry breaking.

  • In the case of nucleons – protons and neutrons – QCD binding energy forms about 99% of the nucleon’s mass. That is if assuming that the kinetic energy of the hadron’s constituents, moving at near the speed of light, which contributes greatly to the hadron mass, is part of QCD binding energy.
  • For protons, the sum of the rest masses of the three valence quarks (two up quarks and one down quark) is approximately 9.4 MeV/c2, while the proton’s total mass is about 938.3 MeV/c2.
  • For neutrons, the sum of the rest masses of the three valence quarks (two down quarks and one up quark) is approximately 11.9 MeV/c2, while the neutron’s total mass is about 939.6 MeV/c2.

Considering that nearly all of the atom’s mass is concentrated in the nucleons, this means that about 99% of the mass of everyday matter (baryonic matter) is, in fact, chromodynamics binding energy.

Radiant energy

Radiant energy is the potential energy stored in the fields of propagated by electromagnetic radiation (such as light, X-rays, gamma rays, and thermal radiation) which may be described in terms of either discrete packets of energy, called photons, or continuous electromagnetic waves.

Radiant Energy to electricity

Solar energy can be used to produce electricity. Two ways to make electricity from solar energy are photovoltaic systems and systems using thermal energy.

Rest energy

The rest energy \(E_0\) of a particle is defined as \(E_0 = m_0c^2\) where \(c\) is the speed of light in vacuum. In general, only differences in energy have physical significance.

The concept of rest energy follows from the special theory of relativity that leads to Einstein’s famous conclusion about the equivalence of energy and mass. On the other hand, the concept of the equivalent Dirac invariant rest mass may be defined in terms of the self-energy corresponding to the product of a geometric matter current and a generalized potential as part of a single definition of mass in a unified geometric theory.

Soundwave energy

Soundwave energy is kinetic, and potential energy through a transmission medium (such as a gas, liquid, or solid) due to a sound propagated a wave of pressure (a particular form of a mechanical wave).

The sound is transmitted through gases, plasma, and liquids as longitudinal waves also called compression waves. It requires a medium to propagate. Through solids, however, it can be transmitted as both longitudinal waves and transverse waves. Longitudinal sound waves are waves of alternating pressure deviations from the equilibrium pressure, causing local regions of compression and rarefaction, while transverse waves (in solids) are waves of alternating shear stress at a right angle to the direction of propagation.

Thermal energy

It is called thermal energy that type of energy that anybody has at a temperature above zero. This condition represents an extensive quantity and is directly proportional to the temperature that the body generates. Thermal energy is the kinetic energy of the microscopic motion of particles, a form of a disordered equivalent of mechanical energy; refers to the energy contained within a system that is responsible for its temperature. The faster the particles move within an object or system, the higher the temperature that is recorded. Thermal energy is a term used loosely as a synonym for more rigorously-defined thermodynamic quantities such as the internal energy of a system. Heat is the flow of thermal energy.

The sum of the kinetic energy of all the particles of a system constitutes an energy form of matter called thermal energy.

In the context of mechanics problems, thermal energy play a role in ensuring the conservation of energy. Almost every transfer of energy that takes place in real-world physical systems does so with efficiency less than 100% and results in some thermal energy. This energy is usually in the form of low-level thermal energy. Here, low-level means that the temperature associated with the thermal energy is close to that of the environment. It is only possible to extract work when there is a temperature difference, so low-level thermal energy represents ‘the end of the road’ of energy transfer. No further useful work is possible; the energy is now “lost to the environment.”

Thermal energy can be produced from friction, drag, combustion, and chemical reactions. Thermal energy can be effectively stored and retrieved by means of sensible heat and latent heat principles. The other way of storing and releasing thermal energy can be performed through chemical reaction principles.

Wind wave energy

Wind waves energy has a certain amount of randomness: subsequent waves differ in height, duration, and shape with limited predictability. They can be described as a stochastic process, in combination with the physics governing their generation, growth, propagation, and decay—as well as regulating the interdependence between flow quantities such as the water surface movements, flow velocities, and water pressure. The key statistics of wind waves (both seas and swells) in evolving sea states can be predicted with wind wave models.

Energy harvesting

Energy harvesting (also known as power harvesting or energy scavenging or ambient power) is a method of generating electrical energy from normally unused energy sources available in the surrounding environment. In other words, it is the process by which energy, coming from alternative energy sources (commonly available in the environment: thermal energy, kinetic energy, chemical energy, potential or solar energy, etc.) is captured and accumulated. This process converts energy into a directly usable electrical current.

Energy harvesting holds great promise for both low-voltage and low-power applications in a wide range of portable or mobile markets such as medical equipment, consumer devices, transportation, industrial controls, and military. Energy conversion takes place in different ways depending on the environmental source. The energy can be captured from a variety of sources deemed wasted or otherwise unusable for any practical purpose.

  • Mechanical sources: translational and rotational kinetic and potential energies, inertia, gravitational field, vibrations, elastic energy, piezoelectricity, triboelectric effect, acoustic waves, sea/ocean waves, and wind energy. For example, the conversion of mechanical motion can take place through piezoelectric crystals or particular polymers, which subjected to mechanical deformation stresses, generate small electrical potentials.
  • Electromagnetic sources: radio waves, magnetic induction, electromagnetic radiation, photovoltaic, potential energy due to electric fields or magnetic fields. For example, energy from broadcasting or theoretically from any electromagnetic emission can be collected. A typical use of this technique is used to power the RFID (Radio Frequency Identification) identifiers.
  • Thermal sources: temperature gradients, pyroelectricity, thermoelectrics. In the presence of thermal gradients, thermoelectric generators can be used.
  • Chemical and biological sources: exothermic reactions, potential energy due to chemical bonds, ionization energy, levels of glucose in the blood, salinity gradients, tree-based metabolic energy.

Unconventional energy

This sector includes geothermal energy, wind power, and tidal power. Sustainable energy sources is a growing area.

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