Coefficient of performance (COP) - a term that can be applied, perhaps, to every system and device. Even a person has an efficiency, though, probably, there is 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 efficiency of a particular system in relation to the return or conversion of energy. Efficiency is a measureless value and is represented either as a 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 the efficiency is written as follows:
Ƞ=A/Q, where A is the useful energy/work done by the system, and Q is the energy consumed by this system to organize the process of obtaining a useful output.
The efficiency factor, unfortunately, is always less than one or equal to it, since, according to the law of conservation of energy, we cannot get more work than the energy spent. In addition, the efficiency, in fact, is extremely rarely equal to one, since useful work is always accompanied by losses, for example, for heating the mechanism.
Heat engine efficiency
A heat engine is a device that converts thermal energy into mechanical energy. 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 source, T2 is the temperature of the cold source.
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 relation to the conversion of electrical energy into mechanical energy. The formula for finding the efficiency of an electric motor looks like this:
- Ƞ=P2/P1, where P1 is the supplied electrical power, P2 is the useful mechanical power generated by the engine.
Electrical power is found as the product of system current and voltage (P=UI), and mechanical power is found as the ratio of work to unit time (P=A/t)
transformer efficiency
A transformer is a device that converts alternating current of one voltage into alternating current of another voltage while maintaining frequency. In addition, transformers can also convert AC to DC.
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 delivered 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 find descriptions of the type - efficiency of the order of 130%, but in this case, you need to understand that the term is not used quite correctly, and, most likely, the author or the manufacturer understands a slightly different characteristic by this abbreviation.
For example, heat pumps are distinguished by the fact that they can give off more heat than they consume. Thus, the refrigerating machine can remove more heat from the cooled object than is spent in energy equivalent for the organization of the removal. The efficiency indicator of a refrigerating machine is called the coefficient of performance, denoted by the letter Ɛ and is 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 coefficient of performance is also called the efficiency of the refrigeration machine.
It is also interesting that the efficiency of boilers running on fossil fuels is usually calculated on the basis of the lower calorific value, while it can turn out to be more than one. However, it is still traditionally referred to as efficiency. It is possible to determine the efficiency of the boiler by the gross calorific value, and then it will always be less than one, but in this case it will be inconvenient to compare the performance of the boilers with the data of other installations.
Due to the fact that part of the heat during the operation of heat engines is inevitably transferred to the refrigerator, the efficiency of the engines cannot be equal to unity. It is of great interest to find the maximum possible efficiency of a heat engine operating with a heater at temperature Tg and a refrigerator at temperature T2. This was first done by the French engineer and scientist Sadi Carnot.
Carnot's ideal heat engine
Carnot came up with an ideal heat engine with an ideal gas as the working fluid. All processes in the Carnot machine are considered as equilibrium (reversible).
A circular process or cycle is carried out in the machine, in which the system, after a series of transformations, returns to its original state. The Carnot cycle consists of two isotherms and
two, the adiabat (Fig. 5.16). Curves 1-2 and 3-4 are isotherms, and curves 2-3 and 4-1 are adiabats.
First, the gas expands isothermally at a temperature T1. At the same time, it receives an amount of heat from the heater. Then it expands adiabatically and does not exchange heat with the surrounding bodies. Followed by
isothermal gas compression at o~ ^
temperature T2. The gas gives off in this rice g jg
In the process of the refrigerator, the amount of heat Q2 Finally, the gas is compressed adiabatically and returns to its initial state.
During isothermal expansion, the gas does work\u003e 0, equal to the amount of heat. With adiabatic expansion 2-3, the positive work A "3 is equal to the decrease in internal energy when the gas is cooled from temperature 7\ to temperature T2: A" 3 \u003d -AU12 \u003d WTX) - U(T2).
Isothermal compression at temperature T2 requires work A2 to be performed on the gas. The gas performs, respectively, negative work A 2
Q2. Finally, adiabatic compression requires work to be done on the gas A4 = AU21. The work of
Carnot Nicola Leonard Sadi (1796-1832) - a talented French engineer and physicist, one of the founders of thermodynamics. In his work “Thinking about the driving force of fire and about machines capable of developing this force” (1824), he first showed that heat engines can do work only in the process of transferring heat from a hot body to a cold one. Carnot came up with an ideal heat engine, calculated the efficiency of an ideal engine and proved that this coefficient is the maximum possible for any real heat engine. gas A\ \u003d -L4 \u003d -At / 2i \u003d - WTx). Therefore, the total
The work of the gas in two adiabatic processes is equal to zero.
The gas does work in a cycle
A "= A[ + A" 2 \u003d Q1 + Q2 \u003d IQJ - |Q2 |. (5.12.1)
This work is numerically equal to the area of the figure bounded by the cycle curve (shaded in Fig. 5.16).
To calculate the efficiency, you need to calculate the work for isothermal processes 1-2 and 3-4. The calculations lead to the following result:
(5.12.2) The efficiency of the Carnot heat engine is equal to the ratio of the difference between the absolute temperatures of the heater and cooler to the absolute temperature of the heater.
It is possible to express the work done by the machine per cycle, and the amount of heat given to the refrigerator Q2 through the efficiency of the machine and the amount of heat received from the heater According to the definition of efficiency
L" \u003d l Amount of heat
Q2 = A" - = TlQi - Qi = QiOl - D- (5.12.4)
Since t) |Q2| = (1-71)QI. (5.12.5)
Ideal Chiller
The Carnot cycle is reversible, so it can be drawn in the opposite direction. It will no longer be a heat engine, but an ideal refrigerating machine.
The processes will go in reverse order. Work A is done to drive the machine. The amount of heat Qx is transferred by the working fluid to the heater of a higher temperature, and the amount of heat Q2 is supplied to the working fluid from the refrigerator (Fig. 5.17). Heat is transferred from a cold body to a hot one, which is why the machine is called a refrigeration machine.?
Quantity of heat Q
"G
Quantity of heat Q2
WorkA
REFRIGERATOR temperature T2
Rice. 5.17
But this does not contradict the second law of thermodynamics: heat does not transfer by itself, but due to the performance of work.
We express the quantities of heat Q1 and Q2 in terms of the work A and the efficiency of the machine T|. Since according to the formula (5.12.3) A" \u003d riQj \u003d -A, then
(5.12.6)
The amount of heat transferred by the working fluid, as always, is negative. Obviously, |Qj| = ^. According to the expression
(5.12.4) amount of heat Q2 = QiCn ~ 1) or taking into account relation (5.12.3) (5.12.7)
q2= V1a>0- This amount of heat is received by the working fluid from the refrigerator.
The chiller works like a heat pump. The amount of heat Qj transferred to the hot body is greater than the amount taken from the cooler. According to the formula (5.12.7) Q2 = ^ -A = -Qj - A. Hence
| Q1\=A + Q2. (5.12.8)
The efficiency of the refrigeration machine is determined by the
solution є \u003d -g, since its purpose is to take away as much as possible
more heat from the cooled system while doing as little work as possible. The value of є is called the coefficient of performance. For an ideal refrigerator according to formulas (5.12.7) and (5.12.2)
Qn T2
i.e., the coefficient of performance is the greater, the smaller the temperature difference, and the smaller, the lower the temperature of the body from which heat is taken. Obviously, the coefficient of performance can be greater than one. For real refrigerators, it is more than three. A variation of the refrigeration machine is the air conditioner, which takes heat from the room and transfers it to the surrounding air.
Heat pump
When heating rooms with electric heaters, it is energetically more profitable to use a heat pump, and not just a spiral heated by current. The pump will additionally transfer the amount of heat Q2 from the ambient air into the room. However, this is not done because of the high cost of the refrigeration unit compared to a conventional electric stove or fireplace.
When using a heat pump, the amount of heat Qj received by the heated body is of practical interest, and not the amount of heat Q2 given off to the cold body. Therefore, the characteristic of the heat pump is so
lQi|
calable heating coefficient?from= .
For an ideal machine, taking into account relations (5.12.6) and (5.12.2), we will have
1 1 ~ 1 2
where 7 "1 is the absolute temperature of the heated room, and Г2 is the absolute temperature of the atmospheric air. Thus, the heating coefficient is always greater than one. For real devices at ambient temperature t2 = 0 ° C and room temperature tl = 25 ° C єot = 12 The amount of heat transferred to the room is almost 12 times greater than the amount of electricity consumed.
Maximum efficiency of thermal machines
(Carnot's theorem)
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 heater of temperature Tt and a refrigerator of temperature T2 cannot have an efficiency exceeding the efficiency of an ideal heat engine.
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 T1–T2.
Let us assume that the efficiency of another heat engine (not working according to the Carnot cycle) is r\"\u003e T|. The machines work with a common heater and a common refrigerator. Let the Carnot machine work in the reverse cycle (like a refrigerator), and the other machine in the direct cycle (Fig. 5.18) The heat engine performs work equal, according to formulas (5.12.3) and (5.12.5)
A" = r\"Q[ = ^_,\Q"2\. (5.12.11)
A refrigerating machine can always be designed so that it takes the amount of heat Q2 = \Q2\ from the refrigerator.
Then, according to formula (5.12.7), work will be performed on it
A = (5.12.12)
Since according to the condition G|" > m|, then A" > A. Therefore, the heat engine can set the refrigeration machine in action, 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 T| > T |", then you can make another machine work in a reverse cycle, and Carnot's machine in a direct one. We again come to a contradiction with the second law of thermodynamics. Therefore, two machines operating in reversible cycles have the same efficiency: r | " = Г|.
It is a different matter if the second machine operates in an irreversible cycle. If we assume Γ)" > Γ), then we again come to a contradiction with the second law of thermodynamics. However, assumption Γ)"
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 temperature of the refrigerator is equal to absolute zero, G | = 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 the efficiency here are still large. So, for a steam turbine, the initial and final steam temperatures are approximately as follows: T1 = 800 K and T2 = 300 K. At these temperatures, the maximum value of the efficiency is
T1 - T2
Lmax \u003d 0.62 \u003d 62%.
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 thermal
engine cannot exceed the maximum
T1~T2
possible value
11
temperature of the heater, and T2 is the absolute
refrigerator temperature.
Increasing the efficiency of heat engines and bringing it closer to the maximum possible is the most important
technical task.
Topic: “The principle of operation of a heat engine. Heat engine with the highest efficiency.
Form: Combined lesson using computer technology.
Goals:
- Show the importance of using a heat engine in human life.
- To study the principle of operation of real heat engines and an ideal engine operating on the Carnot cycle.
- Consider possible ways to increase the efficiency of a real engine.
- To develop students' curiosity, interest in technical creativity, respect for the scientific achievements of scientists and engineers.
Lesson plan.
No. p / p |
Questions |
Time |
| 1 | Show the need for the use of heat engines in modern conditions. | |
| 2 | Repetition of the concept of "heat engine". Types of heat engines: internal combustion engines (carburetor, diesel), steam and gas turbines, turbojet and rocket engines. | |
| 3 | Explanation of new theoretical material. Scheme and device of a heat engine, principle of operation, efficiency. Carnot cycle, ideal heat engine, its efficiency. Comparison of the efficiency of a real and ideal heat engine. |
|
| 4 | Solution of problem No. 703 (Stepanova), No. 525 (Bendrikov). | |
| 5 | Working with a model of a heat engine. |
|
| 6 | Summarizing. Homework § 33, tasks No. 700 and No. 697 (Stepanova) |
Theoretical material
Since ancient times, a person wanted to get rid of physical efforts or to facilitate them when moving something, to have more strength, speed.
Tales were created about carpets of airplanes, seven-league boots and wizards who carry a person to distant lands with a wave of a wand. Carrying weights, people invented carts, because it is easier to roll. Then they adapted animals - oxen, deer, dogs, most of all horses. So there were wagons, carriages. In the carriages, people strived for comfort, more and more improving them.
The desire of people to increase speed accelerated the change of events in the history of transport development. From the Greek "autos" - "self" and the Latin "mobilis" - "mobile" in European languages, the adjective "self-propelled", literally "auto - mobile" has developed.
It applied to watches, automatic puppets, to all sorts of mechanisms, in general, to everything that served as an addition to the “continuation”, “improvement” of a person. In the 18th century, they tried to replace manpower with steam power and applied the term “car” to trackless carts.
Why is the age of the car counted from the first "gasoline" with an internal combustion engine, invented and built in 1885-1886? As if forgetting about steam and battery (electric) carriages. The fact is that the internal combustion engine has made a real revolution in transport technology. For a long time, he proved to be the most consistent with the idea of \u200b\u200bthe car and therefore retained his dominant position for a long time. The share of vehicles with internal combustion engines today is more than 99.9% of world road transport.<Annex 1 >
The main parts of a heat engine
In modern technology, mechanical energy is obtained mainly from the internal energy of the fuel. Devices that convert internal energy into mechanical energy are called heat engines.<Annex 2 >
To perform work by burning fuel in a device called a heater, you can use a cylinder in which the gas heats up and expands and moves the piston.<Appendix 3 > Gas, the expansion of which causes the piston to move, is called the working fluid. The gas expands because its pressure is higher than the external pressure. But as the gas expands, its pressure drops, and sooner or later it will become equal to the external pressure. Then the expansion of the gas will end, and it will stop doing work.
What should be done so that the operation of the heat engine does not stop? In order for the engine to work continuously, it is necessary that the piston, after expanding the gas, returns each time to its original position, compressing the gas to its original state. Compression of the same gas can occur only under the action of an external force, which in this case does work (the gas pressure force in this case does negative work). After that, the processes of expansion and compression of the gas can again occur. This means that the operation of a heat engine must consist of periodically repeating processes (cycles) of expansion and contraction.
Figure 1 shows graphically the processes of gas expansion (line AB) and compression to the original volume (line CD). The work done by the gas during expansion is positive ( AF > 0 ABEF. The work done by the gas during compression is negative (because AF< 0
) and is numerically equal to the area of the figure CDEF. Useful work for this cycle is numerically equal to the difference between the areas under the curves AB and CD(shaded in the picture).
The presence of a heater, a working fluid and a refrigerator is a fundamentally necessary condition for the continuous cyclic operation of any heat engine.
Heat engine efficiency
The working fluid, receiving a certain amount of heat Q 1 from the heater, gives a part of this amount of heat, modulo equal to |Q2|, to the refrigerator. Therefore, the work done cannot be more A = Q 1 - |Q 2 |. The ratio of this work to the amount of heat received by the expanding gas from the heater is called efficiency thermal machine:
The efficiency of a heat engine operating in a closed cycle is always less than one. The task of thermal power engineering is to make the efficiency as high as possible, i.e., to use as much of the heat received from the heater as possible to obtain work. How can this be achieved?
For the first time, the most perfect cyclic process, consisting of isotherms and adiabats, was proposed by the French physicist and engineer S. Carnot in 1824.
Carnot cycle.
Let us assume that the gas is in a cylinder, the walls and piston of which are made of a heat-insulating material, and the bottom is made of a material with high thermal conductivity. The volume occupied by the gas is V1.
Let's bring the cylinder into contact with the heater (Figure 2) and let the gas expand isothermally and do work. . At the same time, the gas receives a certain amount of heat from the heater Q1. This process is graphically represented by an isotherm (curve AB).
When the volume of the gas becomes equal to a certain value V1'< V 2 ,
the bottom of the cylinder is isolated from the heater ,
After that, the gas expands adiabatically to a volume V2, corresponding to the maximum possible stroke of the piston in the cylinder (adiabatic sun). The gas is then cooled to a temperature T2< T 1 .
The cooled gas can now be compressed isothermally at a temperature T2. To do this, it must be brought into contact with a body having the same temperature. T 2 , i.e. with refrigerator ,
and compress the gas with an external force. However, in this process, the gas will not return to its original state - its temperature will always be lower than T 1 .
Therefore, isothermal compression is brought to some intermediate volume V2 '>V1(isotherm CD). In this case, the gas gives off a certain amount of heat to the refrigerator. Q2, equal to the work of compression done on it. The gas is then compressed adiabatically to a volume V1, while its temperature rises to T 1(adiabatic DA). Now the gas has returned to its original state, in which its volume is equal to V 1, the temperature is T1, pressure - p1 and the cycle can be repeated again.
So, in the area ABC gas does work (A > 0), and on the site CDA work done on the gas (A< 0).
On the plots sun and AD work is done only by changing the internal energy of the gas. Because the change in internal energy UBC=-UDA, then the work for adiabatic processes is equal to: ABC = -ADA. Therefore, the total work done per cycle is determined by the difference in the work done during isothermal processes (sections AB and CD). Numerically, this work is equal to the area of \u200b\u200bthe figure bounded by the cycle curve ABCD.
Only part of the amount of heat is actually converted into useful work. qt, received from the heater, equal to QT 1 - |QT 2 |. So, in the Carnot cycle, the useful work A = QT 1 - |QT 2 |.
The maximum efficiency of an ideal cycle, as shown by S. Carnot, can be expressed in terms of the heater temperature (T 1) and refrigerator (T 2):
In real engines, it is not possible to implement a cycle consisting of ideal isothermal and adiabatic processes. Therefore, the efficiency of the cycle carried out in real engines is always less than the efficiency of the Carnot cycle (at the same temperatures of heaters and coolers):
It can be seen from the formula that the efficiency of engines is greater, the higher the temperature of the heater and the lower the temperature of the refrigerator.
Problem #703
The engine runs on the Carnot cycle. How will the efficiency of the heat engine change if, at a constant refrigerator temperature of 17 ° C, the heater temperature is increased from 127 to 447 ° C?
Problem #525
Determine the efficiency of the tractor engine, which required 1.5 kg of fuel with a specific heat of combustion of 4.2 107J/kg to perform work of 1.9 107J.
Performing a computer test on the topic.<Appendix 4 > Work with the model of the heat engine.
Topics of the USE codifier: principles of operation of thermal engines, efficiency of a thermal engine, thermal engines and environmental protection.
In short, thermal machines convert heat into work or, conversely, work into heat.
There are two types of heat engines - depending on the direction of the processes occurring in them.
1. Heat engines convert heat from an external source into mechanical work.
2. Refrigeration machines transfer heat from a less heated body to a more heated one due to the mechanical work of an external source.
Consider these types of heat engines in more detail.
Heat engines
We know that doing work on a body is one of the ways to change its internal energy: the work done, as it were, dissolves in the body, turning into the energy of chaotic movement and interaction of its particles.
Rice. 1. Heat engine
A heat engine is a device that, on the contrary, extracts useful work from the "chaotic" internal energy of a body. The invention of the heat engine radically changed the face of human civilization.
A schematic diagram of a heat engine can be depicted as follows ( fig. 1). Let's understand what the elements of this scheme mean.
working body engine is gas. It expands, moves the piston and thereby performs useful mechanical work.
But in order to force the gas to expand, overcoming external forces, it is necessary to heat it to a temperature that is significantly higher than the ambient temperature. To do this, the gas is brought into contact with heater- burning fuel.
In the process of fuel combustion, significant energy is released, part of which is used to heat the gas. The gas receives heat from the heater. It is due to this heat that the engine performs useful work.
This is all clear. What is a refrigerator and why is it needed?
With a single expansion of the gas, we can use the incoming heat as efficiently as possible and turn it entirely into work. To do this, it is necessary to expand the gas isothermally: the first law of thermodynamics, as we know, gives us in this case .
But no one needs a one-time expansion. The engine must run cyclically, providing periodic repetition of piston movements. Therefore, at the end of the expansion, the gas must be compressed, returning it to its original state.
In the process of expansion, the gas does some positive work. In the process of compression, positive work is done on the gas (and the gas itself does negative work). As a result, the useful work of the gas per cycle: .
Of course it should be class="tex" alt="(!LANG:A>0"> , или (иначе никакого смысла в двигателе нет).!}
By compressing the gas, we must do less work than the gas did when expanding.
How to achieve this? Answer: compress the gas at lower pressures than were during the expansion. In other words, on the -diagram, the compression process should go below expansion process, i.e. the loop must be traversed clockwise(Fig. 2).
Rice. 2. Heat engine cycle
For example, in the cycle in the figure, the work done by the gas during expansion is equal to the area of the curvilinear trapezoid. Similarly, the work done by a gas during compression is equal to the area of a curvilinear trapezoid with a minus sign. As a result, the work of the gas per cycle is positive and equal to the area of the cycle.
Okay, but how to make the gas return to its original state along a lower curve, i.e. through states with lower pressures? Recall that for a given volume, the pressure of a gas is the lower, the lower the temperature. Therefore, during compression, the gas must pass through states with lower temperatures.
This is exactly what a refrigerator is for. cool gas during compression.
The cooler can be the atmosphere (for internal combustion engines) or cooling running water (for steam turbines). When cooled, the gas gives off a certain amount of heat to the refrigerator.
The total amount of heat received by the gas per cycle is equal to . According to the first law of thermodynamics:
where is the change in the internal energy of the gas per cycle. It is equal to zero: , since the gas returned to its original state (and the internal energy, as we remember, is state function). As a result, the work done by the gas per cycle is equal to:
(1)
As you can see, it is not possible to completely convert the heat coming from the heater into work. Part of the heat has to be given to the refrigerator - to ensure the cyclical process.
An indicator of the efficiency of converting the energy of the burning fuel into mechanical work is the efficiency of the heat engine.
Heat engine efficiency is the ratio of mechanical work to the amount of heat received from the heater:
Taking into account relation (1), we also have
(2)
The efficiency of a heat engine, as we see, is always less than unity. For example, the efficiency of steam turbines is approximately , and the efficiency of internal combustion engines is about .
Refrigeration machines
Everyday experience and physical experiments tell us that in the process of heat transfer, heat is transferred from a hotter body to a less heated one, but not vice versa. Processes are never observed in which, due to heat transfer, energy spontaneously passes from a cold body to a hot one, as a result of which the cold body would cool down even more, and the hot body would heat up even more.
Rice. 3. Chiller
The key word here is "spontaneously". If you use an external source of energy, then it is quite possible to carry out the process of transferring heat from a cold body to a hot one. This is what refrigerators do.
cars.
Compared to a heat engine, the processes in a refrigeration machine have the opposite direction (Fig. 3).
working body refrigeration machine is also called refrigerant. For simplicity, we will consider it a gas that absorbs heat during expansion and releases heat during compression (in real refrigeration units, a refrigerant is a volatile solution with a low boiling point, which takes heat during evaporation and releases during condensation).
Refrigerator in a refrigeration machine, this is the body from which heat is removed. The refrigerator transfers the amount of heat to the working fluid (gas), as a result of which the gas expands.
During compression, the gas gives off heat to a hotter body - heater. In order for such heat transfer to take place, the gas must be compressed at higher temperatures than when it was expanded. This is possible only due to the work done by an external source (for example, an electric motor (in real refrigeration units, the electric motor creates low pressure in the evaporator, as a result of which the refrigerant boils and takes heat; on the contrary, in the condenser the electric motor creates high pressure, under which the refrigerant condenses and gives off heat)). Therefore, the amount of heat transferred to the heater turns out to be greater than the amount of heat taken from the refrigerator, just by the value:
Thus, on the -diagram, the operating cycle of the refrigeration machine goes counterclock-wise. The cycle area is the work done by an external source (Fig. 4).
Rice. 4. Chiller cycle
The main purpose of a refrigeration machine is to cool a certain reservoir (for example, a freezer). In this case, this tank plays the role of a refrigerator, and the environment serves as a heater - the heat removed from the tank is dissipated into it.
An indicator of the efficiency of the refrigeration machine is coefficient of performance, equal to the ratio of heat removed from the refrigerator to the work of an external source:
The coefficient of performance may be greater than one. In real refrigerators, it takes values approximately from 1 to 3.
There is another interesting application: the refrigeration machine can work as Heat pump. Then its purpose is to heat a certain reservoir (for example, heating a room) due to the heat removed from the environment. In this case, this tank will be the heater, and the environment will be the refrigerator.
An indicator of the efficiency of the heat pump is heating coefficient, equal to the ratio of the amount of heat transferred to the heated reservoir to the work of an external source:
The values of the heating coefficient of real heat pumps are usually in the range from 3 to 5.
Carnot heat engine
Important characteristics of a heat engine are the highest and lowest temperatures of the working fluid during the cycle. These values are named respectively heater temperature and refrigerator temperature.
We have seen that the efficiency of a heat engine is strictly less than unity. A natural question arises: what is the maximum possible efficiency of a heat engine with fixed values of the heater temperature and the refrigerator temperature ?
Let, for example, the maximum temperature of the working fluid of the engine be , and the minimum - . What is the theoretical efficiency limit of such an engine?
The answer to this question was given by the French physicist and engineer Sadi Carnot in 1824.
He invented and researched a wonderful heat engine with an ideal gas as a working fluid. This machine works on Carnot cycle, consisting of two isotherms and two adiabats.
Consider direct cycle carnot machine going clockwise (fig. 5). In this case, the machine functions as a heat engine.
Rice. 5. Carnot cycle
Isotherm. In the section, the gas is brought into thermal contact with a temperature heater and expands isothermally. The amount of heat comes from the heater and is completely converted into work in this area: .
adiabat. For the purpose of subsequent compression, it is necessary to transfer the gas to a zone of lower temperatures. To do this, the gas is thermally insulated and then expands adiabatically on the area .
When the gas expands, it does positive work, and due to this, its internal energy decreases: .
Isotherm. The thermal insulation is removed, the gas is brought into thermal contact with the temperature cooler. Isothermal compression occurs. The gas gives off the amount of heat to the refrigerator and does negative work.
adiabat. This section is necessary to return the gas to its original state. In the course of adiabatic compression, the gas does negative work, and the change in internal energy is positive: . The gas is heated to its original temperature.
Carnot found the efficiency of this cycle (calculations, unfortunately, are beyond the scope of the school curriculum):
(3)
Moreover, he proved that The efficiency of the Carnot cycle is the maximum possible for all heat engines with a heater temperature and a cooler temperature .
So, in the above example we have:
What is the point of using exactly isotherms and adiabats, and not some other processes?
It turns out that isothermal and adiabatic processes make the Carnot machine reversible. It can be launched by reverse cycle(counterclockwise) between the same heater and refrigerator without involving other devices. In this case, the Carnot machine will function as a refrigeration machine.
The ability to run a Carnot machine in both directions plays a very important role in thermodynamics. For example, this fact serves as a link in the proof of the maximum efficiency of the Carnot cycle. We will return to this in the next article on the second law of thermodynamics.
Heat engines and environmental protection
Heat engines cause serious damage to the environment. Their widespread use leads to a number of negative effects.
The dissipation of a huge amount of thermal energy into the atmosphere leads to an increase in the temperature on the planet. Climate warming threatens to turn into melting glaciers and catastrophic disasters.
The accumulation of carbon dioxide in the atmosphere also leads to climate warming, which slows down the escape of the Earth's thermal radiation into space (greenhouse effect).
Due to the high concentration of fuel combustion products, the environmental situation worsens.
These are civilization-wide problems. To combat the harmful effects of the operation of heat engines, it is necessary to increase their efficiency, reduce emissions of toxic substances, develop new types of fuel and use energy economically.
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 the reverse cycle (like a refrigeration machine), and the other machine in the forward 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 the efficiency here are still large. 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.
