How to write efficiency in physics. The principle of operation of heat engines

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Mathematically, the definition of efficiency can be written as:
η = A Q , (\displaystyle \eta =(\frac (A)(Q)),)
where BUT- useful work (energy), and Q- spent energy.
If the 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 (refrigeration capacity in refrigeration machines); A (\displaystyle A)
For heat pumps use the term 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), hence for the ideal machine ε Γ = ε X + 1 (\displaystyle \varepsilon _(\Gamma )=\varepsilon _(\mathrm (X) )+1)
The best performance indicators for refrigeration machines have the reverse Carnot cycle: in it the coefficient of performance
ε = T X T Γ − T X (\displaystyle \varepsilon =(T_(\mathrm (X) ) \over (T_(\Gamma )-T_(\mathrm (X) )))), since, in addition to the energy taken into account A(e.g. electrical), to heat Q there is also energy taken from a cold source.
Efficiency (efficiency) - a characteristic of the efficiency of a system (device, machine) in relation to the conversion or transfer of energy. It is determined by the ratio of useful energy used 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 BUT- useful work, and Q- spent energy.

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

Heat engine efficiency- the ratio of the perfect useful work of the engine, to the energy received from the heater. The efficiency of a heat engine can be calculated using the following formula
,
where - the amount of heat received from the heater, - the amount of heat given to the refrigerator. The highest efficiency among cyclic machines operating at given hot spring temperatures T 1 and cold T 2, have heat engines operating on the Carnot cycle; this limiting 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 "", they may have other properties, in particular, exceed 100%.

boiler efficiency

Main article: Boiler thermal balance

The efficiency of fossil fuel boilers is traditionally calculated from the net 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 is condensed, the heat of condensation is usefully used. When calculating the efficiency according to the lower calorific value, it can eventually turn out to be more than one. In this case, it would be more correct to consider it according to the gross calorific value, which takes into account the heat of steam condensation; however, the performance of such a boiler is difficult to compare with data from other installations.

Heat pumps and chillers

The advantage of heat pumps as a heating technique is the ability to sometimes receive more heat than the energy spent on their work; 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 chillers) 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 best performance indicators for such machines have the reverse Carnot cycle: in it the coefficient of performance
,
where , are the temperatures of the hot and cold ends, . This value, obviously, can be arbitrarily large; although practically it is difficult to approach it, 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), into heat Q there is also energy taken from a cold source.

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

Wikimedia Foundation. 2010 .
Synonyms:
- TurboPascal
- efficiency
See what "" is in other dictionaries:
World of Tanks is a computer game that has swept the whole world. It is played by players from all over the world. Many people stay awake at night while playing tank simulator. After some time after the start of the game, the gamer becomes interested in how much he has succeeded in his achievements. It will help to make efficiency. Many new players are wondering what efficiency is in World of Tanks.

What is efficiency?

Literally, the abbreviation efficiency stands for efficiency. In other words, this indicator indicates how useful a player can be to his team, as well as how good his skills are in battle.

Efficiency is calculated on the basis of statistical data. When calculating efficiency, it takes into account the number of victories and defeats, capturing an enemy base and knocking down the capture of an allied base, detecting and destroying opponents. In addition, the player's technique affects the level of efficiency. On high-level vehicles, it is easier to increase this indicator.

Why is efficiency needed?

Also, beginners are thinking about what the efficiency of World of Tanks is for. Everything is very simple. There are two explanations. The main one is that since the efficiency reflects the skills and abilities in battle, they definitely pay attention to it when they are taken to the clan. It is difficult to get into a good clan if this indicator is low.

In addition, efficiency gives many players an additional incentive. After all, you want to be the best among others. As a result, the player strives to improve his statistics and efficiency. Increasing this indicator to amuse the pride of any gamer.

How to find out your efficiency?

In the game, efficiency can be viewed as a personal rating. But experienced players argue that the calculation of the efficiency within the game is carried out according to an unfair algorithm, as a result of which the winners do not always get the laurels. This means that a player can show himself well in battle, but at the same time increase his efficiency very slightly.

To find out how useful a player is to his team, and what skills he has, the efficiency is looked at on special online resources. To check your personal indicator, just enter your nickname and click the "Define" or "Upload data" button. The most popular sites where you can see the efficiency in World of Tanks are:
- wot-news.com;
- wotgame.com
- wot-noobs.ru.
Olenemetr comes to the rescue

Directly in the game, the efficiency of the players helps to determine the " Deer meter". This is a special mod that is installed in the game. It got its name because it helps to determine the experience of the enemy and to detect "deer", that is, inexperienced players.

The mod highlights all players with a certain color depending on statistics and skills. The red players don't know how to play at all, the orange ones are a little better than the first ones. Gamers with yellow color are considered average, and gamers with green are considered good. High-class craftsmen are highlighted in blue, and unique players are highlighted in purple.

But the "Olenemeter" is often wrong, so when you see the enemy team, in which most of the players are highlighted in red, you should not relax, since in this case the risk of defeat is very high. By the way, if you miss good online games, then be sure to go here, on this site you will find a lot of interesting virtual entertainment. Sometimes it is worth distracting from the "tanks".

How to increase efficiency in World of Tanks?

After the answer to the question "What is efficiency in the World of Tanks?" is found, many players think about how to increase this important indicator. The strategy here is very simple: you need to score capture points, knock down the enemy’s capture, destroy enemies and help your team and allies in every possible way, but at the same time remain alive until the end of the battle. In addition, to improve the efficiency, you should choose a technique not lower than level 8, and even higher is better.
Content:
In the process of moving charges within a closed circuit, a certain work is performed by the current source. It can be useful and complete. In the first case, the current source moves charges in the external circuit, while doing work, and in the second case, the charges move in the entire circuit. In this process, the efficiency of the current source, defined as the ratio of the external and total resistance of the circuit, is of great importance. If the internal resistance of the source and the external resistance of the load are equal, half of all power will be lost in the source itself, and the other half will be released at the load. In this case, the efficiency will be 0.5 or 50%.

Electric circuit efficiency

The considered efficiency is primarily associated with physical quantities characterizing the rate of conversion or transmission of electricity. Among them, in the first place is the power, measured in watts. There are several formulas for its definition: P = U x I = U2/R = I2 x R.

In electrical circuits, there can be a different voltage value and charge value, respectively, and the work performed is also different in each case. Very often there is a need to estimate the speed with which electricity is transmitted or converted. This speed is the electrical power corresponding to the work performed in a certain unit of time. In the form of a formula, this parameter will look like this: P=A/∆t. Therefore, the work is displayed as the product of power and time: A=P∙∆t. The unit of measure for work is .

In order to determine how efficient a device, machine, electrical circuit or other similar system is, in terms of power and work, efficiency is used - efficiency. This value is defined as the ratio of useful energy spent to the total amount of energy supplied to the system. The efficiency is denoted by the symbol η, and mathematically defined as the formula: η \u003d A / Q x 100% \u003d [J] / [J] x 100% \u003d [%], in which A is the work done by the consumer, Q is the energy given by the source . In accordance with the law of conservation of energy, the efficiency value is always equal to or below unity. This means that useful work cannot exceed the amount of energy spent on its completion.

Thus, the power losses in any system or device are determined, as well as the degree of their usefulness. For example, in conductors, power losses are formed when an electric current is partially converted into thermal energy. The amount of these losses depends on the resistance of the conductor, they are not an integral part of the useful work.

There is a difference, expressed by the formula ∆Q=A-Q, which clearly shows the power loss. Here, the relationship between the growth of power losses and the resistance of the conductor is very clearly visible. The most striking example is an incandescent lamp, the efficiency of which does not exceed 15%. The remaining 85% of the power is converted into thermal, that is, into infrared radiation.

What is the efficiency of the current source

The considered efficiency of the entire electrical circuit makes it possible to better understand the physical essence of the efficiency of the current source, the formula of which also consists of various quantities.

In the process of moving electric charges along a closed electrical circuit, a certain work is performed by the current source, which differs as useful and complete. During the performance of useful work, the current source moves charges in the external circuit. At full work, the charges, under the action of a current source, move already throughout the circuit.

In the form of formulas, they are displayed as follows:
- Useful work - Apolesis = qU = IUt = I2Rt.
- Complete work - Afull = qε = Iεt = I2(R +r)t.
Based on this, it is possible to derive formulas for the useful and total power of the current source:
- Useful power - Рpolez = Apolez / t = IU = I2R.
- Apparent power - Рfull = Apfull/t = Iε = I2(R + r).
As a result, the formula for the efficiency of the current source takes the following form:
- η = Ause/ Atot = Ruse/ Ptot = U/ε = R/(R + r).
The maximum useful power is achieved at a certain value of the resistance of the external circuit, depending on the characteristics of the current source and load. However, attention should be paid to the incompatibility between maximum net power and maximum efficiency.

Investigation of the power and efficiency of the current source

The efficiency of a current source depends on many factors, which should be considered in a certain sequence.

To determine, in accordance with Ohm's law, there is the following equation: i \u003d E / (R + r), in which E is the electromotive force of the current source, and r is its internal resistance. These are constant values that do not depend on the variable resistance R. With their help, you can determine the useful power consumed by the electrical circuit:
- W1 \u003d i x U \u003d i2 x R. Here R is the resistance of the consumer of electricity, i is the current in the circuit, determined by the previous equation.
Thus, the power value using finite variables will be displayed as follows: W1 = (E2 x R)/(R + r).

Since it is an intermediate variable, in this case the function W1(R) can be analyzed for an extremum. To this end, it is necessary to determine the value of R, at which the value of the first derivative of the useful power associated with the variable resistance (R) will be equal to zero: dW1 / dR = E2 x [(R + r)2 - 2 x R x (R + r) ] = E2 x (Ri + r) x (R + r - 2 x R) = E2(r - R) = 0 (R + r)4 (R + r)4 (R + r)3

From this formula, we can conclude that the value of the derivative can be zero only under one condition: the resistance of the power receiver (R) from the current source must reach the value of the internal resistance of the source itself (R => r). Under these conditions, the value of the efficiency η will be determined as the ratio of the useful and total power of the current source - W1/W2. Since at the maximum point of useful power the resistance of the energy consumer of the current source will be the same as the internal resistance of the current source itself, in this case the efficiency will be 0.5 or 50%.

Tasks for current power and efficiency

The main significance of the formula (5.12.2) obtained by Carnot for the efficiency of an ideal machine is that it determines the maximum possible efficiency of any heat engine.
Carnot proved, based on the second law of thermodynamics*, the following theorem: any real heat engine operating with a temperature heaterT 1 and refrigerator temperatureT 2 , cannot have an efficiency exceeding the efficiency of an ideal heat engine.
* Carnot actually established the second law of thermodynamics before Clausius and Kelvin, when the first law of thermodynamics had not yet been formulated rigorously.
Consider first a heat engine operating on a reversible cycle with a real gas. The cycle can be any, it is only important that the temperatures of the heater and refrigerator are T 1 and T 2 .
Let us assume that the efficiency of another heat engine (not operating according to the Carnot cycle) η ’ > η . The machines work with a common heater and a common cooler. Let the Carnot machine work in a reverse cycle (like a refrigeration machine), and the other machine in a direct cycle (Fig. 5.18). The heat engine performs work equal, according to formulas (5.12.3) and (5.12.5):
The refrigeration machine can always be designed so that it takes the amount of heat from the refrigerator Q 2 = ||
Then, according to formula (5.12.7), work will be performed on it
(5.12.12)
Since by condition η" > η , then A" > A. Therefore, the heat engine can drive the refrigeration engine, and there will still be an excess of work. This excess work is done at the expense of heat taken from one source. After all, heat is not transferred to the refrigerator under the action of two machines at once. But this contradicts the second law of thermodynamics.
If we assume that η > η ", then you can make another machine work in a reverse cycle, and Carnot's machine in a straight line. We again come to a contradiction with the second law of thermodynamics. Therefore, two machines operating on reversible cycles have the same efficiency: η " = η .
It is a different matter if the second machine operates in an irreversible cycle. If we allow η " > η , then we again come to a contradiction with the second law of thermodynamics. However, the assumption m|"< г| не противоречит второму закону термодинамики, так как необратимая тепловая машина не может работать как холодильная машина. Следовательно, КПД любой тепловой машины η" ≤ η, or
This is the main result:
(5.12.13)
Efficiency of real heat engines
Formula (5.12.13) gives the theoretical limit for the maximum efficiency of heat engines. It shows that the heat engine is more efficient, the higher the temperature of the heater and the lower the temperature of the refrigerator. Only when the refrigerator temperature is equal to absolute zero, η = 1.
But the temperature of the refrigerator practically cannot be much lower than the ambient temperature. You can increase the temperature of the heater. However, any material (solid) has limited heat resistance, or heat resistance. When heated, it gradually loses its elastic properties, and melts at a sufficiently high temperature.
Now the main efforts of engineers are aimed at increasing the efficiency of engines by reducing the friction of their parts, fuel losses due to its incomplete combustion, etc. The real opportunities for increasing efficiency are still large here. So, for a steam turbine, the initial and final steam temperatures are approximately as follows: T 1 = 800 K and T 2 = 300 K. At these temperatures, the maximum value of the efficiency is:
The actual value of the efficiency due to various kinds of energy losses is approximately 40%. The maximum efficiency - about 44% - have internal combustion engines.
The efficiency of any heat engine cannot exceed the maximum possible value
, where T 1 - absolute temperature of the heater, and T 2 - absolute temperature of the refrigerator.
Increasing the efficiency of heat engines and bringing it closer to the maximum possible- the most important technical challenge.

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How to write efficiency in physics. The principle of operation of heat engines

Encyclopedic YouTube

boiler efficiency

Heat pumps and chillers

Literature

Notes

See what "" is in other dictionaries:

What is efficiency?

Why is efficiency needed?

How to find out your efficiency?

Olenemetr comes to the rescue

How to increase efficiency in World of Tanks?

Electric circuit efficiency

What is the efficiency of the current source

Investigation of the power and efficiency of the current source

Tasks for current power and efficiency

Efficiency of real heat engines