Energy

In general, the concept of energy refers to "the potential for causing changes". The word is used in several different contexts. The scientific use has a precise, well-defined meaning, whilst the many non-scientific uses often do not.

In physics the energy of a system in a certain state is defined as the work needed to bring the system to that state from some reference state. Because work is defined via force involved, forms of energy are usually classified according to that force (elastic, gravitational, nuclear, electric, etc). Energy is a conserved quantity: it is neither created nor destroyed, but only transferred from place to place or from one form to another. Ultimately, this is because the laws of nature do not change with time.

Etymology

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 PENIS operation"; it is later used by Aristotle in a meaning of "activity, operation" or "vigour", and by Diodorus Siculus for "force of an engine."

Historical perspective

Energy, in the distant past, was discussed in terms of easily observable effects it has on the properties of objects or changes in state of various systems. It was generally construed that behind all changes, some sort of energy was involved. 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. While in spiritualism they were reflected in changes in a person, in physical sciences it is reflected in different forms of energy. For example, 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.

Energy in Natural Sciences

The concept of energy change from one form to another, as a "driver" for natural processes, is useful in explaining many phenomena. In particular, since energy cannot be created or destroyed, the driver of energetic processes is not creation of energy per se, but rather the transformation of energy in such a way that the energy can diffuse in space toward areas of less energy concentration (that is, toward areas of less energy per volume). Such changes are associated with increases in entropy.

In modern theory, the universe began with the Big Bang, in which a great deal of space (or volume) was created, but the creation of this volume by was so rapid that energy (and matter) was not uniformly distributed into it, and was not distributed in lowest energy states. This is fortuitous for our time 13.7 billion years later, for the continuted spontaneous diffusion of concentrated energy into the volume available to it (i.e., entropy increase), still powers all of the spontaneous transformations which cause the universe to continue to change, from day to day.

The exact context of such changes and transformations varies from one natural science to another. Some examples include:

Physics: Energy is the ability to do work (work is, simplistically, a force applied through a distance), and has several different forms. However, no matter what the form, physical energy uses the same units as work: a force applied through a distance. For example, kinetic energy is the amount of work to accelerate a body to a given velocity, gravitational potential energy is the amount of work to elevate or move a mass against a gravitational pull, etc. Because work is frame dependent (= can only be defined relative to certain initial state or reference state of the system), energy also becomes frame dependent. For example, a speeding bullet has kinetic energy in the reference frame of non-moving observer, but it has zero kinetic energy in its proper (co-moving) reference frame -- because it takes zero work to accelerate a bullet from zero speed to zero speed. Of course, the selection of a reference state (or reference frame) is completely arbitrary - and usually is dictated to maximally simplify the problem to be dealt with. However, when a certain amount of total energy cannot be removed from a system by simple choice of frame, that energy is associated with an invariant mass in the system.

Chemistry: The spontaneous exchange and transformation of energy with the environment is the cause and effect of all chemical transformations that a substance can undergo. These transformations can be a decomposition, synthesis or a reaction of molecules or atoms.

A chemical transformation is possible only if so-called free energy considerations are fulfilled. The concept of free energy is a synthesis of energy and entropy. It is important in the context of chemistry, because energy consideration alone are not sufficient to decide whether a chemical reaction is possible or not.

The speed of a permitted spontaneous chemical reaction is also determined by another concept, activation energy. It refers to the minimum energy reactant molecules must have in order to be able to produce product molecules.

Biology: Energy transformation, from greater to lesser concentrated forms, is essential for the sustanance of life. Energy diffusion is the motive source of all biological processes since they are a subset of chemical processes. Biological chemical processes involve molecular biology and biochemistry -- the making and breaking of certain chemical bonds, in the molecules found in biological organisms.

A typical feature of living organisms is that they survive because of exchange of energy. Nearly all transformations of energy in biology ultimately derives from transformation of sunlight to heat (see photosynthesis). In a living organism chemical bonds are constantly broken and made to make the exchange and transformation of energy possible. These chemical bonds are most often bonds in carbohydrates, including sugars. Other chemical bonds include bonds in ATP and acetate. These molecules, along with oxygen, are common stores of concentrated energy for biological processes. When they break, the heat which is evolved and diffuses away, supplies the net diffusion of energy which is necessary for the local concentration of energy which happens in anabolic processes, as organisms grow or evolve.

Meteorology The Earth's weather patterns, including dramatic concentrative processes like lightning, hurricanes, snow avalanches, and floods, are all powered ultimately by the energy of sunlight striking the Earth. Like biological processes, weather processes involve turning energy from a concentrated form such as sunlight (i.e., heat radiation which occurs at the temperature of the sun, and therefore is concentrated into a few photons), ultimately into a less concentrated from, such as far infrared radiation (i.e., heat radiation at the much smaller characteristic temperatures that occur on Earth, and thus is diffused into many photons).

Geology: volcanos, earthquakes, landslides, and tsunamis are all results of sudden releases of stored energy flows in the crust of earth. The source of this energy is heat released from the interior of the Earth. About half of this energy is left over from the gravitational condensation of the Earth, and about half from continuing radioactive decay within the Earth (as confirmed by recent measurements of neutrino production from the Earth's interior).

Cosmology all stellar phenomena (including of course solar activity) are driven by various forms of energy release. The source of all of this energy is ultimately derived either from gravitational collapse of matter which was distributed in the Big Bang, or else from fusion of light elements (primarily hydrogen) created in the Big Bang, but spread too fast and too thinnly in that process to be able to form the most stable and low-energy kinds of atoms, which have medium-sized atomic nuclei like iron and nickel.

Forms of energy

Engergy is usually divided into two broad categories.

Kinetic energy is the energy of motion (an object which has speed can perform work on another object by colliding with it). The formula for kinetic engergy is: $E_{k}={1 \over {2}}mv^{2}$ $E_{k}={1 \over {2}}mv^{2}$ where m is mass and v velocity magnitude.
- Kinetic thermal energy also known as Heat energy is present in all objects in the universe. Even if an object lacked kinetic thermal engery, existing at absolute zero, we couldn't observe it. It is the kinetic energy associated with the various motions of sub-microscopic particles, atoms and molecules. The average thermal energy per particle within a sample of matter is proportional to the sample's temperature. To raise the temperature of a sample of matter, work is required to accelerate the particles to higher kinetic energies, and also work is required to move particles against the electromagnetic forces which store their potential energy. Thermal energy is a particularly diffused and randomly directed form of energy, which cannot be transformed to other types of energy in a closed system in thermal equilibrium. Thus, although some heat consists of kinetic energy, this kinetic energy is directed in random directions and cannot be used to perform work unless allowed to diffuse into a larger volume. Some heat may be turned into other types of energy if directed by allowing it to flow toward a region of lower temperature, but this is equivalent to allowing energy diffusion into a larger volume or space. Average kinetic thermal engery is approximated by: ${\overline {E_{kT}}}={3 \over {2}}kT$ where k is the Boltzmann constant and T is absolute temperature.
- Radiant energy also known as Light energy is the energy of photons and is responsible for the various sorts of electromagnetic radiation (work is required to create photons). Photons are the force carrying particles of the electromagnetic force, which move at the speed of light and carries energy and information with it. Other kinds of energy are stored in electric and magnetic fields which do not change, or which change in ways which are not characteristic of electromagnetic radiation. These, too, however, count as energy. For example, a great deal of energy may be transferred between the windings of an electrical transformer, but it is not, strictly speaking, transferred by photons or electromagnetic radiation. Rather, it is transferred by other types of fluctuations in the electromagnetic field (see virtual particles). Light energy is equal to: ${\!E_{kR}}=hf$ where f is the frequency of the photon and h is the Planck's constant.

Potential energy is stored unreleased energy (a positive quantity, like monitary savings), or else required energy (like monitary debt). This sort of energy may be positive or negative because it can represent work done on a system (against a force) or work done by a system as a force result. Negative engergy is a mathematical construct in reference to another system. For instance, using the power of a compressed spring to launch a dart uses the elastic potential energy stored within the spring. When the spring is released, this energy is converted into kinetic energy, and work is performed. There is a form of potential energy for each of the four basic forces in nature: gravity, electromagnetic, and strong and weak nuclear forces.
- Gravitational potential energy is seen when are masses are moved apart (such as when a building is erected), or when masses move together (as when a metiorite falls to Earth). If the masses of the objects are considered point masses, gravitational potential engery is equal to: $E_{pG}=-{GmM \over r}$ where m and M are the two masses in question, r is the distance between them, and G is the Gravitational constant.
- Electromagnetic potential energy results from moving charges against a field, and also includes the common chemical potential energies (energy required to break chemical bonds or obtained from forming them. The energy released in lightning, or from burning a litre of fuel oil, are common kinds of electromagnetic potential energy. gravitational potential engery is equal to: $E_{pE}={qQ \over 4\pi \epsilon _{0}r}$ where q and Q are the electric charges on the objects in question, r is the distance between them, and ε₀ is the Electric constant of a vacuum.
- Potential thermal energy results from the electromagnetic potential energy when kinetic energy interacts with various electromagnetic fields between atoms, which contain it (this results in energy storage: in a solid, heat is about evenly divided between kinetic and potential energy; for gasses the division increasingly favors kinetic energy).
- Potential chemical energy is the energy stored in the bonds of chemical structures. It is released in chemical reactions.
- Potential elastic energy is the energy stored in the elastic nature of objects. In the ideal case, of Hooke's Law, the energy is equal to: $\!E_{pE}={1 \over 2kx^{2}}$ where k is the spring constant, dependant on the individual spring, and x is the deformation of the object.
- Nuclear potential energy ultimately provides the energy released from nuclear fission and nuclear fusion processes. In both cases nuclear forces act to bind nuclear particles more strongly and closely, after the reaction has completed. Weak nuclear forces provide the potential energy for certain kinds of radioactive decay, such as beta decay.Ultimately, the energy released in nuclear processes is according to: $\!E_{pN}={\Delta mc^{2}}$ where Δm is the amount of mass of the particles turned into energy and c is the speed of light in a vacuum.

Conservation of energy

Energy is subject to the law of conservation of energy (which is a mathematical restatement of shift symmetry of time). Thus, energy cannot be made or destroyed, it can only be converted from one form to another, that is, transformed. In practice, during any energy transformation in (macroscopic) system, some energy is converted into incoherent microscopic motion of parts of the system (which is usually called heat or thermal motion), and the entropy of the system increases. Due to mathematical impossibility to invert this process (see statistical mechanics), the efficiency of energy conversion in a macroscopic system is always less than 100%.

The first law of thermodynamics states 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. In other words, energy is neither created nor destroyed, only converted between forms. 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.

The law of conservation of energy, a fundamental principle of physics, 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. The fact that energy is not always conserved in quantum mechanics is a property of the the uncertainty principle, which relates the mutual uncertainty of time and energy as follows:

\Delta E\Delta t\geq h

As such, quantum mechanical 'violations' of the conservation of energy are not really violations at all, but rather an example of the priority the uncertainty principle takes over more classical laws. Since there is always a degree of mutual uncertainty between time and energy, it follows that the more accurately time is measured, the less accurate measurements of energy can be. When the time scales become small enough that this quantum uncertainty becomes significant, energy may not be conserved. However. within the limits set by the uncertainty principle, conservation of energy holds.

Conversion of energy into different forms

As a consequence of energy conservation law, one form of energy can often 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. In all cases, as long as no energy is allowed to escape from the system, the sum of all the different energies in the system remains constant, no matter how many changes take place.

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

Another 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 rarely perfectly conserved when a system changes state; in large systems (consisting of many atoms), some energy will be converted into 'useless' (non-available) energies, such as those associated with heat. This fraction, however, may be reduced arbitrarily toward zero. In large systems with little friction (such as a planet orbiting its sun), motion may continue nearly indefinitely because useable energy is traded between usable kinetic and potential energies with so little conversion into heat. In small systems such the atom or in a vibrating molecule, where there may be no friction associated with the motion of electrons or the mututal vibration of nuclei, the possibility of indefinite motion, with perpetual conversion of kinetic and potential energy, is the case.

While energy in forms other than heat may be freely converted to other forms (including into heat) with efficiency approaching or even equaling 100%, once energy has been converted into heat, there are severe limitations in re-converting this energy into other useful forms, and efficiency never reaches 100%. If this were not so, the creation of certain kinds of perpetual motion machines (those which evolve heat, but use that heat to continue running) would be possible.

Heat, therefore, deserves to be placed in a special class of energy, which has been "degraded" by giving it access to all parts of a system. While most heat consists of kinetic and potential energies associated with atomic motion, or with certain kinds of radiant energy (i.e., electromagnetic energy with a blackbody spectrum), the energy associated with heat is in a "diffused" and non-direction form, in which the energy has spread out to occupy all of the possible states of a system which can store it. This happens at a certain equilibrium temperature, where "temperature" is a measure of energy concentration in a system. When all parts of a system reach the same temperature, the energy of heat cannot be directed into particular other kinds of energy (or used to do work), unless the system is "enlarged" in some fashion which allows the heat is allowed to diffuse into a particular direction, in which it is even less concentrated (such as when the heat is allowed to flow to a region of lower temperature). Thus we see that heat is energy which has already reached a sort of minimal concentration or diffusion in the system it is in, and is useless for doing any kind of work unless the system is opened in such a way as to let the heat have access to a larger system.

Energy is always conserved in closed systems, if heat is taken into account. But the amount of useful energy is usually not conserved, since once energy is converted to heat, it loses some of its ability to do work, and therefore its ability to be convertable to other kinds of energy.

Relations between different forms

In the context of natural sciences, 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 and potential energy of atoms and molecules; chemical energy can be visualized to be the potential energy difference between different arrangements atoms within molecules; electrical energy can be visualized to be the potential of electric fields and charges; similarly radiant energy can be visualized to be the potential of the electromagnetic field and nuclear energy as associated with differences in the potential energy of the electric and nuclear fields in atomic nuclei.

The SI unit of measurement for energy is the Joule.

Work

Because energy is defined in terms of work, a definition of work is crucial to the understanding 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 the kind of force F involved, work of this force results in corresponding kind of energy (gravitational, electrostatic, kinetic, etc).

For example, the gravitational force F=-mg acting on a mass m when the mass is elevated from some height h₁ (reference height) to the height h₂ is therefore:

W = -mg(h₁ - h₂)= mgh₂ - mgh₁

and we call this work by the term "gravitational potential energy" U = mgh.

Similar, work by the force F = ma to accelerate a bullet from zero velocity to the velocity v is

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

= mv²/2

and we call this work by the term "kinetic energy" K = mv²/2.

Other forms of energy are similarly defined via work.

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. When two bodies of different temperature come in to thermal contact, they will exchange internal energy until the temperature is equalized. 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.

Energy in the economy

In the context of economics the word energy is synonymous to energy resources, it refers to substances like fuels, petroleum products and electric power installations. This difference vis a vis energy in natural sciences can lead to some confusion, because energy resources are not conserved in nature in the same way as the energy is conserved in the context of say physics. People often talk about energy crisis and the need to conserve energy, something contrary to the spirit of natural sciences. Thus, production and consumption of energy is very important to the global economy. All economic activity therefore require energy, whether to manufacture goods, provide transportation, feed electricity into computers and other machines, or to grow food to feed workers, or even to harvest new fuels.

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. Scarcity of cheap fuels, pollution, and global warming are key concerns in future energy development.

Some attempts have been made to define "embodied energy" - the sum total of energy expended to deliver a good or service as it travels through the economy.

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