The main value of the received Carnot formulas(5.12.2) 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 value thermal efficiency 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%. Maximum efficiency - about 44% - have engines internal combustion.
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.
Historically, the emergence of thermodynamics as a science was associated with the practical task of creating an efficient heat engine(thermal engine).
heat engine
A heat engine is a device that performs work due to the heat supplied to the engine. This machine is periodic.
The heat engine includes the following mandatory elements:
- working fluid (usually gas or steam);
- heater;
- fridge.
Figure 1. The cycle of operation of a heat engine. Author24 - online exchange of student papers
In Fig. 1, we depict the cycle according to which a heat engine can operate. In this cycle:
- gas expands from volume $V_1$ to volume $V_2$;
- the gas is compressed from volume $V_2$ to volume $V_1$.
In order to get more than zero work done by a gas, the pressure (and hence the temperature) must be greater during expansion than during compression. For this purpose, the gas receives heat in the process of expansion, and during compression, heat is taken away from the working fluid. From this, he will conclude that, in addition to the working fluid, two more external bodies must be present in the heat engine:
- a heater that gives off heat to the working fluid;
- refrigerator, a body that takes heat from the working fluid during compression.
After the cycle is completed, the working body and all mechanisms of the machine return to their previous state. This means that the change in the internal energy of the working fluid is zero.
Figure 1 indicates that during the expansion process, the working fluid receives an amount of heat equal to $Q_1$. In the process of compression, the working fluid gives the cooler an amount of heat equal to $Q_2$. Therefore, in one cycle, the amount of heat received by the working fluid is:
$\Delta Q=Q_1-Q_2 (1).$
From the first law of thermodynamics, given that in a closed cycle $\Delta U=0$, the work done by the working body is:
$A=Q_1-Q_2 (2).$
To organize repeated cycles of a heat engine, it is necessary that it give up part of its heat to the refrigerator. This requirement is in agreement with the second law of thermodynamics:
It is impossible to create a perpetual motion machine that periodically completely transforms the heat received from a certain source completely into work.
So, even for an ideal heat engine, the amount of heat transferred to the refrigerator cannot be equal to zero, there is a lower limit of $Q_2$.
heat engine efficiency
It is clear that how efficiently a heat engine works should be assessed, taking into account the completeness of the conversion of the heat received from the heater into the work of the working fluid.
The parameter that shows the efficiency of a heat engine is the coefficient of performance (COP).
Definition 1
The efficiency of a heat engine is the ratio of the work performed by the working fluid ($A$) to the amount of heat that this body receives from the heater ($Q_1$):
$\eta=\frac(A)(Q_1)(3).$
Taking into account the expression (2) the efficiency of the heat engine, we find as:
$\eta=\frac(Q_1-Q_2)(Q_1)(4).$
Relation (4) shows that the efficiency cannot be greater than one.
Chiller efficiency
Let's reverse the cycle shown in Fig. one.
Remark 1
Inverting a loop means changing the direction of the loop.
As a result of cycle inversion, we obtain the cycle of the refrigeration machine. This machine receives heat $Q_2$ from a body with a low temperature and transfers it to a heater with a higher temperature, the amount of heat $Q_1$, and $Q_1>Q_2$. The work done on the working body is $A'$ per cycle.
The efficiency of our refrigerator is determined by a coefficient, which is calculated as:
$\tau =\frac(Q_2)(A")=\frac(Q_2)(Q_1-Q_2)\left (5\right).$
Efficiency of reversible and irreversible heat engine
The efficiency of an irreversible heat engine is always less than the efficiency of a reversible machine when the machines operate with the same heater and cooler.
Consider a heat engine consisting of:
- a cylindrical vessel that is closed by a piston;
- gas under the piston;
- heater;
- refrigerator.
- The gas receives some heat $Q_1$ from the heater.
- The gas expands and pushes the piston, doing the work $A_+0$.
- The gas is compressed, heat $Q_2$ is transferred to the refrigerator.
- Work is done on the working body $A_-
The work done by the working body per cycle is equal to:
To fulfill the condition of reversibility of processes, they must be carried out very slowly. In addition, it is necessary that there is no friction of the piston against the walls of the vessel.
Let us denote the work done in one cycle by a reversible heat engine as $A_(+0)$.
Let's execute the same cycle with high speed and in the presence of friction. If the gas expansion is carried out quickly, its pressure near the piston will be less than if the gas is expanded slowly, since the rarefaction that occurs under the piston spreads to the entire volume at a finite speed. In this regard, the work of the gas in an irreversible increase in volume is less than in a reversible one:
If you compress the gas quickly, the pressure near the piston is greater than when you compress it slowly. This means that the value of the negative work of the working fluid in irreversible compression is greater than in reversible one:
We obtain that the work of gas in the cycle $A$ of an irreversible machine, calculated by formula (5), performed due to the heat received from the heater, will be less than the work performed in the cycle by a reversible heat engine:
The friction present in an irreversible heat engine leads to the transfer of part of the work done by the gas into heat, which reduces the efficiency of the engine.
So, we can conclude that the efficiency of a heat engine of a reversible machine is greater than that of an irreversible one.
Remark 2
The body with which the working fluid exchanges heat will be called a heat reservoir.
A reversible heat engine completes a cycle in which there are sections where the working fluid exchanges heat with a heater and a refrigerator. The process of heat exchange is reversible only if, upon receiving heat and returning it during the return stroke, the working fluid has the same temperature, equal to the temperature of the thermal reservoir. More precisely, the temperature of the body that receives heat must be a very small amount less than the temperature of the reservoir.
Such a process can be an isothermal process that occurs at the temperature of the reservoir.
For a heat engine to function, it must have two heat reservoirs (a heater and a cooler).
The reversible cycle, which is carried out in the heat engine by the working fluid, must be composed of two isotherms (at the temperatures of the thermal reservoirs) and two adiabats.
Adiabatic processes occur without heat exchange. In adiabatic processes, the gas (working fluid) expands and contracts.
A thermal engine is an engine that performs work at the expense of a source of thermal energy.
Thermal energy ( Q heater) from the source is transferred to the engine, while part of the received energy the engine spends on doing work W, unspent energy ( Q refrigerator) is sent to a refrigerator, the role of which can be performed, for example, by ambient air. The heat engine can only work if the temperature of the refrigerator is less than the temperature of the heater.
The coefficient of performance (COP) of a heat engine can be calculated by the formula: Efficiency = W/Q ng.
Efficiency = 1 (100%) if all thermal energy is converted into work. Efficiency=0 (0%) if no thermal energy is converted into work.
The efficiency of a real heat engine lies in the range from 0 to 1, the higher the efficiency, the more efficient the engine.
Q x / Q ng \u003d T x / T ng Efficiency \u003d 1- (Q x / Q ng) Efficiency \u003d 1- (T x / T ng)
Considering the third law of thermodynamics, which states that the temperature of absolute zero (T=0K) cannot be reached, we can say that it is impossible to develop a heat engine with efficiency=1, since T x >0 is always.
The efficiency of the heat engine will be the greater, the higher the temperature of the heater, and the lower the temperature of the refrigerator.
Physics, grade 10
Lesson 25 Efficiency of heat engines
The list of questions considered in the lesson:
1) The concept of a heat engine;
2) The device and principle of operation of a heat engine;
3) efficiency of the heat engine;
4) Carnot cycle.
Related Glossary
Heat engine - a device in which the internal energy of the fuel is converted into mechanical energy.
efficiency ( coefficient of performance) is the ratio of the useful work done by this engine to the amount of heat received from the heater.
Internal combustion engine- an engine in which fuel burns directly in the working chamber (inside) of the engine.
Jet engine- an engine that creates the traction force necessary for movement by converting the internal energy of the fuel into the kinetic energy of the jet stream of the working fluid.
Carnot cycle is an ideal circular process consisting of two adiabatic and two isothermal processes.
Heater- a device from which the working body receives energy, part of which is used to perform work.
Fridge- a body that absorbs part of the energy of the working body (environment or special devices for cooling and condensing exhaust steam, i.e. capacitors).
working body- a body that, when expanding, does work (it is a gas or steam)
Basic and additional literature on the topic of the lesson:
1. Myakishev G.Ya., Bukhovtsev B.B., Sotsky N.N. Physics. Grade 10. Textbook for general educational organizations M.: Education, 2017. - S. 269 - 273.
2. Rymkevich A.P. Collection of problems in physics. 10-11 class. -M.: Bustard, 2014. - S. 87 - 88.
Open electronic resources on the topic of the lesson
Theoretical material for self-study
Tales and myths of different nations testify that people have always dreamed of moving quickly from one place to another or quickly doing this or that work. To achieve this goal, devices were needed that could do work or move in space. Observing the world around them, the inventors came to the conclusion that in order to facilitate labor and move quickly, it is necessary to use the energy of other bodies, for example, water, wind, etc. Is it possible to use the internal energy of gunpowder or another type of fuel for your own purposes? If we take a test tube, pour water into it, close it with a stopper and heat it up. When heated, the water will boil, and the resulting water vapor will push out the cork. The steam expands and does work. In this example, we see that the internal energy of the fuel has been converted into the mechanical energy of the moving plug. When replacing the cork with a piston capable of moving inside the tube, and the tube itself with a cylinder, we will get the simplest heat engine.
Heat engine - A heat engine is a device in which the internal energy of a fuel is converted into mechanical energy.
Recall the structure of the simplest internal combustion engine. An internal combustion engine consists of a cylinder inside which a piston moves. The piston is connected to the crankshaft by means of a connecting rod. There are two valves at the top of each cylinder. One of the valves is called the inlet and the other is called the outlet. To ensure a smooth piston stroke on crankshaft reinforced heavy flywheel.
The working cycle of an internal combustion engine consists of four cycles: intake, compression, power stroke, exhaust.
During the first stroke, the intake valve opens while the exhaust valve remains closed. The downward moving piston sucks into the cylinder combustible mixture.
In the second stroke, both valves are closed. The upward moving piston compresses the combustible mixture, which heats up during compression.
In the third stroke, when the piston is in the upper position, the mixture is ignited by an electric spark of a candle. The ignited mixture forms hot gases, the pressure of which is 3-6 MPa, and the temperature reaches 1600-2200 degrees. The pressure force pushes the piston down, the movement of which is transmitted to the crankshaft with a flywheel. Having received a strong push, the flywheel will continue to rotate by inertia, ensuring the movement of the piston during subsequent strokes. During this stroke, both valves remain closed.
In the fourth stroke, the exhaust valve opens and the exhaust gases are pushed out by the moving piston through the muffler (not shown in the figure) into the atmosphere.
Any heat engine includes three main elements: a heater, a working fluid, a refrigerator.
To determine the efficiency of a heat engine, the concept of efficiency is introduced.
Efficiency is the ratio of the useful work done by a given engine to the amount of heat received from the heater.
Q 1 - the amount of heat received from heating
Q 2 - the amount of heat given to the refrigerator
is the work done by the engine per cycle.
This efficiency is real, i.e. just this formula is used to characterize real heat engines.
Knowing the power N and the operating time t of the engine, the work done per cycle can be found by the formula
Transfer of the unused part of the energy to the refrigerator.
In the 19th century, as a result of work on heat engineering, the French engineer Sadi Carnot proposed another way to determine the efficiency (through thermodynamic temperature).
The main meaning of this formula is that any real heat engine operating with a heater at temperature T 1 and a refrigerator at temperature T 2 cannot have an efficiency that exceeds the efficiency of an ideal heat engine. Sadi Carnot, figuring out in which closed process the heat engine will have the maximum efficiency, suggested using a cycle consisting of 2 adiabatic and 2 isothermal processes
The Carnot cycle is the most efficient cycle with maximum efficiency.
There is no heat engine that has an efficiency of 100% or 1.
The formula gives a theoretical limit for the maximum value of the 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 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.
Increasing the efficiency of heat engines and bringing it closer to the maximum possible is the most important technical challenge.
Heat engines - steam turbines, are also installed at all nuclear power plants to produce steam high temperature. Heat engines are mainly used in all major types of modern transport: in automobiles - piston engines internal combustion; on the water - internal combustion engines and steam turbines; on the railway - diesel locomotives with diesel plants; in aviation - piston, turbojet and jet engines.
Let's compare performance characteristics thermal engines.
Steam engine - 8%.
Steam turbine - 40%.
Gas turbine - 25-30%.
Internal combustion engine - 18-24%.
Diesel engine - 40–44%.
Jet engine - 25%.
The widespread use of heat engines does not pass without a trace for the environment: the amount of oxygen gradually decreases and the amount of carbon dioxide in the atmosphere increases, the air is polluted with chemical compounds harmful to human health. There is a threat of climate change. Therefore, finding ways to reduce environmental pollution is one of the most urgent scientific and technical problems today.
Examples and analysis of problem solving
1 . What is the average power developed by a car engine if, at a speed of 180 km/h, gasoline consumption is 15 liters per 100 kilometers and the engine efficiency is 25%?
In order for the engine to do work, a pressure difference is needed on both sides of the engine piston or turbine blades. In all heat engines, this pressure difference is achieved by increasing the temperature of the working fluid by hundreds of degrees compared to the ambient temperature. This increase in temperature occurs during the combustion of fuel.
The working fluid for all heat engines is a gas (see § 3.11), which does work during expansion. Let us denote the initial temperature of the working fluid (gas) through T 1 . This temperature in steam turbines or machines is acquired by steam in a steam boiler. In internal combustion engines and gas turbines, the temperature increase occurs when fuel is burned inside the engine itself. Temperature T 1 called the heater temperature.
The role of the refrigerator
As work is done, the gas loses energy and inevitably cools to a certain temperature. T 2 . This temperature cannot be lower than the ambient temperature, otherwise the gas pressure will become less than atmospheric pressure and the engine will not be able to work. Usually temperature T 2 slightly above ambient temperature. It is called the temperature of the refrigerator. The refrigerator is the atmosphere or special devices for cooling and condensing the exhaust steam - condensers. In the latter case, the temperature of the refrigerator may be somewhat lower than the temperature of the atmosphere.
Thus, in the engine, the working fluid during expansion cannot give all its internal energy to do work. Part of the energy is inevitably transferred to the atmosphere (refrigerator) along with exhaust steam or exhaust gases from internal combustion engines and gas turbines. This part of internal energy is irretrievably lost. This is exactly what Kelvin's second law of thermodynamics says.
A schematic diagram of a heat engine is shown in Figure 5.15. The working body of the engine receives the amount of heat during the combustion of fuel Q 1 , does the job BUT" and transfers the amount of heat to the refrigerator | Q 2 | <| Q 1 |.
Heat engine efficiency
According to the law of conservation of energy, the work done by the engine is
(5.11.1)
where Q 1 - the amount of heat received from the heater, a Q 2 - the amount of heat given to the refrigerator.
The efficiency of a heat engine is the ratio of work BUT", performed by the engine, to the amount of heat received from the heater:
(5.11.2)
In a steam turbine, the heater is a steam boiler, and in internal combustion engines, the products of combustion of the fuel themselves.
Since in all engines some amount of heat is transferred to the refrigerator, then η< 1.
The use of heat engines
Of greatest importance is the use of heat engines (mainly powerful steam turbines) in thermal power plants, where they drive the rotors of electric current generators. About 80% of all electricity in our country is generated at thermal power plants.
Thermal engines (steam turbines) are also installed in nuclear power plants. At these stations, the energy of atomic nuclei is used to produce high-temperature steam.
Heat engines are predominantly used in all major types of modern transport. On automobiles, piston internal combustion engines with an external formation of a combustible mixture (carburetor engines) and engines with the formation of a combustible mixture directly inside the cylinders (diesels) are used. The same engines are installed on tractors.
On rail transport until the middle of the 20th century. the main engine was a steam engine. Now diesel locomotives and electric locomotives are mainly used. But electric locomotives also receive energy from thermal engines of power plants.
In water transport, both internal combustion engines and powerful turbines for large ships are used.
In aviation, piston engines are installed on light aircraft, and turboprop and jet engines, which also belong to heat engines, are installed on huge liners. Jet engines are also used in space rockets.
Modern civilization is unthinkable without heat engines. We would not have cheap electricity and would be deprived of all types of modern high-speed transport.