Efficiency of an ideal heat engine. What is the efficiency percentage of the refrigerator. Main parts of a heat engine
Topics of the Unified State Examination codifier: principles of operation of heat engines, efficiency of a heat engine, heat engines and environmental protection.
In short, heat engines convert heat into work or, conversely, work into heat.
Heat engines come in two types, depending on the direction of the processes occurring in them.
1. Heat engines convert heat coming 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.
Let us 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 seems to dissolve in the body, turning into the energy of random 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 the body. The invention of the heat engine radically changed the face of human civilization.
The schematic diagram of a heat engine can be depicted as follows (Fig. 1). Let's figure out what the elements of this diagram mean.
Working fluid 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.
During the combustion of fuel, significant energy is released, part of which is used to heat the gas. The gas receives an amount of 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 gas expansion, we can use the incoming heat as efficiently as possible and convert it entirely into work. To do this, we need 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 be running cyclically, ensuring periodic repeatability of the piston movements. Therefore, after expansion is completed, the gas must be compressed, returning it to its original state.
During the expansion process, the gas does some positive work. During the compression process, positive work is done on the gas (and the gas itself does negative work). As a result, the useful work of gas per cycle is: .
Of course, there should be class="tex" alt="A>0"> , или (иначе никакого смысла в двигателе нет).!}
When compressing a gas, we must do less work than the gas did during expansion.
How to achieve this? Answer: compress the gas under lower pressures than during expansion. In other words, on the -diagram the compression process should proceed below expansion process, i.e. the cycle must go through 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 curved trapezoid. Similarly, the work done by a gas during compression is equal to the area of a curved trapezoid with a minus sign. As a result, the work done by the gas per cycle turns out to be positive and equal to the area of the cycle.
Okay, but how do you force the gas to return to its original state along a lower curve, that is, through states with lower pressures? Let us remember that for a given volume, the lower the temperature, the lower the gas pressure. Therefore, when compressed, the gas must go through states with lower temperatures.
That's exactly what a refrigerator is for: to cool gas in the process of compression.
The cooler can be the atmosphere (for internal combustion engines) or cooling running water (for steam turbines). When cooled, the gas gives off some 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 has returned to its original state (and the internal energy, as we remember, is state function). As a result, the gas work 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 nature of the process.
An indicator of the efficiency of converting the energy of burning fuel into mechanical work is the efficiency of a 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 approximately .
Refrigeration machines
Everyday experience and physical experiments tell us that in the process of heat exchange, heat is transferred from a more heated body to a less heated one, but not vice versa. Processes in which, due to heat exchange, 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. Refrigerator
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 are in the opposite direction (Fig. 3).
Working fluid refrigeration machine is also called refrigerant. For simplicity, we will consider it a gas that absorbs heat during expansion and releases during compression (in real refrigeration units, the refrigerant is a volatile solution with a low boiling point, which absorbs heat during evaporation and releases during condensation).
Fridge in a refrigeration machine, it is the body from which heat is removed. The refrigerator transfers an amount of heat to the working fluid (gas), as a result of which the gas expands.
During compression, the gas transfers heat to a hotter body - heater. For such heat transfer to occur, the gas must be compressed at higher temperatures than during expansion. This is possible only due to the work performed 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 away heat; on the contrary, in the condenser the electric motor creates high pressure, under which the refrigerant condenses and releases warm)). Therefore, the amount of heat transferred to the heater turns out to be greater than the amount of heat taken from the refrigerator by exactly the amount:
Thus, on the -diagram the working cycle of the refrigeration machine goes counterclock-wise. The cycle area is the work done by an external source (Fig. 4).
Rice. 4. Refrigerator cycle
The main purpose of a refrigeration machine is to cool a certain reservoir (for example, a freezer). In this case, this reservoir plays the role of a refrigerator, and the environment serves as a heater - the heat removed from the reservoir is dissipated into it.
An indicator of the efficiency of a refrigeration machine is coefficient of performance, equal to the ratio of heat removed from the refrigerator to the work of an external source:
The refrigeration coefficient can be greater than one. In real refrigerators it takes values from approximately 1 to 3.
There is another interesting application: a 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 a heat pump is heating coefficient, equal to the ratio of the amount of heat transferred to the heated reservoir to the work of the external source:
The heating coefficient values 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 called accordingly 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 highest possible efficiency of a heat engine with fixed values of the heater temperature and refrigerator temperature?
Let, for example, the maximum temperature of the engine working fluid be , and the minimum - . What is the theoretical limit to the efficiency 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 remarkable heat engine with an ideal gas as a working fluid. This machine works according to Carnot cycle, consisting of two isotherms and two adiabats.
Let's consider direct cycle Carnot machine, going clockwise (Fig. 5). In this case, the machine functions as a heat engine.
Rice. 5. Carnot cycle
Isotherm. At this point, the gas is brought into thermal contact with a temperature heater and expands isothermally. An amount of heat comes from the heater and is entirely converted into work in this area: .
Adiabata. For subsequent compression, the gas must be transferred to a zone of lower temperatures. To do this, the gas is thermally insulated and then expands adiabatically in the area.
When expanding, the gas 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 a temperature refrigerator. Isothermal compression occurs. The gas transfers heat to the refrigerator and does negative work.
Adiabata. This section is necessary to return the gas to its original state. During adiabatic compression, the gas performs 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, go beyond the scope of the school curriculum):
(3)
Moreover, he proved that Carnot cycle efficiency is the maximum possible for all heat engines with heater temperature and cooler temperature .
So, in the example above we have:
What is the point of using isotherms and adiabats, and not some other processes?
It turns out that isothermal and adiabatic processes make a 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 temperature on the planet. Climate warming threatens to result in melting glaciers and catastrophic disasters.
Climate warming is also caused by the accumulation of carbon dioxide in the atmosphere, which slows down the escape of the Earth's thermal radiation into space (the greenhouse effect).
Due to the high concentration of fuel combustion products, the environmental situation is deteriorating.
These are problems on the scale of the entire civilization. To combat the harmful effects of heat engines, it is necessary to increase their efficiency, reduce toxic emissions, develop new types of fuel and use energy sparingly.
« Physics - 10th grade"
What is a thermodynamic system and what parameters characterize its state.
State the first and second laws of thermodynamics.
It was the creation of the theory of heat engines that led to the formulation of the second law of thermodynamics.
The reserves of internal energy in the earth's crust and oceans can be considered practically unlimited. But to solve practical problems, having energy reserves is not enough. It is also necessary to be able to use energy to set in motion machine tools in factories and factories, vehicles, tractors and other machines, to rotate the rotors of electric current generators, etc. Humanity needs engines - devices capable of doing work. Most of the engines on Earth are heat engines.
Heat engines- these are devices that convert the internal energy of fuel into mechanical work.
Operating principle of heat engines.
In order for an engine to do work, there needs to be a pressure difference on both sides of the engine piston or turbine blades. In all heat engines, this pressure difference is achieved by increasing the temperature working fluid(gas) by hundreds or thousands of degrees compared to the ambient temperature. This temperature increase occurs when fuel burns.
One of the main parts of the engine is a gas-filled vessel with a movable piston. The working fluid of all heat engines is gas, which does work during expansion. Let us denote the initial temperature of the working fluid (gas) by T 1 . This temperature in steam turbines or machines is achieved by the steam in the steam boiler. In internal combustion engines and gas turbines, the temperature rise occurs as fuel burns inside the engine itself. Temperature T 1 is called heater temperature.
The role of the refrigerator.
As work is performed, the gas loses energy and inevitably cools to a certain temperature T2, which is usually slightly higher than the ambient temperature. They call her refrigerator temperature. The refrigerator is the atmosphere or special devices for cooling and condensing waste steam - capacitors. In the latter case, the temperature of the refrigerator may be slightly lower than the ambient temperature.
Thus, in an engine, the working fluid during expansion cannot give up all its internal energy to do work. Some of the heat is inevitably transferred to the refrigerator (atmosphere) along with waste steam or exhaust gases from internal combustion engines and gas turbines.
This part of the internal energy of the fuel is lost. A heat engine performs work due to the internal energy of the working fluid. Moreover, in this process, heat is transferred from hotter bodies (heater) to colder ones (refrigerator). The schematic diagram of a heat engine is shown in Figure 13.13.
The working fluid of the engine receives from the heater during fuel combustion the amount of heat Q 1, does work A" and transfers the amount of heat to the refrigerator Q 2< Q 1 .
In order for the engine to operate continuously, it is necessary to return the working fluid to its initial state, at which the temperature of the working fluid is equal to T 1. It follows that the engine operates according to periodically repeating closed processes, or, as they say, in a cycle.
Cycle is a series of processes as a result of which the system returns to its initial state.
Coefficient of performance (efficiency) of a heat engine.
The impossibility of completely converting the internal energy of gas into the work of heat engines is due to the irreversibility of processes in nature. If heat could return spontaneously from the refrigerator to the heater, then the internal energy could be completely converted into useful work by any heat engine. The second law of thermodynamics can be stated as follows:
Second law of thermodynamics:
It is impossible to create a perpetual motion machine of the second kind, which would completely convert heat into mechanical work.
According to the law of conservation of energy, the work done by the engine is equal to:
A" = Q 1 - |Q 2 |, (13.15)
where Q 1 is the amount of heat received from the heater, and Q2 is the amount of heat given to the refrigerator.
The coefficient of performance (efficiency) of a heat engine is the ratio of the work "A" performed by the engine to the amount of heat received from the heater:
Since all engines transfer some amount of heat to the refrigerator, then η< 1.
Maximum efficiency value of heat engines.
The laws of thermodynamics make it possible to calculate the maximum possible efficiency of a heat engine operating with a heater at temperature T1 and a refrigerator at temperature T2, as well as to determine ways to increase it.
For the first time, the maximum possible efficiency of a heat engine was calculated by the French engineer and scientist Sadi Carnot (1796-1832) in his work “Reflections on the driving force of fire and on machines capable of developing this force” (1824).
Carnot came up with an ideal heat engine with an ideal gas as a working fluid. An ideal Carnot heat engine operates on a cycle consisting of two isotherms and two adiabats, and these processes are considered reversible (Fig. 13.14). First, a vessel with gas is brought into contact with the heater, the gas expands isothermally, doing positive work, at temperature T 1, and it receives an amount of heat Q 1.
Then the vessel is thermally insulated, the gas continues to expand adiabatically, while its temperature drops to the temperature of the refrigerator T 2. After this, the gas is brought into contact with the refrigerator; during isothermal compression, it gives the amount of heat Q 2 to the refrigerator, compressing to a volume V 4< V 1 . Затем сосуд снова теплоизолируют, газ сжимается адиабатно до объёма V 1 и возвращается в первоначальное состояние. Для КПД этой машины было получено следующее выражение:
As follows from formula (13.17), the efficiency of a Carnot machine is directly proportional to the difference in the absolute temperatures of the heater and refrigerator.
The main significance of this formula is that it indicates the way to increase efficiency, for this it is necessary to increase the temperature of the heater or lower the temperature of the refrigerator.
Any real heat engine operating with a heater at temperature T1 and a refrigerator at temperature T2 cannot have an efficiency exceeding that of an ideal heat engine: 
The processes that make up the cycle of a real heat engine are not reversible.
Formula (13.17) gives a theoretical limit for the maximum efficiency value of heat engines. It shows that a heat engine is more efficient, the greater the temperature difference between the heater and refrigerator.
Only at a refrigerator temperature equal to absolute zero does η = 1. In addition, it has been proven that the efficiency calculated using formula (13.17) does not depend on the working substance.
But the temperature of the refrigerator, whose role is usually played by the atmosphere, practically cannot be lower than the ambient air temperature. You can increase the heater temperature. However, any material (solid) has limited heat resistance or heat resistance. When heated, it gradually loses its elastic properties, and at a sufficiently high temperature it melts.
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 incomplete combustion, etc.
For a steam turbine, the initial and final steam temperatures are approximately the following: T 1 - 800 K and T 2 - 300 K. At these temperatures, the maximum efficiency value is 62% (note that efficiency is usually measured as a percentage). The actual efficiency value due to various types of energy losses is approximately 40%. The maximum efficiency - about 44% - is achieved by Diesel engines.
Environmental protection.
It is difficult to imagine the modern world without heat engines. They are the ones who provide us with a comfortable life. Heat engines drive vehicles. About 80% of electricity, despite the presence of nuclear power plants, is generated using thermal engines.
However, during the operation of heat engines, inevitable environmental pollution occurs. This is a contradiction: on the one hand, humanity needs more and more energy every year, the main part of which is obtained through the combustion of fuel, on the other hand, combustion processes are inevitably accompanied by environmental pollution.
When fuel burns, the oxygen content in the atmosphere decreases. In addition, the combustion products themselves form chemical compounds that are harmful to living organisms. Pollution occurs not only on the ground, but also in the air, since any airplane flight is accompanied by emissions of harmful impurities into the atmosphere.
One of the consequences of the engines is the formation of carbon dioxide, which absorbs infrared radiation from the Earth's surface, which leads to an increase in atmospheric temperature. This is the so-called greenhouse effect. Measurements show that the atmospheric temperature rises by 0.05 °C per year. Such a continuous increase in temperature can cause ice to melt, which, in turn, will lead to changes in water levels in the oceans, i.e., to the flooding of continents.
Let us note one more negative point when using heat engines. So, sometimes water from rivers and lakes is used to cool engines. The heated water is then returned back. An increase in temperature in water bodies disrupts the natural balance; this phenomenon is called thermal pollution.
To protect the environment, various cleaning filters are widely used to prevent the release of harmful substances into the atmosphere, and engine designs are being improved. There is a continuous improvement of fuel that produces less harmful substances during combustion, as well as the technology of its combustion. Alternative energy sources using wind, solar radiation, and nuclear energy are being actively developed. Electric cars and cars powered by solar energy are already being produced.
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.
Ideal Carnot heat engine
Carnot came up with an ideal heat engine with an ideal gas as a working fluid. All processes in a 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, adiabat (Fig. 5.16). Curves 1-2 and 3-4 are isotherms, and 2-3 and 4-1 are adiabats.
First, the gas expands isothermally at 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. Gas gives off in this rice g jg
process in the refrigerator, the amount of heat Q2 Finally, the gas is compressed adiabatically and returns to its initial state.
During isothermal expansion, the gas performs work > 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 = -AU12 = ШТХ) - U (T2).
Isothermal compression at temperature T2 requires work A2 to be performed on the gas. The gas performs correspondingly negative work A 2
Q2. Finally, adiabatic compression requires work done on the gas A4 = AU21. The work itself
Carnot Nicolas Leonard Sadi (1796-1832) - a talented French engineer and physicist, one of the founders of thermodynamics. In his work “Reflections on the driving force of fire and on machines capable of developing this force” (1824), he first showed that heat engines can perform 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 the ideal machine and proved that this coefficient is the maximum possible for any real heat engine. gas А\ = -Л4 = -At/2i = - ШТх). Therefore, the total ra
The flow rate of the gas during two adiabatic processes is zero.
During a cycle, the gas does work
A"= A[ + A"2=Q1 + Q2 = IQJ - |Q2|. (5.12.1)
This work is numerically equal to the area of the figure limited 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. Calculations lead to the following result:
(5.12.2) The efficiency of a Carnot heat engine is equal to the ratio of the difference between the absolute temperatures of the heater and refrigerator to the absolute temperature of the heater.
We can express the work done by the machine per cycle and the amount of heat Q2 transferred to the refrigerator through the efficiency of the machine and the amount of heat received from the heater. According to the definition of efficiency
L" = l Amount of heat
Q2 = A" - = TlQi - Qi = QiOl - D- (5.12.4)
Since t) |Q2| = (1-71)QI. (5.12.5)
The ideal refrigeration machine
The Carnot cycle is reversible, so it can be done in the opposite direction. It will no longer be a heat engine, but an ideal refrigeration 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 a heater at 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 is transferred not by itself, but by doing work.
Let us express the amounts of heat Q1 and Q2 through the work A and the efficiency of the machine T|. Since according to formula (5.12.3) A" = riQj = -A, then
(5.12.6)
The amount of heat transferred by the working fluid is, as always, 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 refrigerator works like a heat pump. The amount of heat Qj transferred to the hot body is greater than the amount taken from the refrigerator. According to formula (5.12.7) Q2 = ^ -A = -Qj - A. Hence
| Q1\=A + Q2. (5.12.8)
The efficiency of a refrigeration machine is determined by
є = -г, since its purpose can be taken away as much as possible
greater amount of heat from the cooled system while doing as little work as possible. The value є is called the coefficient of performance. For an ideal refrigeration machine according to formulas (5.12.7) and (5.12.2)
Qn T2
that is, the lower the temperature difference, the greater the coefficient of refrigeration, and the lower, the lower the temperature of the body from which heat is removed. Obviously, the coefficient of performance can be greater than one. For real refrigerators it is more than three. A type of refrigeration machine is an air conditioner, which takes heat from a 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, rather than just a coil 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 due to 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, and not the amount of heat Q2 given to the cold body, is of practical interest. Therefore, the characteristic of a heat pump is:
lQi|
called heating coefficient?from= .
For an ideal machine, taking into account relations (5.12.6) and (5.12.2), we will have Єot=m^V" (5.12.10)
1 1 ~ 1 2
where 7"1 is the absolute temperature of the heated room, and G2 is the absolute temperature of the atmospheric air. Thus, the heating coefficient is always greater than unity. For real devices at ambient temperature t2 = 0 °C and room temperature t-l = 25 °C єot = 12 The amount of heat transferred into the room is almost 12 times greater than the amount of electricity expended.
Maximum efficiency of heat engines
(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 at temperature Tt and a refrigerator at temperature T2 cannot have an efficiency that exceeds the efficiency of an ideal heat engine.
Let us first consider a heat engine operating in a reversible cycle with a real gas. The cycle can be anything, 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 operating on a Carnot cycle) g\" > Г|. The machines operate with a common heater and a common refrigerator. Let the Carnot machine operate on a reverse cycle (like a refrigeration machine), and the other machine on a forward cycle (Fig. 5.18) The heat engine performs work equal to, according to formulas (5.12.3) and (5.12.5)
A" = r\"Q[ = ^_,\Q"2\. (5.12.11)
A refrigeration 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 done on it
A = (5.12.12)
Since by condition G|" > m|, then A" > A. Therefore, a heat engine can power a refrigeration machine, and there will still be an excess of work left. This excess work is done by heat taken from one source. After all, heat is not transferred to the refrigerator when two machines operate at once. But this contradicts the second law of thermodynamics.
If we assume that T| > T|", then you can force another machine to work in a reverse cycle, and a Carnot machine - in a forward cycle. We again come to a contradiction with the second law of thermodynamics. Consequently, two machines operating in reversible cycles have the same efficiency: r|" = Г|.
It’s a different matter if the second machine operates on an irreversible cycle. If we assume G)" > G), then we again come to a contradiction with the second law of thermodynamics. However, assumption G)"
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 value of heat engines. It shows that the higher the temperature of the heater and the lower the temperature of the refrigerator, the more efficient a heat engine is. Only at a refrigerator temperature equal to absolute zero, Г| = 1.
But the temperature of the refrigerator practically cannot be much lower than the ambient temperature. You can increase the heater temperature. However, any material (solid body) has limited heat resistance, or heat resistance. When heated, it gradually loses its elastic properties, and at a sufficiently high temperature it melts.
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 incomplete combustion, etc. Real opportunities for increasing efficiency here still remain great. Thus, for a steam turbine, the initial and final temperatures of the steam are approximately as follows: T1 = 800 K and T2 = 300 K. At these temperatures, the maximum value of the efficiency coefficient is
T1 - T2
Lmax= =0.62 = 62%.
The actual efficiency value due to various types of energy losses is approximately 40%. The maximum efficiency - about 44% - is achieved by internal combustion engines.
The efficiency of any thermal
engine cannot exceed the maximum
T1~T2
possible value Lshchakh = -^-» - absolute
11
is the 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 problem.
where T 1 is the absolute temperature of the heater, and T 2 is the absolute temperature of the refrigerator. Increasing the efficiency of heat engines and bringing it closer to the maximum possible is the most important technical task. Efficiency coefficient of a heat engine The working fluid, receiving a certain amount of heat Q 1 from the heater, gives part of this amount of heat, modulo equal to |Q2|, to the refrigerator. Therefore, the work done cannot be greater 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 heat engine: 
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, that is, to use as much of the heat received from the heater as possible to produce 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. 42. Entropy. Second law of thermodynamics. Entropy in natural sciences is a measure of the disorder of a system consisting of many elements. In particular, in statistical physics - a measure of the probability of the occurrence of any macroscopic state; in information theory - a measure of the uncertainty of any experience (test), which can have different outcomes, and therefore the amount of information; in historical science, to explicate the phenomenon of alternative history (invariance and variability of the historical process). Entropy in computer science is the degree of incompleteness and uncertainty of knowledge. The concept of entropy was first introduced by Clausius in thermodynamics in 1865 to determine the measure of irreversible energy dissipation, the measure of deviation of a real process from an ideal one. Defined as the sum of reduced heats, it is a function of state and remains constant during reversible processes, while in irreversible processes its change is always positive. , where dS is the entropy increment; δQ - minimum heat supplied to the system; T is the absolute temperature of the process; Use in various disciplines § Thermodynamic entropy is a thermodynamic function that characterizes the measures of disorder of a system, that is, the heterogeneity of the location of the movement of its particles of a thermodynamic system. § Information entropy is a measure of the uncertainty of the source of messages, determined by the probabilities of the appearance of certain symbols during their transmission. § Differential entropy - entropy for continuous distributions § Entropy of a dynamic system - in the theory of dynamic systems, a measure of chaos in the behavior of system trajectories. § Reflection entropy is part of the information about a discrete system that is not reproduced when the system is reflected through the totality of its parts. § Entropy in control theory is a measure of the uncertainty of the state or behavior of a system under given conditions. Entropy is a function of the state of the system, equal in an equilibrium process to the amount of heat imparted to the system or removed from the system, related to the thermodynamic temperature of the system. Entropy is a function that establishes a connection between macro- and micro-states; the only function in physics that shows the direction of processes. Entropy is a function of the state of the system, which does not depend on the transition from one state to another, but depends only on the initial and final position of the system. The second law of thermodynamics is a physical principle that imposes restrictions on the direction of heat transfer processes between bodies. The second law of thermodynamics states that spontaneous transfer of heat from a less heated body to a more heated body is impossible. The second law of thermodynamics prohibits the so-called perpetual motion machines of the second kind, showing that the efficiency cannot be equal to unity, since for a circular process the temperature of the refrigerator should not be equal to 0. The second law of thermodynamics is a postulate that cannot be proven within the framework of thermodynamics. It was created on the basis of a generalization of experimental facts and received numerous experimental confirmations. 43.Effective scattering cross section. Average free path of molecules. Mean free path of molecules Let us assume that all molecules except the one under consideration are motionless. We will consider the molecules to be spheres with diameter d. Collisions will occur whenever the center of a stationary molecule is at a distance less than or equal to d from the straight line along which the center of the molecule in question is moving. During collisions, the molecule changes the direction of its movement and then moves in a straight line until the next collision. Therefore, the center of a moving molecule, due to collisions, moves along a broken line (Fig. 1).
| rice. 1 |
The molecule will collide with all stationary molecules whose centers are located within a broken cylinder with a diameter of 2d. In a second, a molecule travels a distance equal to . Therefore, the number of collisions occurring during this time is equal to the number of molecules whose centers fall inside a broken cylinder having a total length and radius d. Let us take its volume to be equal to the volume of the corresponding straightened cylinder, i.e. equal to If there are n molecules in a unit volume of gas, then the number of collisions of the molecule in question in one second will be equal to
 | (3.1.2) |
In reality, all molecules move. Therefore, the number of collisions in one second will be somewhat larger than the obtained value, since due to the movement of surrounding molecules, the molecule in question would experience a certain number of collisions even if it itself remained motionless. The assumption of the immobility of all molecules that the molecule in question collides with will be removed if in formula (3.1.2) instead of the average speed we represent the average speed of the relative motion of the molecule under consideration. In fact, if the incident molecule moves with an average relative speed , then the molecule it collides with turns out to be at rest, as was assumed when formula (3.1.2) was obtained. Therefore, formula (3.1.2) should be written in the form:
Since the angles and velocities and encountered by the molecules are obviously independent random variables, then the average
Taking into account the last equality, formula (3.1.4) can be rewritten as:
Mean free path of a molecule is the average distance (denoted by λ) that a particle travels during its free path from one collision to the next.
The mean free path of each molecule is different, therefore, in kinetic theory the concept of mean free path is introduced (<λ>). Magnitude<λ>is a characteristic of the entire set of gas molecules at given values of pressure and temperature.
Where σ is the effective cross section of the molecule, n is the concentration of molecules.
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 that exceeds 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 strictly.
Let us first consider a heat engine operating in a reversible cycle with a real gas. The cycle can be anything, 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 operate with a common heater and a common refrigerator. Let the Carnot machine operate in a reverse cycle (like a refrigeration machine), and let the other machine operate in a forward cycle (Fig. 5.18). The heat engine performs work equal to, according to formulas (5.12.3) and (5.12.5):
A 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 done on it
(5.12.12)
Since by condition η" > η , That A" > A. Therefore, a heat engine can drive a refrigeration machine, and there will still be an excess of work left. This excess work is done by heat taken from one source. After all, heat is not transferred to the refrigerator when two machines operate 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 a Carnot machine in a forward cycle. We will again come to a contradiction with the second law of thermodynamics. Consequently, two machines operating on reversible cycles have the same efficiency: η " = η .
It’s a different matter if the second machine operates on an irreversible cycle. If we assume η "
>
η ,
then we will again come to a contradiction with the second law of thermodynamics. However, the assumption t|"< 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 value of heat engines. It shows that the higher the temperature of the heater and the lower the temperature of the refrigerator, the more efficient a heat engine is. Only at a refrigerator temperature equal to absolute zero does η = 1.
But the temperature of the refrigerator practically cannot be much lower than the ambient temperature. You can increase the heater temperature. However, any material (solid body) has limited heat resistance, or heat resistance. When heated, it gradually loses its elastic properties, and at a sufficiently high temperature it melts.
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 incomplete combustion, etc. Real opportunities for increasing efficiency here still remain great. Thus, 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 efficiency value is:
The actual efficiency value due to various types of energy losses is approximately 40%. The maximum efficiency - about 44% - is achieved by 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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