# Efficiency

Efficiency of an incandescent lamp (represented as a Sankey diagram )

The degree of efficiency describes the efficiency of a technical device or system as a ratio of the dimension number or percentage , usually the ratio of the useful energy to the energy supplied . If there is no corruption by stored energy, the power can be calculated as the ratio of the useful power to the supplied power . Usually, the efficiency is designated with the Greek letter ( eta ) and can have values ​​between 0 and 1: ${\ displaystyle E _ {\ mathrm {from}}}$${\ displaystyle E _ {\ mathrm {zu}}}$ ${\ displaystyle P _ {\ mathrm {from}}}$${\ displaystyle P _ {\ mathrm {zu}}}$${\ displaystyle \ eta}$

${\ displaystyle \ eta = {\ frac {E _ {\ mathrm {from}}} {E _ {\ mathrm {to}}}}}$  or  ${\ displaystyle \ eta = {\ frac {P _ {\ mathrm {from}}} {P _ {\ mathrm {to}}}}}$

${\ displaystyle P _ {\ mathrm {from}}}$is, for example, the mechanical power that an electric motor delivers to the shaft and the electrical power that is fed to the motor. ${\ displaystyle P _ {\ mathrm {zu}}}$

The quality grade , on the other hand, only describes internal losses in a machine and is usually considerably better.

The difference between the input and output power is referred to as the power loss .

In addition to the general definition, other terms such as degree of utilization or performance have established themselves, which, depending on the specialist area, take into account certain boundary conditions and special features of the energy flow in the systems under consideration. For example, degrees of utilization or performance figures often relate to an observation period (usually one year) over which the energies are added up.

The currently consumed or released power or energy can be very different regardless of the degree of efficiency if power or energy consumption and output occur at different times, for example when charging and discharging a battery , or when solar energy is absorbed by plants and their plants later release by burning.

## Range of values

The theoretically possible range of values ​​is from 0 to 1 or 0 to 100%. The highest value (1 or 100%) cannot be achieved in practice with machines, because in all processes energy is converted into thermal energy through heat or friction . In the case of heat engines, the efficiency is also limited by the exhaust gas loss and can never exceed the ideal efficiency of the Carnot process .

An efficiency greater than 1 would correspond to a perpetual motion machine of the first type, which violates the law of conservation of energy . Devices that emit more energy than they absorb or have stored are not possible.

Efficiency comparisons between devices with different technologies are only meaningful if all energy flows are included in the calculation. With many technologies, however, even efficiency data determined in accordance with the standards only relate to the maximum energy that can be exploited by the respective technology, for example the typical efficiency data for wood-burning stoves is not related to the complete combustion enthalpy, but to the lower calorific value of the wood. If devices are compared with regard to their efficiency, then, due to the actually inadmissible use of the same frame of reference, efficiency figures above 1 can be found. For example, in the case of boilers with condensing technology , a fictitious boiler efficiency> 1 is often specified if the additional heat of condensation is added to the calorific value as with conventional combustion .

## Mechanical efficiency

The mechanical efficiency is specified , for example, for gearboxes or bearings and is part of the overall efficiency of a system (e.g. drive train ). It takes into account the losses due to friction, which reduce the mechanical input power output and lead to the heating of the components ( waste heat ). Frictional losses occur as a result of direct friction between moving surfaces ( slippage ), through shearing of lubricating films or flow losses in fluids , especially air friction with fast flows or when pumping in piston engines .

## Biological efficiencies

Muscles convert chemical energy from food into mechanical energy. Here, too, an efficiency can be estimated from the ratio of the energy consumed as food and the mechanical work released. For the flight muscles of pigeons approx. 20% -25% are given, for trout approx. 45%.

Such efficiencies can be determined with indirect calorimetry , for example .

## Heat efficiencies

### Thermal efficiency (process efficiency)

#### temperature

The upper limit for any thermal efficiency is the Carnot efficiency :

${\ displaystyle \ eta _ {\ mathrm {C}} = 1 - {\ frac {T _ {\ mathrm {n}}} {T _ {\ mathrm {h}}}}}$,

where the lowest and highest temperatures occurring in the process are in Kelvin. ${\ displaystyle T _ {\ mathrm {n}}}$${\ displaystyle T _ {\ mathrm {h}}}$

#### power

The mechanical or thermal efficiency or process efficiency is the ratio of the mechanical power gained to the heat flow supplied in a heat engine , e.g. B. a steam turbine on:

${\ displaystyle \ eta _ {\ mathrm {th}} = {\ frac {P _ {\ mathrm {mech}}} {\ dot {Q}}}}$

with as the thermal efficiency, with (in watts) as the mechanical power gained and with (in watts) as the supplied heat flow. ${\ displaystyle \ eta _ {\ mathrm {th}}}$${\ displaystyle P}$${\ displaystyle {\ dot {Q}}}$

#### energy

If the specific heating energy of the fuel ( in kWh / kg) and the specific fuel consumption of the machine ( in kg / kWh) are known, the mechanical or thermal efficiency (power from heat) can be calculated: ${\ displaystyle H_ {i}}$${\ displaystyle b_ {e}}$

${\ displaystyle \ eta _ {th} = {\ frac {1} {{H_ {i}} \ cdot {b_ {e}}}}}$

### Firing efficiency

The combustion efficiency (FTW) indicates the use of the heat resulting from the combustion of a fuel at nominal output . It only takes into account the heat loss due to the cooling of the exhaust gases to ambient temperature. An evaluation of the energetic efficiency of a heat generator with the help of this exhaust gas loss alone is possible if all other losses are negligible. Until the end of the 20th century, this approximate calculation was common for heating systems; today, the system efficiency or annual degree of utilization is considered.

The FTW is the difference between 1 (100%) and the exhaust gas loss : ${\ displaystyle q _ {\ mathrm {a}}}$

${\ displaystyle \ eta _ {\ text {FTW}} = 1-q _ {\ mathrm {a}}}$

Modern systems increase efficiency by lowering the exhaust gas temperatures and by recovering the heat of condensation from water vapor and hydrocarbons. They use the calorific value of a fuel, whereas in old systems only the calorific value could be used. There are high demands on the fireplace system. Some of the exhaust gases have to be actively removed (e.g. blower), as they are no longer warm enough to ascend by themselves. The chimney is exposed to corrosive attack from the combustion residues dissolved in the condensed water ( sooting ). Under certain conditions, tar also forms, which must be collected and returned to the incineration.

Full condensing boilers , the air / flue gas system or the heating of adjoining rooms also use the latent residual heat of the flue gas below the return temperature of the normal heating system in condensing boilers. It should be noted, however, that gases have a low heat storage capacity and a higher monetary benefit could sometimes be achieved with better thermal insulation of the house or other energy-saving measures "for the same money".

The heat output due to the enthalpy of reaction in the formation of nitrogen oxides or the reduction of the same by lowering the combustion temperatures with the aid of pore burners or catalytic burners is not taken into account in the calculation method of the combustion efficiency (which is no longer state-of-the-art and is therefore outdated).

### Boiler efficiency

The boiler efficiency hK (%) is the ratio of nominal heat output as a percentage of the nominal heat load when measured in constant continuous operation at nominal heat output. Like the FTW, it also takes into account the exhaust gas loss, but also the heat loss to the surroundings of the installation room.

### Exergetic efficiency

The exergetic efficiency, also called isentropic efficiency, is mostly used to describe heat engines that not only emit mechanical or electrical energy, but also deliver useful heat. Here the two different energy qualities (cf. with the 2nd law of thermodynamics ) have to be brought to a common denominator. Exergy stands for the technical ability to work; isentropic processes do not change the entropy.

Thermal energy cannot be completely converted into other forms of energy (e.g. electrical energy, mechanical energy). The two terms anergy and exergy describe which part of the thermal energy can be converted into useful physical work (exergy) and which part has to be released into the environment as unusable waste heat (anergy) in order to dissipate the entropy of the energy conversion. The following applies:

${\ displaystyle {\ text {Energy}} = {\ text {Anergy}} + {\ text {Exergy}}}$

The generation of heat is always associated with entropy production, even in a condensing boiler with a nominally 100% efficiency. Thus, low-temperature heat consists of a lot of anergy and little exergy. The exergy content of heat corresponds to the Carnot factor.

The efficiency of a real heat engine is always less than or equal to that of the ideal heat engine, the Carnot efficiency

${\ displaystyle \ eta _ {\ mathrm {C}} = 1 - {\ frac {T_ {i}} {T_ {s}}}}$

with T i as the lower temperature (inferior) and T s as the upper temperature (superior).

The exergetic efficiency of an energy conversion relates all incoming and outgoing energy flows to the exergy content, i.e. the ability to work.

${\ displaystyle \ eta _ {\ text {exergetic}} = {\ frac {\ text {Exergy output}} {\ text {Exergy input}}}}$

### Gross and net efficiency

In the case of thermal power plants in particular , a distinction is made between gross and net efficiency. The gross efficiency relates to the gross output , i.e. the electrical output without taking into account internal consumers such as B. Feed water pump : ${\ displaystyle P _ {\ text {gross}}}$

${\ displaystyle \ eta _ {\ text {gross}} = {\ frac {P _ {\ text {gross}}} {{\ dot {m}} \ cdot H _ {\ text {u}}}}}$

(This is the mass flow of the fuel supplied and the calorific value of the fuel.) ${\ displaystyle {\ dot {m}}}$${\ displaystyle H _ {\ text {u}}}$

The net efficiency, on the other hand, relates to the net output , i.e. the electrical output after deducting the power consumption of internal consumers : ${\ displaystyle P _ {\ mathrm {net}}}$${\ displaystyle P _ {\ mathrm {EB}}}$

${\ displaystyle \ eta _ {\ mathrm {net}} = {\ frac {P _ {\ mathrm {gross}} -P _ {\ mathrm {EB}}} {{\ dot {m}} \ cdot H _ {\ text {u}}}} = {\ frac {P _ {\ mathrm {net}}} {{\ dot {m}} \ cdot H _ {\ text {u}}}}}$

In the German-speaking area, the net efficiency is specified for power plants, unless something else is explicitly stated.

### Plant efficiency and overall efficiency

If several machines and transformers work one after the other, their individual efficiencies are multiplied to the overall efficiency of the system, the system efficiency . ${\ displaystyle \ eta _ {\ text {total}}}$

${\ displaystyle \ eta _ {\ text {total}} = \ eta _ {1} \ cdot \ eta _ {2} \ cdot \ ldots \ cdot \ eta _ {n}}$

Example:

Overall efficiency : or 34%. ${\ displaystyle \ eta _ {\ text {total}} = 0 {,} 40 \ cdot 0 {,} 99 \ cdot 0 {,} 95 \ cdot 0 {,} 90 = \ mathbf {0 {,} 34} }$

In this example it is assumed that the energy transfer between the individual machines occurs without loss. If this is not the case, the efficiency of the energy transmission must also be taken into account.

If the waste heat released during a thermal conversion process is further used, for example for air preheating, oil preheating or district heating, as is the case with combined heat and power plants (see table below), the efficiency of the system increases, as part of the actually used for the process lost heat can still be used.

### Annual efficiency

The annual degree of utilization is the annual average system efficiency over all operating cycles of a heat generator.

It enables a more realistic cost-benefit calculation for energy-saving measures than is possible with the approximate calculation of the FTW. Since even average houses consume less and less energy by improving the insulation , the consideration of other losses becomes more and more important. This includes heat loss from the heat generator due to radiation , loss due to condensation of the water in the fuel, required heat due to frequent starts of the heating system with poor efficiency in the start-up phase, short burner runtime due to the boiler being too large.

Even if modern individual devices in a heating system usually have an efficiency of over 90% at nominal output, the annual efficiency is only 60–80%, which is emitted by the radiator.

### Standard utilization rate

The standard degree of utilization includes the new technology of the condensing boiler with modulating output control ( partial load operation ) through graduated partial load operating points of 12.8%, 30.3%, 38.8%, 47.6% and 62.6% of the nominal output.

The calculation is specified in accordance with DIN 4702 Part 8 for

1. Heating mode,
2. combined heating operation with only around five percent hot water heating,
3. Hot water heating.

## Efficiency greater than 100%

Machines with efficiencies greater than 100% are referred to as “first type perpetual motion machines”. Such machines can not even exist theoretically because of the law of conservation of energy . If, in practice, efficiencies over 100% are given, the cause is the establishment of an incomplete energy balance equation .

One example are condensing boilers, some of which have calorific value-related efficiencies of over 100%. The calorific value of the fuel is used under “energy used” . However, the calorific value is calculated from the total heat released minus the evaporation heat for the water produced during combustion. The calorific value therefore only includes part of the total fuel energy. In contrast to “conventional” boilers, the flue gas in the condensing boiler is cooled down to such an extent that the water that has evaporated during combustion condenses. The heat of condensation released in the process benefits the useful energy , but was not initially accounted for as input energy .

If the efficiency is not calculated on the basis of the calorific value but on the basis of the calorific value of the fuel, an efficiency of 100% is ideally achieved.

Heat pumps and refrigeration systems - e.g. B. Air conditioners and refrigerators - function as a reverse heat engine . In the specialist literature, in addition to the term “efficiency”, the coefficient of performance ( ) is used as a measure of efficiency for these devices . However, the manufacturer's specifications often refer to the coefficient of performance for refrigeration systems as "efficiency". The heat pump draws the heat energy from the environment and brings it to the desired temperature level. The total heat output provided is greater than the heat output generated during the compression process. Therefore, “efficiencies” of over 100% are achieved for this process. Typical values ​​are between 300% and 800%, which corresponds to an efficiency (= performance figure) of 3 to 8. To avoid confusion, the thermal efficiency of heat pumps and refrigerating machines as is COP (engl. C oefficient O f P erformance) referred to which is less than the reciprocal Carnot efficiency. ${\ displaystyle \ varepsilon}$

## Examples

Efficiency, examples
Machine, process Energy used Useful energy Efficiency [%]
Provision of useful energy
Nuclear power plant nuclear electric 33
Combined cycle power plant ( natural gas ) chemically electric 50-62
Best before generator kinetic electric 30 (max.)
Solar cell electromagnetic (solar radiation) electric 5–27 (40)
Thermocouple (thermoelectric generator) thermal electric 3-8
Thermal power plant ( coal ) chemically electric 25-50
Thermal power plant or engine
with combined heat and power
chemically electrical & (thermal) **) 30–40 & (50–60)
Hydroelectric power plant mechanically electric 80-90
Wind turbine mechanically electric 50 (max.)
Electrolysis of water electric chemically 70-80
Thermolysis of water thermal chemically 90 (fictional)
machines and devices
Fuel cell chemically electric 20-60
Steam engine chemically mechanically 3-44
Stirling engine thermal mechanically 10-66
Detonator jet engine chemically mechanically ?
Otto engine (1000 PS at the best point) chemically mechanically 35-40
Diesel engine
(10,000 PS with turbo and charge air cooling)
chemically mechanically 50
Two-stroke marine diesel (100,000 HP exhaust
valve-controlled, with turbo and charge air cooling)
chemically mechanically 55
Electric motor at its best electric mechanically 94-99.5 (> 90)
bicycle mechanically mechanically 90 (min.)
Bicycle dynamo mechanically electric 20-65
Gas compressor / gas turbine mechanically mechanically 90 (approx.)
generator mechanically electric 95-99.3
Incandescent lamp (no halogen lamp) electric electromagn. (visible light) 3-5
High voltage direct current transmission electric electric 95
speaker electric acoustically 0.1–40, typ. 0.3 for hi-fi
LED electric electromagn. (visible light) 5-25
Switching power supply (for el. Devices) electric electric 50-95
Transmitter electric electromagnetic ( radio waves ) 30-80
Thermocouple thermal electric 3-8
transformer electric electric 50-99.7
Turbine engine (civil aviation ) chemically mechanically 40 (max.)
Inverter electric electric 93-98
Gear pump mechanically mechanically 90 (max.)
Heat production
Gas stove (household) chemically thermal 30-40
Electric stove (household) electric thermal 50-60
Gas heating chemically thermal 80-90
Coal stove (household) chemically thermal 30-50
Coal furnace (industry) chemically thermal 80-90
Campfire (hotplate) chemically thermal 15 (max.)
Open fireplace chemically thermal 10-30
Solar collector electromagnetic (solar radiation) thermal 85 (max.)
Boiler , immersion heater electric thermal 80-98
Natural processes
Photosynthesis reaction electromagnetic (sunlight) chemically 35
Firefly ( glow reaction) chemically electromagnetic (light) 95 (max.)
Human ( skeletal muscles ) chemically mechanically 0-30
Larger processes
Coal mining (mining of coal and
subsequent combustion)
chemically thermal 30–60 (?)
Photosynthesis (production of biomass and
subsequent combustion)
electromagnetic (sunlight) chemically 0.1-2.5

Remarks:

1. a b c It is generally not possible to specify an efficiency for useful variables that have a dimension other than energy or power. In the case of light sources e.g. B. the useful variable is the luminous flux , which takes into account the spectral sensitivity of the human eye. The parameter for the efficiency of a light source is the light output (unit: lumen per watt ). However, it is possible to specify the efficiency as the ratio of the radiation power in an “ideal spectrum” to the consumption power. If you choose an ideal spectrum that corresponds to the black body spectrum in the visible range between 400 and 700 nanometers and is zero outside of this, this results in an efficiency of about 5% for a black body spectrum at 2700 Kelvin (approximately standard incandescent lamp 60 watts). However, due to the blurred boundaries of the visible spectrum to the infrared and ultraviolet range, such a definition is not unambiguous.
In Dietrich Pelte: The future of our energy supply: An analysis from a mathematical and scientific perspective . Springer DE, November 26, 2009, ISBN 978-3-8348-0989-6 , p. 32– (accessed on February 10, 2013). an incandescent lamp is assumed to be a black body with a temperature of 2000 K. This results in an efficiency based on the visible radiation spectrum of 10%. An overall efficiency of 5% is given due to further heat losses through convection.
2. When taking heat into account, one speaks more often of the degree of utilization . The efficiency for generating electricity is lower when heat is extracted than without heat extraction.
3. The efficiency of wind power plants is limited by the fact that, according to Betz's law, a maximum of 59.3% of the mechanical power contained in the wind can be converted into useful power. Since the ratio of the power delivered to the rotor shaft to the power that the flow lacks in the wake is between 70 and 85% in a modern wind turbine, the given value is calculated from 85% of 59.3%.
4. The efficiency of almost all bicycle dynamos is around 20%, particularly effective dynamos with friction wheels reach 25–30%. Values ​​of 65% can only be achieved with alternative designs, such as hub dynamos in the optimal speed range.
5. According to the Siemens website (PDF): 'In terms of aerodynamics, the efficiency is already 92%', reveals Bernard Becker. 'Two to three percentage points may still be there.'
6. Gas and steam turbines have an efficiency of over 95%. In thermal power plants, Carnot's cycle limits the overall efficiency to 35–60%. In addition, there are forming and line losses up to the end user. Water turbines have a hydraulic efficiency of over 95%, but the effective efficiency of a machine group (reservoir pressure pipe turbine generator or dam turbine generator) is usually 70 to a maximum of 87% due to mechanical and electromagnetic friction / heat losses.
7. without line losses
8. ↑ In contrast to stage loudspeakers, sound-neutral reproduction is more important than “loud” efficiency with home loudspeakers and studio monitors. In the case of loudspeakers, the so-called “efficiency” is often given in the data, which is not at all. What you can find there is the characteristic sound pressure level in dB / W / m - dB per watt at a distance of one meter, or better dB / (W * m) - which, ignorantly, is often referred to as efficiency.
9. Thermocouples are also used for some purposes to provide useful energy.
10. a b A gas stove heats the area. An electric induction cooker specifically heats the cookware, with heat losses in the induction electronics. However, only the efficiency at the place of conversion is taken into account and not the energy loss during power generation. If this is taken into account, a gas stove is at least as efficient as an electric stove - depending on the efficiency of the power plant.
11. A campfire is the calorific value of the fuel with high efficiency into heat (distinction between focal - and calorific note). But only a small part of the heat heats a pot hanging over the fire. Most of it heats the surrounding air.
12. Light reaction , i.e. the splitting of water into protons, electrons and oxygen.
13. The minimum of 0 results from the fact that the muscles also consume energy during activities in which no work is performed (see holding work ). Example to illustrate: a table , unlike a muscle, can hold a heavy object in position without the need for an energy supply.
14. Efficiency of coal extraction: How many tons of lignite or hard coal do I have to extract and convert into electricity for the production facilities in order to be able to sell one ton?
15. overall efficiency, d. H. including energy that is required to provide the reaction molecules.

**) The specification of an efficiency with different "target energy types", in this case electrical & thermal, does not make sense, as these energy types have a different "valence" (see also entropy). In this way electrical and mechanical energy can be converted 100% into heat, in the other direction this only works within the limits mentioned above. Example: a combined heat and power unit with conversion into 30% electrical and 60% thermal energy would result in a (false) "efficiency" of 30% + 60% = 90% according to this consideration. With a combined cycle power plant with 60% electrical efficiency, I can provide 30% electrical energy and operate a heat pump with the remaining 30% electrical energy. With a usage figure of 5, I get 150% heat (e.g. for heating) - that is, 2.5 times the amount of the combined heat and power unit.

## Specification of the efficiency for loudspeaker data

Acoustic efficiency η (Eta) of a loudspeaker:

${\ displaystyle \ eta = {\ frac {P _ {\ mathrm {ak}}} {P _ {\ mathrm {e}}}} \,}$

P ak = given acoustic power

P e = supplied electrical power

The definition of the acoustic efficiency corresponds to that of the acoustic conversion efficiency.

In the loudspeaker data, the very low efficiency is never given in percent, but the characteristic sound pressure level in dB / W / m (or dB / (W · m)), which is incorrectly referred to as "efficiency". The efficiency is between 0.002 and 0.02 - so only between 0.2 and 2 percent. It can be converted into the characteristic sound pressure:

${\ displaystyle {\ text {sound pressure level in dB}} = 112 + 10 \ cdot \ log _ {10} ({\ text {efficiency}}) \,}$
Efficiency in percent Characteristic sound pressure level
0.05 5% 99 dB
0.02 2% 95 dB
0.01 1 % 92 dB
0.005 0.5% 89 dB
0.002 0.2% 85 dB

## literature

• Adolf J. Schwab: Electrical energy systems - generation, transport, transmission and distribution of electrical energy. Springer Verlag, 2006, ISBN 3-540-29664-6 , p. 76.
• Joachim Grehn, Joachim Krause: Metzler Physics . Schroedel Verlag, 1998, ISBN 3-507-10700-7 , pp. 156-167.
• Gerold Schneider, Irmingard Thannhausser: Physics . Trauner, Linz 1986, ISBN 3-85320-364-7 .