energy

This article deals with physical quantity. For further meanings see energy (disambiguation) .

Physical size
Surname	energy
Formula symbol	${\displaystyle E}$
Size and unit system unit dimension SI J = kg · m 2 · s -2 = N · m = W · s L 2 · M · T −2 cgs erg L 2 · M · T −2

Energy is a fundamental physical quantity that plays a central role in all areas of physics as well as in technology , chemistry , biology and economics . Your SI unit is the joule . The practical importance of energy often is that a physical system to the degree heat give off work afford or radiation can emit, where its energy is reduced. In a system that is closed off from the environment , the total energy does not change (law of conservation of energy ). The importance of energy in theoretical physics lies, among other things, in the fact that the law of conservation of energy, originally a fact of experience, can already be inferred from the fact that the fundamental physical laws of nature are unchangeable over time.

Energy comes in various forms of energy that can be converted into one another . Examples of forms of energy are potential , kinetic , electrical , chemical and thermal energy (thermal energy). Examples of such conversions of energy are that a person lifts a package or accelerates a bicycle , that a battery is charged, that a living being does metabolism or that a heater gives off heat.

The energy of a system depends on its state , i. H. on the parameters of the system and the current values ​​of its variables . The form of this dependency determines the temporal development of the system in every detail according to Hamilton's equations of motion , the Schrödinger equation or the Dirac equation .

According to the theory of relativity , rest energy and mass are linked by the equivalence of mass and energy ( ). ${\displaystyle E=mc^{2}}$

History of the term

Hermann von Helmholtz

Nicolas Léonard Sadi Carnot

The word energy goes back to the ancient Greek ἐνέργεια , energeia , which in ancient Greece had a purely philosophical meaning in the sense of “living reality and effectiveness” (see also “ act and potency ”). As a scientific term, the word itself was first introduced into mechanics in 1807 by the physicist Thomas Young . The new quantity of energy should indicate the strength of very specific effects that a moving body can produce through its movement, and that cannot be determined solely through its impulse (“mass times speed”). Since the investigation of the impact of two bodies by Christiaan Huygens , Christopher Wren and John Wallis around the year 1668, it has been known about the impulse that it is retained in elastic and inelastic bodies, i.e. the right measure for the changes caused and thus for the indestructible "greatness of movement" is. In other processes, however, bodies of different mass cause effects of different magnitude, even if they have the same impulse. This includes, for example, the height that a body reaches when moving upwards, or the depth of the hole that it makes in a soft mass on impact. The effect does not increase proportionally with the speed, like the impulse, but with the square of the speed. Therefore, in 1686 Gottfried Wilhelm Leibniz designated size as the true measure of the size of the movement and called it vis viva ("living force"). This name followed the language used at the time, in which a body could only cause effects through its inherent forces . The name living force , however, "caused a disastrous confusion of ideas and an innumerable host of misunderstandings through its confusion with Newton's concept of force" (according to Max Planck in his award-winning presentation of the history of the conservation of energy in 1887). Leibniz argued as follows: ${\displaystyle mv}$ ${\displaystyle mv^{2}}$

Lifting a weight to a height requires just as much work as lifting a weight to a height (lever law). According to Galileo Galilei is in free fall , so the final speed in the first case is twice as high as in the second case. If one starts with the inherent (living) force with which one wants to measure this work ( latent form of the living force ), then the living force is preserved , that is and not as the followers of Descartes thought. ${\displaystyle m}$ ${\displaystyle 4h}$ ${\displaystyle 4m}$ ${\displaystyle h}$ ${\displaystyle v\sim {\sqrt {h}}}$ ${\displaystyle m\,f(v)}$ ${\displaystyle m\,f(2v)=4\,m\,f(v)}$ ${\displaystyle f(v)=v^{2}}$ ${\displaystyle f\sim v}$

Daniel Bernoulli derived the correct factor in the kinetic energy as early as 1726. With him, as with other analytical mechanics of the 18th century such as Leonhard Euler (e.g. treatment of elastic deformation), Joseph Louis Lagrange (Mécanique Analytique 1788), there are also forerunners of the concept of potential energy (the term potential function comes from George Green In 1828 and independently it was introduced by Carl Friedrich Gauß in 1840, but was already known as Lagrange and Laplace as potential). The concept was already known to Leibniz (in its derivation from ) and Johann I Bernoulli , who was the first to formulate the principle of the preservation of living forces in 1735 (Leibniz also had the idea, for example in his 5th letter to Samuel Clarke ), in particular from Leibniz student Christian Wolff was spread. At that time, one spoke of potential energy as the latent form of living force which, for example, is distributed to smaller particles of the body during inelastic collisions. ${\displaystyle {\frac {1}{2}}}$ ${\displaystyle mv^{2}}$

In order to be able to predict the mentioned effects of the movement of the body , Young defined the quantity energy as the ability of the body to cover a certain distance against a resisting force. He also noticed that work that is done in the form of lifting work on a body is later quantitatively reflected in its energy, but did not yet come up with the concept of converting various forms of energy and also retained Leibniz's formula and was in large measure Still a supporter of the Cartesian standpoint of forces . ${\displaystyle \textstyle mv^{2}}$

In the 18th century, mechanics and physics were not particularly interested in energy; important researchers such as Euler saw the dispute over the Vis Viva , the true measure of force, as a matter for philosophers and the solution to the equations of motion was primarily concerned with celestial mechanics. The concept of energy in today's sense did not originate with the analytical mechanics of the 18th century, but with the applied mathematicians of the French school, including Lazare Carnot , who wrote that living force is either as force times way (as latent living force ) can manifest. A quantitative definition of work (“force times way” or ) was given simultaneously by Coriolis and Poncelet in 1829 , apparently independently of each other and also by Young. Coriolis also found the right expression for kinetic energy , which Rankine first called kinetic energy in 1853 . ${\displaystyle mv^{2}}$ ${\displaystyle \textstyle \int {\vec {F}}\cdot d{\vec {s}}}$ ${\displaystyle {\tfrac {1}{2}}mv^{2}}$

In connection with the steam engine, the idea developed that thermal energy is the cause of moving energy or mechanical work in many processes. The starting point was that water is converted into a gaseous state through heat and the gas expansion is used to move a piston in a cylinder. The power movement of the piston reduces the stored thermal energy of the water vapor. The connection between mechanical energy and heat was demonstrated in experiments by Benjamin Thompson (Count Rumford, Munich 1796, 1798) and Humphry Davy (1799), which have become famous .

The physicist Nicolas Carnot recognized that performing mechanical work requires a change in the volume of the steam. He also found out that the cooling of the hot water in the steam engine is not just done by conduction. Carnot published these findings in 1824 in a widely acclaimed paper on the functional principle of the steam engine. Émile Clapeyron brought Carnot's findings into a mathematical form in 1834 and developed the graphical representation of the Carnot cycle that is still used today .

In 1841 the German doctor Julius Robert Mayer published his idea that energy can neither be created nor destroyed, but only converted. He wrote to a friend: "My claim is ...: Falling force, movement, heat, light, electricity and the chemical difference of the ponderabilia are one and the same object in different manifestations." The amount of heat that is lost in a steam engine corresponds exactly to that mechanical work that the machine does. This is known today as "conservation of energy", or also "first law of thermodynamics".

In 1854, the physicist Rudolf Clausius improved ideas about energy conversion. He showed that only part of the thermal energy can be converted into mechanical work. A body in which the temperature remains constant cannot do any mechanical work. Clausius developed the second law of thermodynamics and introduced the concept of entropy. According to the second law, it is impossible for heat to pass independently from a colder to a warmer body.

In 1847 Hermann von Helmholtz formulated the principle “about the conservation of power” and the impossibility of a perpetual motion machine ( perpetuus , lat. Eternal; mobilis , lat .: movable) type 1. At that time, many inventors still wanted to manufacture machines that could do more Generated energy when put into it. Helmholtz found his findings by working with electrical energy from galvanic elements, in particular a zinc / bromine cell. In later years he linked the entropy and heat development of a chemical conversion to free energy . In the 1840s, however, both Mayer and Helmholtz had difficulties in publishing their findings, as both were initially regarded as outsiders outside the field and physicists in Germany were and are defensive against the natural philosophy of the circle around Schelling , which had been influential since the end of the 18th century both suspected of being supporters of this speculative physics .

In 1878, Josiah Gibbs came to similar findings as Helmholtz did with electrochemical cells. Chemical reactions only take place when the free energy decreases. The free energy can be used to predict whether a chemical conversion is even possible or how the chemical equilibrium of a reaction will behave when there is a change in temperature.

After Wilhelm Wien (1900), Max Abraham (1902), and Hendrik Lorentz (1904) had already published reflections on electromagnetic mass, Albert Einstein published in 1905, as part of his special theory of relativity, the knowledge that mass and energy are equivalent .

Forms of energy and energy conversion

→ Main article : Energy converter

Steam engines convert heat into mechanical energy.

A bicycle dynamo converts mechanical energy into electrical energy.

A fire converts chemical energy into heat.

Energy can be contained in a system in different ways. These possibilities are called forms of energy . Examples of forms of energy are kinetic energy , chemical energy , electrical energy or potential energy . Different forms of energy can be converted into one another, whereby the sum of the amounts of energy over the various forms of energy is always the same before and after the energy conversion.

A conversion can only take place in such a way that all other conserved quantities of the system have the same value before and after the conversion. For example, the conversion of kinetic energy is restricted by maintaining the momentum and the angular momentum of the system. A gyroscope can only be slowed down and thus lose energy if it is also emitting angular momentum. There are also such restrictions at the molecular level. Many chemical reactions that are energetically possible do not take place spontaneously because they would violate conservation of momentum. Other conserved quantities are the number of baryons and the number of leptons . They restrict the conversion of energy through nuclear reactions . The energy contained in the mass of matter can only be completely converted into another form of energy with an equal amount of antimatter . Without antimatter, the conversion with the help of nuclear fission or nuclear fusion only succeeds to a small extent.

The thermodynamics is the second law of thermodynamics another condition for conversion before: the entropy of a closed system can not decrease. Removal of heat without other processes running in parallel means cooling. A lower temperature, however, corresponds to a reduced entropy and is thus in contradiction to the second law. In order to still convert heat into another form of energy, another part of the system must be heated in return for cooling. The conversion of thermal energy into other forms of energy therefore always requires a temperature difference. In addition, not the entire amount of heat stored in the temperature difference can be converted. Heat engines are used to convert heat into mechanical energy. The ratio of the maximum possible work given by the second law to the amount of heat consumed is called the Carnot efficiency . The greater the temperature difference with which the heat engine works, the greater it is.

Other transformations are not as affected by the constraints of conservation laws and thermodynamics. In this way, electrical energy can be converted almost completely into many other forms of energy with little technical effort. For example, electric motors convert them into kinetic energy.

Most of the transformations do not take place entirely into a single form of energy, but rather some of the energy is converted into heat. In mechanical applications, the heat is mostly generated by friction . In electrical applications, electrical resistance or eddy currents are often the cause of the generation of heat. This heat is usually not used and is referred to as loss. In connection with electrical current, the emission of electromagnetic waves can also occur as an undesirable loss. The ratio between successfully converted energy and energy used is called efficiency .

A number of energy conversions are often coupled in technical applications. In a coal-fired power station , the chemical energy of the coal is first converted into heat through combustion and transferred to water vapor. Turbines convert the heat of the steam into mechanical energy and in turn drive generators , which convert the mechanical energy into electrical energy.

Energy in classical mechanics

The pendulum of a pendulum clock regularly converts kinetic energy into potential energy and vice versa. The clock uses the positional energy of the weights in the earth's gravitational field to compensate for friction losses.

In classical mechanics the energy of a system is its ability to work to do. The work converts energy between different forms of energy. The special form of Newton's laws ensures that the sum of all energies does not change. Friction and the associated energy losses are not taken into account in this consideration.

The Noether theorem allows a more general definition of energy, which automatically takes into account the aspect of energy conservation. All natural laws of classical mechanics are invariant with regard to shifts in time. They are characterized by the fact that they apply unchanged in the same form at all times. The Noether theorem now states that there is a physical quantity for this symmetry in relation to the shift in time, the value of which does not change over time. That quantity is energy.

From the law of conservation of energy and inevitable energy losses through friction it follows that it is impossible to build a mechanical machine that can run for any length of time ( perpetual motion machine ). In addition, the conservation of energy together with the conservation of momentum allows statements to be made about the result of collisions between objects without the need to know the exact mechanism of the collision.

Energy and movement

The kinetic energy is the energy that is inherent in the state of motion of a body. It is proportional to the mass and to the square of the speed relative to the inertial system in which the body is described. ${\displaystyle E_{\mathrm {kin} }}$ ${\displaystyle m}$ ${\displaystyle v}$

${\displaystyle E_{\mathrm {kin} }\,=\,{\tfrac {1}{2}}mv^{2}\,}$.

The amount of kinetic energy depends on the point of view from which the system is described. Often an inertial system is used which is at rest in relation to the ground.

In addition to a translational movement, an extended body can also perform a rotary movement. The kinetic energy contained in the rotational movement is called rotational energy . This is proportional to the square of the angular velocity and the moment of inertia of the body.

Energy and potential

Potential energy , also called positional energy , comes to a body through its position in a force field , provided that it is a conservative force . This could, for example, be the earth's gravity field or the force field of a spring . The potential energy decreases in the direction of the force and increases against the direction of force; it is constant perpendicular to the direction of force. If the body moves from a point at which it has a high potential energy to a point at which it is lower, it does just as much physical work as its potential energy has decreased. This statement applies regardless of the way the body got from one point to the other.

The potential energy of a body with mass in a homogeneous gravitational field with gravitational acceleration is proportional to the height above the origin of the coordinate system: ${\displaystyle m}$ ${\displaystyle g}$ ${\displaystyle h}$

${\displaystyle E_{\text{pot}}=m\,g\,h\,}$.

In free fall , this potential energy is converted into kinetic energy by accelerating the body.

Since the origin of the coordinates can be chosen arbitrarily, the positional energy of the body is never given absolutely and cannot be measured. Only their changes are measurable.

With periodic movements, potential is regularly converted into kinetic energy and back into potential energy. In the case of a pendulum , for example, the potential energy is maximum at the reversal points; the kinetic energy is zero here. When the thread is hanging vertically, the mass reaches its maximum speed and thus also its maximum kinetic energy; the potential energy has a minimum here. A planet has the highest potential but also the lowest kinetic energy at its point furthest from the sun. Up to the point closest to the sun, its orbital speed increases just enough that the increase in kinetic energy precisely compensates for the decrease in potential energy.

Elastic energy is the potential energy of the atoms or molecules displaced from their rest position in an elastically deformed body, for example a mechanical spring . In general, the energy that is stored (or released) in the body during elastic or plastic deformation is called deformation energy .

Energy in Thermodynamics

Fig. 1 Thermal energy and the main principles of thermodynamics (the order of the energies in the outer circle is arbitrary).

Fig. 2 Exergy components in the fuel, after combustion in the flue gas, after the heat transfer to water vapor and after the transition into a heated room

Fig. 3 Exergy in the flue gas

Figure 4 Exergy in water vapor at 32 bar and 350 ° C

Fig. 5 Simplified exergy and energy flow diagram of electricity generation and distribution from a steam power plant

Thermal energy is the energy thatis storedin the disordered movement of the atoms or molecules of a substance . It is also known colloquially as "heat energy" or "heat content". The conversion of thermal energy into other forms of energy is described by thermodynamics . A distinction is made here between the energy contained in the system ( internal energy , enthalpy ) and heat , thethermal energy transportedacross the system boundary .

The sum of thermal energy, vibrational energy in the body and binding energy is called internal energy . In some sources, a distinction is made between thermal internal energy , chemical internal energy and nuclear energy as internal energy , which, however, leaves the framework of thermodynamics.

Conversion of thermal energy into mechanical work

While all forms of energy can be completely converted into thermal energy under certain conditions (see # Forms of Energy and Energy Conversion ) ( first law of thermodynamics ), the reverse is not true. The second law of thermodynamics describes a very important limitation here (Fig. 1). Depending on the temperature at which the heat is available, only a more or less large proportion can be converted into mechanical work via a cycle , while the rest is released into the environment. In technical thermodynamics, the convertible parts of a form of energy are also referred to as exergy . The exergy is not a state variable in the strict sense, because it not only depends on the state of the system, but also on the state of the environment , which is given in the individual case, must generally be assumed. Then, using exergy flow diagrams, an energy conversion chain can be traced where avoidable losses (friction or other dissipative processes ) are to be found. In Fig. 2 you can see that when chemical energy (100% exergy) is converted into heat at an average temperature of 1000 ° C, the exergy share is only 80%. If this energy is transferred as heat in a steam boiler to water vapor at 273 ° C, only about 50% remains and when it is transferred to a room heated to 20 ° C, only about 7% remains. An ambient temperature of 0 ° C was always assumed.

Calculation of the maximum work (exergy)

In calculating the exergetic proportion of thermal energy is to consider whether the heat source or has a constant temperature, such as in one-boiling water reactor is the case at approximately 270 ° C, whether the heat output of a itself cooling medium flue gas takes place, . In the first case, the exergetic part can be determined via the Carnot efficiency from the upper process temperature and the ambient temperature, otherwise the heat and the exergy are obtained from the area integral , which is derived from the TS diagram in Figure 3 and from the TS Diagram in Figure 4 can be seen. The formula is:

${\displaystyle {E_{\mathrm {ex} }}=H_{1}-H_{U}-T_{U}\cdot {\left(S_{1}-S_{U}\right)}\,}$.

The relationship can also be read directly from the diagrams. Here: T is the absolute temperature in K, S is the entropy in J / K, H is the enthalpy in J, index 1: initial state, index U: ambient state.

The enthalpy difference is essentially (in this case) the energy supplied as heat from the fuel to the combustion air. It appears as the area under the curve of the isobaric heat input. The exergetic part is above the ambient temperature, the other non-usable part, called “ anergy ”, is below this line. The decrease in exergy in an energy conversion chain is also called energy depreciation .

When the heat from the flue gas is transferred to the working medium, the water, which is evaporated and overheated in the process, a further loss of exergy occurs . The maximum mechanical power that can be obtained from the steam mass flow for a process with superheated steam of, for example, 16 bar and 350 ° C must under no circumstances be calculated using the Carnot efficiency with this temperature. The result with an efficiency of 52% would be wrong. It would contradict the second law, since the mean temperature of the heat input in the water-steam cycle is lower. If there is no internal heat transfer ( regenerative feed water preheating ) from condensing steam to the feed water, as is the case with steam engines, in which in the theoretically most favorable case the steam can be reversibly brought to water with ambient conditions, a maximum efficiency of 34 is only achieved at 15 ° C ambient temperature , 4%. The reversible Clausius-Rankine process in Figure 4 with a vapor pressure of 32 bar and condensation at 24 ° C, however, reaches 37.2%. With these steam parameters, the real processes only achieve far lower efficiencies.

Energy and exergy flow diagram of electricity generation

In Figure 5, a simplified energy flow diagram of electricity generation by a large steam power plant ( live steam condition 260 bar, 545 ° C, feed water preheating to 276 ° C) with the distribution to the end consumer is compared with a corresponding exergy flow diagram. It can be seen from this that a significant part of the energy depreciation does not take place in the condenser or in the downstream cooling tower of the power plant, where the waste heat is dissipated, but rather when the chemical energy of the fuel is converted into thermal energy ( combustion ) and when the heat is transferred from the flue gas to the Steam. The numerical values ​​for the power distribution are reference values; they may differ slightly in individual cases.

Solar energy

The solar energy that reaches the earth through radiation also experiences an exergy loss on the way to the earth's surface . While the internal energy of the sun at around 15 million K still consists practically of pure exergy, the sun radiates with a surface temperature of around 6000 K on the earth's surface, the temperature of which is to be set at around 300 K. By concentrating the sun's rays in a collector you would not get above the temperature of the sun's surface - even in high mountains, where absorption by the earth's atmosphere hardly plays a role. The Carnot factor would result in an efficiency of approx. 95%. But then no more energy would be transmitted. The thermodynamic limit is below this at an absorber temperature of 2500 K with an efficiency of approx. 85%. In practice, there are also dissipative losses, starting with absorption in the atmosphere, through the material properties of the crystalline cells to the ohmic resistance of the photovoltaic systems , so that efficiencies of less than 20% can be achieved to date. The highest efficiency currently achieved is 18.7%.

Combined heat and power (CHP)

Energy balance of district heating (red: exergy, blue: anergy)

Energy balance of the heat pump (red: exergy, blue: anergy)

→ Main article : Combined heat and power

Heat with only a small amount of exergy is usually required for heating. That is why heating with electrical current via resistance heating is a "waste of energy". Wherever mechanical energy or electricity is generated from heat and there is a need for heat at the same time, it makes more sense to use waste heat for heating than to provide heat separately. In a thermal power station , if it is operated with steam, steam is extracted from the turbine, the temperature of which is just high enough to conduct the condensation heat to the consumer via a district heating network . Alternatively, the waste heat from stationary combustion engines is also used in block-type thermal power stations (BHKW) . The heat pump should also be mentioned here. It uses work to absorb heat (energy) from the environment and, together with the drive work, release it as thermal heat at a correspondingly high temperature. If groundwater with 10 ° C is available as a heat source and a room has to be heated with 20 ° C, a heat pump with Carnot process could deliver 29 kWh of heat by using one kilowatt hour of drive work (coefficient of performance = 29). Real heat pumps that are operated with alternately evaporating and condensing refrigerants at different pressures achieve coefficients of performance of approx. 3 to 5.

Chemical energy

→ Main article : chemical energy

Chemical energy is the form of energy that is stored in the form of a chemical compound in an energy carrier and can be released during chemical reactions . It describes the energy that is associated with electrical forces in atoms and molecules and can be divided into, on the one hand, the kinetic energy of the electrons in the atoms and, on the other hand, the electrical energy of the interaction between electrons and protons.

It is released in exothermic reactions and has to be added for endothermic reactions .

Energy in electrodynamics

In an electric field , if there is no time-varying magnetic field , an electric potential can be defined. A charge carrier then has a potential electrical (electrostatic) energy that is proportional to the potential and its amount of charge. Since the zero point of the potential can be freely determined, the energy is also not absolutely defined. For two points in the potential field, however, the difference in energies is independent of the choice of the potential zero point. In electrical engineering , potential differences correspond to voltages ; The potential of the earth is usually chosen as the zero point of the potential scale.

For arrangements of two electrical conductors , the electrostatic energy is proportional to the square of the difference between the electrical potentials of the two conductors. The double of the proportionality constant is called electrical capacitance . Capacitors are electrotechnical components that have a high capacity and can therefore store energy.

Equivalent to the view that the electrostatic energy is carried by charges, the interpretation is that the energy is distributed to the empty space between the charges. With this approach, the energy density, i.e. the energy per volume element, is proportional to the square of the electric field strength. If there is a dielectric in the electric field , the energy is also proportional to the dielectric constant .

If a charge moves in a vacuum to a place where there is a lower electrical potential, the kinetic energy of the charge increases just as much as the potential energy decreases. This happens for example with electrons in an electron tube , in an X-ray tube or in a cathode ray tube screen . If, on the other hand, a charge moves along a potential gradient in a conductor, it immediately releases its absorbed energy in the form of heat to the conductor medium. The power is proportional to the potential gradient and the current strength .

Electrical energy can be transported by charge carriers moving along conductors with no significant potential gradient. This is the case, for example, in overhead lines or in power cables, with the help of which electrical energy flows from the power station to the consumer.

Magnetic energy is contained in magnetic fields such as in superconducting magnetic energy storage .

Energy stored in an ideal electrical oscillating circuit continuously changes between the electrical form and the magnetic form. The sum of the partial energies is the same at any point in time (conservation of energy). The pure magnetic or electrical component of the energy has twice the frequency of the electrical oscillation.

Energy in the theory of relativity

According to the special theory of relativity , the mass of an object at rest corresponds to a rest energy of ${\displaystyle m}$

${\displaystyle E_{\text{Ruhe}}=m\,c^{2}\,}$.

The rest energy is therefore equivalent to the factor (square of the speed of light ) of the mass . The rest energy can be converted into other forms of energy during certain processes and vice versa. The reaction products of nuclear fission and nuclear fusion have measurably lower masses than the starting materials. In elementary particle physics , conversely, the generation of particles and thus of rest energy from other forms of energy is also observed. ${\displaystyle c^{2}}$ ${\displaystyle c\,}$

In classical mechanics, the rest energy is not included, since it is irrelevant as long as particles do not transform into other particles.

The general theory of relativity further generalizes the concept of energy and contains a unified representation of energies and impulses as sources for space curvatures via the energy-momentum tensor . From this, through contractions, variables such as energy density that can be measured by an observer can be obtained . The energy content is decisive for the investigation of the development of spacetime. So one can predict the collapse of space-time to a singularity from energy conditions .

Energy in quantum mechanics

In quantum mechanics , the Hamilton operator determines which energy can be measured in a physical system. Bound states of the system can only correspond to discrete , i.e. not arbitrary, energy values. That is why the particles or rays emitted during transitions between these states have line spectra .

The quantization of energy occurs with electromagnetic waves : A wave of the frequency can only emit energy in packets , whereby the Planckian quantum of action is. ${\displaystyle \nu }$ ${\displaystyle E_{\text{Photon}}=h\,\nu }$ ${\displaystyle h}$

Technical use of energy

A generation of energy is not possible due to the law of conservation of energy. The term energy production is nevertheless used in economic life to express the conversion of a certain form of energy (for example electrical current) from another form (for example chemical energy in the form of coal). Similarly, there is also no energy consumption in the strict physical sense, but what is meant economically is the transition from a readily usable primary energy (e.g. crude oil, gas, coal) to an energy form that can no longer be used ( e.g. waste heat in the environment). From saving energy is mentioned, if more efficient processes are found that require less primary energy for the same purpose, or otherwise, for example by reduced consumption, the primary energy consumption is reduced.

Physics describes the “energy consumption” loosely introduced above with the exact term of the increase in entropy . While the energy is always retained in a closed system, the entropy always increases over time or, at best, remains constant. The higher the entropy, the more difficult it is to use the energy. Instead of an increase in entropy, one can clearly speak of energy depreciation.

In particular, the law of the increase in entropy prevents the direct conversion of thermal energy into kinetic or electrical energy. Instead, a heat source and a heat sink (= cooling ) are always required. According to Carnot , the maximum efficiency can be calculated from the temperature difference.

The borderline case of an energy conversion without an increase in entropy is called a reversible process . A satellite in an elliptical orbit around the earth is an example of an almost reversible energy conversion: At the highest point of the orbit it has high potential energy and low kinetic energy, at the lowest point of the orbit it is exactly the opposite. The conversion can take place thousands of times a year without significant losses. In superconducting resonators, energy can be converted back and forth between radiant energy and electrical energy millions or even billions of times per second, also with losses of less than one per thousand per conversion.

In many processes, which in the past were still associated with high losses, i.e. a considerable increase in entropy, technological progress enables increasingly lower losses. An energy-saving lamp or LED converts electrical energy into light much more efficiently than an incandescent lamp . A heat pump often generates many times more heat than a conventional electric heater with the same output by using heat from the environment with a certain electrical output. In other areas, however, the state of the art has been close to the theoretical maximum for some time, so that only small progress is possible here. Good electric motors convert over 90 percent of the electrical energy used into usable mechanical energy and only a small part into useless heat.

In the physical sense, saving energy means minimizing the depreciation of energy and the increase in entropy when converting or using energy.

Specific energy

In the natural sciences, specific means “based on a certain assessment basis” (related quantity ). The specific energy is related to a certain property of a system, whichcan be describedby a physical quantity .

According to DIN 5485 , the specific energy is specifically mass-related, and the volumetric energy density is the dimensional designation.

Examples

• Energy per volume in J / m (dimension ): enthalpy (thermodynamics), specific latent heat : heat of fusion , heat of vaporization , heat of crystallization or the corresponding enthalpies (Material Science), condensing and heating value (Energy Technology), specific compaction energy (Material Science), specific energy of explosive ${\displaystyle ML^{-1}T^{-2}}$
• Energy per mass in J / kg (dimension ): specific work , specific latent heat (thermodynamics), calorific value and calorific value of solid fuels, specific energy of the energy store (energy technology), electrical capacity and energy density of the plate capacitor (electrical engineering), specific energy of the mass point ( Mechanics) ${\displaystyle L^{2}T^{-2}}$

Thermodynamics and chemistry denote material-related energy values not as specific , but as molar :

• Energy per amount of substance in J / mol (dimension ): molar latent heat (thermodynamics) ${\displaystyle ML^{2}T^{-2}N^{-1}}$

Energy supply and consumption

→ Main article : Energy supply  and energy consumption

Energy consumption is the colloquial term used to describe the use of different energies in forms that people can use. Energy supply refers to the supply of consumers with these forms of energy, including the necessary energy infrastructure .

The most common forms of energy used by humans are thermal energy and electrical energy . Human needs are primarily focused on the areas of heating , food preparation and the operation of facilities and machines to make life easier. Here, the subject is getting around the consumption of, for example, fossil fuels as a fuel for vehicles significant.

The various energy sources can reach the consumers via cables, such as typically fuel gases , electrical energy, process and heating heat . Or they are largely storable and easy to transport, such as hard coal , heating oil , fuels ( petrol , diesel fuels , kerosene ), nuclear fuel , biomass .

The energy demand varies widely around the world and is many times higher in the industrialized countries than, for example, in the Third World (see list of countries with the highest energy consumption ). In industrially highly developed countries, companies have been involved in the generation and supply of energy for general consumption since the 19th century . Today the central generation of electrical energy and the distribution to the individual consumers are in the foreground. The procurement, transport and refining of fuels for heating purposes are also important branches of industry.

Energy source

→ Main article : Source of energy

units

In addition to the derived SI unit Joule , other energy units are also used depending on the area of ​​application. Watt-second (Ws) and newton meter (Nm) are identical to the joule.

The electron volt (eV) is used in atomic physics , nuclear physics and elementary particle physics to indicate particle energies and energy levels. Rydberg occurs less often in atomic physics . The cgs unit erg is often used in theoretical physics.

The calorie was common in calorimetry and is still used colloquially and in the movement of goods in addition to the legal unit Joule when specifying the physiological calorific value of food . Energy suppliers measure the amount of energy delivered to customers in kilowatt hours (kWh). The hard coal unit and the oil unit are used to indicate the energy content of primary energy sources. The TNT equivalent is used to measure the explosive power of explosives.

list

Various energy units and their equivalent in joules (J)

Non-SI unit	Joules
Electron volt (eV)	1,602.176.634  ·  10 -19 J
Hartree energy	4,359.744.722.21  ·  10 -18 J
erg	1  ·  10 −7 yrs
Foot-pound	1,355,817,948,331,400.4 yrs
Calorie (cal)	4.1868 J.
Kilopond meter (kpm)	9.80665 J.
BTU	1,055.055.852.62  ·  10 3 J
Meter ton	9,806.65  ·  10 3 J
Horsepower hour	2,647.795.5  ·  10 6 J
kWh	3.6  ·  10 6 y
kg TNT	4.184  ·  10 6 J.
kg SCE	2,930.76  ·  10 7 J
Gasoline equivalent	3.2  ·  10 7 y
Oil equivalent	4,186.8  ·  10 7 J
Therm	1,055.055.852.62  ·  10 8 J
Planck energy	1.956  ·  10 9 y
Quad	1,055.055.852.62  ·  10 18 J
Foe	1  ·  10 44 y
Literary atmosphere	1,013.25  ·  10 2 J.

Conversions

In the following conversion table, the unit indicated on the left is equal to the number times the unit indicated above:

	Joule (watt second)	Kilowatt hour	Electron volts	Kilopond meter	calorie	erg
1 kg · m² / s²	00 1	00 2.778 · 10 −7	00 6.242 · 10 18	00 0.102	00 0.239	0 10 7
1 kW h	00 3.6 · 10 6	00 1	00 2.25 · 10 25	00 3.667 · 10 5	00 8.60 · 10 5	0 3.6 · 10 13
1 eV	00 1.602 · 10 −19	00 4.45 · 10 −26	00 1	00 1.63 · 10 −20	00 3.83 · 10 −20	00 1.602 · 10 −12
1 kp m	00 9.80665	00 2.72 · 10 −6	00 6.13 · 10 19	00 1	00 2.34	0 9.80665 · 10 7
1 cal IT	00 4.1868	00 1.163 · 10 −6	00 2.611 · 10 19	00 0.427	00 1	0 4.1868 · 10 7
1 g · cm² / s²	00 10 −7	0 2.778 · 10 −14	0 6.242 · 10 11	0 1.02 · 10 −8	0 2.39 · 10 −8	00 1

Orders of magnitude

→ Main article : magnitude (energy)

Energy is a quantity that can have a value that varies by many orders of magnitude in everyday life . Examples are:

1 J = 1 Ws = 1 Nm

Potential energy that is stored in a chocolate bar (approx. 100 g) by 1 meter when it is lifted.

3.6 · 10 ⁶ J = 3600 kJ = 3600 kWs = 1 kWh

Billing unit for electrical energy (coll. Electricity), gas, etc. A European private household needs approx. 2000–4000 kWh of electrical energy per year.

2.9 · 10 ⁷ J = 8.141 kWh = 1 kg SKE

one unit of hard coal corresponds to the amount of energy that is converted when burning 1 kg of hard coal. This is a common measure for specifying primary energy quantities. (In 1998 the worldwide primary energy turnover was 14.1 Gt SCE = 390 · 10 ¹⁸ J)

1 eV = 1.602 176 565 (35) * 10 ^-19 J

The unit electron volt is used, among other things, in solid-state , nuclear and elementary particle physics . A photon of violet light has an energy of approx. 3 eV, one of red approx. 1.75 eV.

1 kg mass ≙ 8.99 · 10 ¹⁶ J

(89,875,517,873,681,764 J) according to Einstein's relationship : E = mc ² .

Formulas

• Tension energy of a tensioned spring :

${\displaystyle E_{\text{pot}}={1 \over 2}\,D\,s^{2}\,}$

where is the spring constant and the deflection of the spring from the rest position. ${\displaystyle D}$ ${\displaystyle s}$

• Potential energy of a body with mass in a homogeneous gravitational field: ${\displaystyle m}$

${\displaystyle E_{\text{pot}}=mgh}$

where is the mass , the acceleration due to gravity and the altitude at which the body is located. ${\displaystyle m}$ ${\displaystyle g}$ ${\displaystyle h}$

• Kinetic energy of a body with mass and speed : ${\displaystyle m}$ ${\displaystyle v}$

${\displaystyle E_{\mathrm {kin} }\,=\,{\tfrac {1}{2}}mv^{2}\,}$.

• Rotational energy of a body:

${\displaystyle E_{\mathrm {rot} }={\frac {1}{2}}J\omega ^{2}}$

where is the moment of inertia about the relevant axis of rotation and the angular velocity . ${\displaystyle J}$ ${\displaystyle \omega }$

• electrical energy in a circuit:

${\displaystyle E_{\text{el.Strom}}=U\cdot I\cdot t}$

where is the electrical voltage , the current through the line and the duration. ${\displaystyle U}$ ${\displaystyle I}$ ${\displaystyle t}$

• Energy of a charged plate capacitor :

${\displaystyle E_{\text{Plattenkondensator}}={\frac {Q^{2}}{2C}}={\frac {C\,U^{2}}{2}}\,}$

where is the charge , the capacitance and the electrical voltage. ${\displaystyle Q}$ ${\displaystyle C}$ ${\displaystyle U}$

• Magnetic field energy of an ideal coil through which current flows:

${\displaystyle E_{\text{Spule}}={\frac {L\,I^{2}}{2}}\,}$

where is the inductance and the electrical current. ${\displaystyle L}$ ${\displaystyle I}$

• Relativistic energy of a free particle of mass with velocity : ${\displaystyle m}$ ${\displaystyle v}$

${\displaystyle E_{\text{relativistisch}}={\frac {m\,c^{2}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}$

where is the speed of light . ${\displaystyle c}$

• Energy of light quanta ( photons ):

${\displaystyle E_{\text{Photon}}=h\,f\,}$

where is Planck's constant and the frequency . ${\displaystyle h}$ ${\displaystyle f}$

• Energy of an earthquake :

${\displaystyle E_{\text{Erdbeben}}=10^{{\frac {3}{2}}(M-2)}}$Tons of TNT ,

where the magnitude is on the Richter scale . ${\displaystyle M}$

• Work (change in energy) is the integral of the force along the distance covered : ${\displaystyle F}$ ${\displaystyle s}$

${\displaystyle W=\int \mathbf {F} \,\mathrm {d} \mathbf {s} \,}$

• The work performed on a system in the time interval can also be defined via the performance : ${\displaystyle [t_{0},t_{1}]}$

${\displaystyle W=\int _{t_{0}}^{t_{1}}P(t)\,\mathrm {d} t}$

See also

Portal: Energy  - Overview of Wikipedia content on the subject of energy

literature

• Jennifer Coopersmith: Energy - the subtle concept. Oxford University Press, 2010, ISBN 0-19-954650-9 .
• Max Jammer : Energy. In: Donald M. Borchert (Ed.): Encyclopedia of Philosophy. Volume 3. Thomson Gale, 2005, pp. 225-234.
• Marc Lange : Energy (Addendum). In: Donald M. Borchert (Ed.): Encyclopedia of Philosophy. Volume 3. Thomson Gale, 2005, pp. 234-237.
• Yehuda Elkana : Discovery of the Conservation of Energy. Harvard University Press 1974, (preface by I. Bernard Cohen ).
• István Szabó : History of Mechanical Principles. Birkhäuser 1979.
• Martin Buchholz : Energy - How do you waste something that cannot be reduced? Springer , Heidelberg / Berlin, ISBN 978-3662497418 .

Web links

Wikiquote: Energy  Quotes

Wiktionary: Energy  - explanations of meanings, word origins, synonyms, translations

• Energy. In: World of Physics. Retrieved January 13, 2017 . 
• What is energy from the alpha-Centauri television series(approx. 15 minutes). First broadcast on Nov 10, 2002.

Individual evidence

1. ↑ Rudolf Eisler: Dictionary of Philosophical Terms (1904) [1]
2. ↑ Leibniz: Brevis demonstratio erroris memorabilis Cartesii. Acta Eruditorum, 1686.
3. ↑ ^{a b} Max Planck: The principle of the conservation of energy. BG Teubner, Leipzig 1887.
4. ↑ Based on Max Jammer, Energy, Encyclopedia of Philosophy
5. ↑ Bernoulli, Examen principiorum mechanicae, Comm. Acad. Petropol. 1726, p. 126. See Szabo, History of Mechanical Principles, Birkhäuser 1979, p. 71
6. ^ Max Jammer: Energy, Encyclopedia of Philosophy. P. 228.
7. ↑ Thomas Young: A course of lectures on natural philosophy and the mechanical arts . Johnson, 1807, p. 44. "The same idea is somewhat more concisely expressed by the term energy which indicates the tendency of a body to ascend or to penetrate to a certain distance in opposition to a retarding force."
8. ↑ Max Jammer: Article Energy, Encyclopedia of Philosophy.
9. ↑ See Szabo: History of Mechanical Principles. P. 78, for ignoring Euler's pamphlet by Immanuel Kant from 1749 on the true estimation of living forces
10. ↑ Max Jammer: Article Energy, Encyclopedia of Philosophy.
11. ↑ Essai sur les machines en general. 1783, 2nd edition 1803 as Principes fondamentaux de l´equilibre et du mouvement.
12. ↑ Alexandre Moatti: Gaspard-Gustave de Coriolis (1792-1843): un mathématicien, théoricien de la mécanique appliquée. Dissertation at the University of Paris, 2011 (PDF; 6.4 MB; French)
13. ↑ Hans Joachim Störig : Small world history of science. Volume 2. Fischer Taschenbuch, Hamburg 1982, ISBN 3-596-26399-9 , pp. 89-91, 1280.
14. ↑ Walther Gerlach: Advances in natural science in the 19th century. In: Propylaea world history. Volume 8 (19th century), 1960.
15. ↑ Friedhelm Kuypers: Physics for Engineers and Natural Scientists: Volume 1 - Mechanics and Thermodynamics . John Wiley & Sons, October 4, 2012, ISBN 978-3-527-66957-8 , pp. 248– (accessed June 13, 2013).
16. ↑ See also: Martin Buchholz: Energy - How do you waste something that cannot be reduced? In: Science Slam Finale 2011. November 19, 2011, accessed April 30, 2020 .  or Martin Buchholz: Energy - How do you waste something that cannot be reduced? 1st edition. Springer, Berlin Heidelberg 2016, ISBN 978-3-662-49741-8 , p. 27 ff .
17. ↑ Peter Kurzweil: Physics formula collection. , 2008, p. 15.