What is the utility coefficient? Heat engine

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  Mathematically, the definition of efficiency can be written as:

  η = A Q , (\displaystyle \eta =(\frac (A)(Q)),)

  Where A- useful work (energy), and Q- energy expended.

  If efficiency is expressed as a percentage, then it is calculated by the formula:

  η = A Q × 100% (\displaystyle \eta =(\frac (A)(Q))\times 100\%) ε X = Q X / A (\displaystyle \varepsilon _(\mathrm (X) )=Q_(\mathrm (X) )/A),

  Where Q X (\displaystyle Q_(\mathrm (X) ))- heat taken from the cold end (in refrigeration machines, cooling capacity); A (\displaystyle A)

  The term used for heat pumps is transformation ratio

  ε Γ = Q Γ / A (\displaystyle \varepsilon _(\Gamma )=Q_(\Gamma )/A),

  Where Q Γ (\displaystyle Q_(\Gamma ))- condensation heat transferred to the coolant; A (\displaystyle A)- the work (or electricity) spent on this process.

  In the perfect car Q Γ = Q X + A (\displaystyle Q_(\Gamma )=Q_(\mathrm (X) )+A), from here to the ideal car ε Γ = ε X + 1 (\displaystyle \varepsilon _(\Gamma )=\varepsilon _(\mathrm (X) )+1)

  The reverse Carnot cycle has the best performance indicators for refrigeration machines: it has a coefficient of performance

  ε = T X T Γ − T X (\displaystyle \varepsilon =(T_(\mathrm (X) ) \over (T_(\Gamma )-T_(\mathrm (X)))), because, in addition to the energy taken into account A(e.g. electric), in heat Q There is also energy taken from the cold source.

  Efficiency, by definition, is the ratio of energy received to energy expended. If an engine burns gasoline and only a third of the resulting heat is converted into vehicle propulsion energy, then the efficiency is one third or (rounded to the nearest whole) 33%. If a light bulb produces light energy fifty times less than the electrical energy consumed, its efficiency is 1/50 or 2%. However, the question immediately arises: what if the light bulb is sold as an infrared heater? After the sale of incandescent lamps was banned, devices exactly the same in design began to be sold as " infrared heaters", since over 95% of electricity is converted into heat.

  (Un)useful warmth

  Typically, the heat generated during the operation of something is recorded as losses. But this is far from certain. A power plant, for example, converts about a third of the heat released during the combustion of gas or coal into electricity, but another part of the energy can be used to heat water. If hot water supply and warm batteries are also included in the useful results of the CHP operation, then the efficiency will increase by 10-15%.

  A similar example is a car “stove”: it transfers part of the heat generated during engine operation into the interior. This heat can be useful and necessary, or it can be considered as loss: for this reason, it usually does not appear in calculations of the efficiency of a car engine.

  Standing apart are devices such as heat pumps. Their efficiency, if we calculate it by the ratio of heat supplied and electricity consumed, is more than 100%, but this does not disprove the basics of thermodynamics. A heat pump pumps heat from a less heated body to a more heated one and expends energy on this, since without energy expenditure such a redistribution of heat is prohibited by the same thermodynamics. If a heat pump takes a kilowatt from the outlet and produces five kilowatts of heat, then four kilowatts will be taken from the air, water or soil outside the home. Environment in the place where the device draws heat, it will cool down, and the house will warm up. But then this heat, together with the energy spent by the pump, will still dissipate in space.

  External circuit of the heat pump: through these plastic pipes a liquid is pumped, taking heat from the water column into the heated building. Mark Johnson/Wikimedia

  Much or effective?

  Some devices have very high efficiency, but at the same time - inappropriate power.

  Electric motors are more efficient the larger they are, but putting an electric locomotive motor into a children's toy is physically impossible and economically pointless. Therefore, the efficiency of engines in a locomotive exceeds 95%, and in a small radio-controlled car - at most 80%. Moreover, in the case of an electric motor, its efficiency also depends on the load: an underloaded or overloaded motor operates with less efficiency. Correct selection equipment can mean even more than just choosing a device with the maximum declared efficiency.

  

  The most powerful production locomotive, the Swedish IORE. Second place is held by the Soviet electric locomotive VL-85. Kabelleger/Wikimedia

  If electric motors are produced for a variety of purposes, from vibrators in phones to electric locomotives, then the ion engine has a much smaller niche. Ion engines are efficient, economical, durable (they work without shutting down for years), but they turn on only in a vacuum and provide very little thrust. They are ideal for sending to deep space scientific vehicles that can fly to a target for several years and for which saving fuel is more important than spending time.

  Electric motors, by the way, consume almost half of all the electricity generated by humanity, so even a difference of one hundredth of a percent on a global scale could mean the need to build another one. nuclear reactor or another power unit of a thermal power plant.

  Effective or cheap?

  Energy efficiency is not always identical to economic efficiency. A good example- LED lamps, which until recently were inferior to incandescent lamps and fluorescent “energy saving” lamps. The complexity of manufacturing white LEDs, the high cost of raw materials and, on the other hand, the simplicity of an incandescent lamp forced the choice of less efficient, but cheaper light sources.

  By the way, for the invention of the blue LED, without which it would have been impossible to make a bright white lamp, Japanese researchers received in 2014 Nobel Prize. This is not the first award given for contributions to the development of lighting: in 1912, the award was given to Nils Dahlen, the inventor who improved acetylene torches for lighthouses.

  

  Blue LEDs are needed to produce white light in combination with red and green. These two colors were learned to be produced in sufficiently bright LEDs much earlier; blue for a long time remained too dull and expensive for mass use

  Another example of efficient but very expensive devices is solar cells based on gallium arsenide (a semiconductor with the formula GaAs). Their efficiency reaches almost 30%, which is one and a half to two times higher than the batteries used on Earth based on the much more common silicon. High efficiency only pays off in space, where delivering one kilogram of cargo can cost almost as much as a kilogram of gold. Then the savings on battery weight will be justified.

  The efficiency of power lines can be increased by replacing copper with better-conducting silver, but silver cables are too expensive and therefore are used only in isolated cases. But to the idea of ​​​​building superconducting power lines from rare earth ceramics that are expensive and require cooling with liquid nitrogen in recent years applied several times in practice. In particular, such a cable has already been laid and connected in the German city of Essen. It is designed for 40 megawatts of electrical power at a voltage of ten kilovolts. In addition to the fact that heating losses are reduced to zero (however, in return it is necessary to power cryogenic installations), such a cable is much more compact than usual and due to this you can save on the purchase of expensive land in the city center or refuse to lay additional tunnels.

  Not according to general rules

  From school course many remember that the efficiency cannot exceed 100% and that the higher the more difference temperatures between the refrigerator and the heater. However, this is true only for the so-called heat engines: steam engine, engine internal combustion, reactive and rocket engines, gas and steam turbines.

  Electric motors and all electrical devices do not obey this rule, since they are not heat engines. For them, the only thing that is true is that the efficiency cannot exceed one hundred percent, and particular restrictions in each case are determined differently.

  In the case of a solar battery, losses are determined both by quantum effects during the absorption of photons, and by losses due to the reflection of light from the surface of the battery and to absorption in the focusing mirrors. The calculations showed that to go beyond 90% solar battery cannot in principle, but in practice values ​​of about 60-70% are achievable, and even those with a very complex structure of photocells.

  Fuel cells have excellent efficiency. These devices receive certain substances that enter into chemical reaction with each other and give electric current. This process, again, is not a cycle of a heat engine, so the efficiency is quite high, about 60%, while diesel or gasoline engine usually don't go beyond 50%.

  It was the fuel elements that were used on those flying to the Moon spaceships Apollo, and they can run on hydrogen and oxygen, for example. Their only drawback is that the hydrogen must be quite pure and, moreover, it must be stored somewhere and somehow transferred from the plant to consumers. Technologies that make it possible to replace ordinary methane with hydrogen have not yet been brought to mass use. Only experimental cars and a few submarines run on hydrogen and fuel cells.

  

  Plasma engines of the SPD series. They are made by OKB Fakel, and they are used to keep satellites in a given orbit. The thrust is created due to the flow of ions that arise after the ionization of an inert gas by an electric discharge. The efficiency of these engines reaches 60 percent

  Ionic and plasma engines already exist, but they also work only in a vacuum. In addition, their thrust is too low and is orders of magnitude lower than the weight of the device itself - they would not take off from the Earth even in the absence of an atmosphere. But during interplanetary flights lasting many months and even years, weak thrust is compensated by efficiency and reliability.

  Coefficient useful action(efficiency) is a term that can be applied, perhaps, to every system and device. Even humans have efficiency, although there is probably no objective formula for finding it yet. In this article we will explain in detail what efficiency is and how it can be calculated for various systems.

  Efficiency definition

  Efficiency is an indicator that characterizes the effectiveness of a system in terms of energy output or conversion. Efficiency is an immeasurable quantity and is represented either numerical value in the range from 0 to 1, or as a percentage.

  General formula

  Efficiency is indicated by the symbol Ƞ.

  The general mathematical formula for finding efficiency is written as follows:

  Ƞ=A/Q, where A is the useful energy/work performed by the system, and Q is the energy consumed by this system to organize the process of obtaining useful output.

  The efficiency factor, unfortunately, is always less than or equal to unity, since, according to the law of conservation of energy, we cannot obtain more work than the energy expended. In addition, the efficiency, in fact, is extremely rarely equal to unity, since useful work is always accompanied by the presence of losses, for example, for heating the mechanism.

  Heat engine efficiency

  A heat engine is a device that converts thermal energy to mechanical. In a heat engine, work is determined by the difference between the amount of heat received from the heater and the amount of heat given to the cooler, and therefore the efficiency is determined by the formula:

  • Ƞ=Qн-Qх/Qн, where Qн is the amount of heat received from the heater, and Qх is the amount of heat given to the cooler.

  It is believed that the highest efficiency is provided by engines operating on the Carnot cycle. In this case, the efficiency is determined by the formula:

  • Ƞ=T1-T2/T1, where T1 is the temperature of the hot spring, T2 is the temperature of the cold spring.

  Electric motor efficiency

  An electric motor is a device that converts electrical energy into mechanical energy, so the efficiency in this case is the efficiency ratio of the device in terms of conversion electrical energy to mechanical. Formula for finding efficiency electric motor looks like this:

  • Ƞ=P2/P1, where P1 is supplied electrical power, P2 is useful mechanical power, generated by the engine.

  Electrical power is found as the product of system current and voltage (P=UI), and mechanical power as the ratio of work per unit time (P=A/t)

  Transformer efficiency

  A transformer is a device that converts alternating current of one voltage to alternating current of another voltage, maintaining the frequency. In addition, transformers can also convert alternating current into direct current.

  The efficiency of the transformer is found by the formula:

  • Ƞ=1/1+(P0+PL*n2)/(P2*n), where P0 - no-load losses, PL - load losses, P2 - active power supplied to the load, n - relative degree of loading.

  Efficiency or not efficiency?

  It is worth noting that in addition to efficiency, there are a number of indicators that characterize the efficiency of energy processes, and sometimes we can come across descriptions like - efficiency of the order of 130%, however in this case we need to understand that the term is not used entirely correctly, and, most likely, the author or the manufacturer understands this abbreviation to mean a slightly different characteristic.

  For example, heat pumps are distinguished by the fact that they can release more heat than they consume. Thus, a refrigeration machine can remove more heat from the object being cooled than was expended in energy equivalent to organize the removal. The efficiency indicator of a refrigeration machine is called the refrigeration coefficient, denoted by the letter Ɛ and determined by the formula: Ɛ=Qx/A, where Qx is the heat removed from the cold end, A is the work expended on the removal process. However, sometimes the refrigeration coefficient is also called the efficiency of the refrigeration machine.

  It is also interesting that the efficiency of boilers operating on organic fuel, is usually calculated based on the lower calorific value, but it can be greater than unity. However, it is still traditionally called efficiency. It is possible to determine the efficiency of a boiler by the higher calorific value, and then it will always be less than one, but in this case it will be inconvenient to compare the performance of boilers with data from other installations.

  Efficiency (Efficiency) - characteristic of the efficiency of a system (device, machine) in relation to the conversion or transmission of energy. It is determined by the ratio of usefully used energy to the total amount of energy received by the system; usually denoted η (“this”). η = Wpol/Wcym. Efficiency is a dimensionless quantity and is often measured as a percentage. Mathematically, the definition of efficiency can be written as:

  X 100%,

  Where A- useful work, and Q- energy expended.

  Due to the law of conservation of energy, efficiency is always less than or equal to unity, that is, it is impossible to obtain more useful work than the energy expended.

  Heat engine efficiency- attitude of the perfect useful work engine, to the energy received from the heater. Efficiency heat engine can be calculated using the following formula

  ,

  where is the amount of heat received from the heater, is the amount of heat given to the refrigerator. Highest efficiency among cyclic machines operating at given hot source temperatures T 1 and cold T 2, have heat engines operating on the Carnot cycle; this marginal efficiency is equal to

  .

  Not all indicators characterizing the efficiency of energy processes correspond to the above description. Even if they are traditionally or erroneously called "efficiency", they can have other properties, in particular exceeding 100%.

  Boiler efficiency

  Main article: Boiler heat balance

  The efficiency of fossil fuel boilers is traditionally calculated based on the lower calorific value; it is assumed that the moisture of the combustion products leaves the boiler in the form of superheated steam. IN condensing boilers this moisture condenses, the heat of condensation is usefully used. When calculating efficiency based on the lower calorific value, it may end up being greater than one. In this case, it would be more correct to calculate it by the higher calorific value, which takes into account the heat of steam condensation; however, the performance of such a boiler is difficult to compare with data on other installations.

  Heat pumps and chillers

  The advantage of heat pumps as heating equipment is the ability to sometimes receive more heat than the energy consumed for their operation; similarly, a refrigeration machine can remove more heat from the cooled end than is expended in organizing the process.

  The efficiency of such heat engines is characterized by coefficient of performance(for refrigeration machines) or transformation ratio(for heat pumps)

  ,

  where is the heat taken from the cold end (in refrigeration machines) or transferred to the hot end (in heat pumps); - the work (or electricity) spent on this process. The reverse Carnot cycle has the best performance indicators for such machines: it has a coefficient of performance

  ,

  where , are the temperatures of the hot and cold ends, . This value, obviously, can be arbitrarily large; Although it is difficult to approach practically, the coefficient of performance can still exceed unity. This does not contradict the first law of thermodynamics, since, in addition to the energy taken into account A(e.g. electric), to heat Q There is also energy taken from the cold source.

  Literature

  • Peryshkin A.V. Physics. 8th grade. - Bustard, 2005. - 191 p. - 50,000 copies. - ISBN 5-7107-9459-7.

  Notes

  
  

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  Synonyms:

  See what “Efficiency factor” is in other dictionaries:

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  Modern encyclopedia

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  The work done by the engine is:

  This process was first considered by the French engineer and scientist N. L. S. Carnot in 1824 in the book “Reflections on driving force fire and about machines capable of developing this force."

  The goal of Carnot's research was to find out the reasons for the imperfection of heat engines of that time (they had an efficiency of ≤ 5%) and to find ways to improve them.

  The Carnot cycle is the most efficient of all. Its efficiency is maximum.

  

  The figure shows the thermodynamic processes of the cycle. During isothermal expansion (1-2) at temperature T 1 , work is done due to change internal energy heater, i.e. due to the supply of heat to the gas Q:

  A 12 = Q 1 ,

  Gas cooling before compression (3-4) occurs during adiabatic expansion (2-3). Change in internal energy ΔU 23 during an adiabatic process ( Q = 0) is completely converted into mechanical work:

  A 23 = -ΔU 23 ,

  The gas temperature as a result of adiabatic expansion (2-3) drops to the temperature of the refrigerator T 2 < T 1 . In process (3-4), the gas is isothermally compressed, transferring the amount of heat to the refrigerator Q 2:

  A 34 = Q 2,

  The cycle ends with the process of adiabatic compression (4-1), in which the gas is heated to a temperature T 1.

  The maximum efficiency value of heat engines operating at ideal gas, according to the Carnot cycle:

  .

  The essence of the formula is expressed in the proven WITH. Carnot's theorem that the efficiency of any heat engine cannot exceed the efficiency of a Carnot cycle carried out at the same temperature of the heater and refrigerator.