A thermal engine is an engine that performs work using a source of thermal energy.
Thermal energy ( Heater Q) is transferred from the source to the engine, and the engine spends part of the received energy to perform work W, unspent energy ( refrigerator Q) is sent to the refrigerator, the role of which can be played, for example, by the surrounding air. The heat engine can only operate 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 using 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 ranges from 0 to 1; the higher the efficiency, the more efficient the engine.
Q x /Q ng = T x /T ng Efficiency = 1-(Q x /Q ng) Efficiency = 1-(T x /T ng)
Considering the third law of thermodynamics, which states that it is impossible to reach the temperature of absolute zero (T=0K), we can say that it is impossible to develop a heat engine with efficiency=1, since Tx is always >0.
The higher the temperature of the heater and the lower the temperature of the refrigerator, the greater the efficiency of a heat engine.
The work done by the engine is:
This process was first considered by the French engineer and scientist N. L. S. Carnot in 1824 in the book “Reflections on the driving force of fire and on machines capable of developing this force.”
The goal of Carnot's research was to find out the reasons for the imperfection of heat engines of that time (they had an efficiency of ≤ 5%) and to find ways to improve them.
The Carnot cycle is the most efficient of all. Its efficiency is maximum.
The figure shows the thermodynamic processes of the cycle. During isothermal expansion (1-2) at temperature T 1 , work is done due to a change in the internal energy of the heater, i.e. due to the supply of heat to the gas Q:
A 12 = Q 1 ,
Gas cooling before compression (3-4) occurs during adiabatic expansion (2-3). Change in internal energy ΔU 23 during an adiabatic process ( Q = 0) is completely converted into mechanical work:
A 23 = -ΔU 23 ,
The gas temperature as a result of adiabatic expansion (2-3) drops to the temperature of the refrigerator T 2 < T 1 . In process (3-4), the gas is isothermally compressed, transferring the amount of heat to the refrigerator Q 2:
A 34 = Q 2,
The cycle ends with the process of adiabatic compression (4-1), in which the gas is heated to a temperature T 1.
Maximum efficiency value of ideal gas heat engines according to the Carnot cycle:
.
The essence of the formula is expressed in the proven WITH. Carnot's theorem that the efficiency of any heat engine cannot exceed the efficiency of a Carnot cycle carried out at the same temperature of the heater and refrigerator.
Topic: “The principle of operation of a heat engine. Thermal engine with the highest efficiency."
Form: Combined lesson using computer technology.
Goals:
Lesson plan.
No. |
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. Diagram and structure of a heat engine, operating principle, 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 heat engine model. |
|
| 6 | Summarizing. Homework § 33, problems No. 700 and No. 697 (Stepanova) |
Theoretical material
Since ancient times, man has wanted to be free from physical effort or to ease it when moving something, to have more strength and speed.
Legends were created about airplane carpets, seven-league boots and wizards carrying a person to distant lands with the wave of a wand. When carrying heavy loads, people invented carts because it’s easier to roll. Then they adapted animals - oxen, deer, dogs, and most of all horses. This is how carts and carriages appeared. In carriages, people sought comfort, improving them more and more.
The desire of people to increase speed also accelerated the change of events in the history of transport development. From the Greek “autos” - “oneself” and the Latin “mobilis” - “mobile”, the adjective “self-propelled”, literally “auto-mobile”, was formed in European languages.
It applied to watches, automatic dolls, to all sorts of mechanisms, in general, to everything that served as a kind of 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 a car started from the first “gasoline cars” with an internal combustion engine, invented and built in 1885-1886? As if forgetting about steam and battery (electric) crews. The fact is that the internal combustion engine made a real revolution in transport technology. For a long time, it turned out to be the most consistent with the idea of a car and therefore retained its dominant position for a long time. The share of vehicles with internal combustion engines today accounts for more than 99.9% of global road transport.<Annex 1 >
Main parts of a heat engine
In modern technology, mechanical energy is obtained mainly from the internal energy of the fuel. Devices in which internal energy is converted into mechanical energy are called heat engines.<Appendix 2 >
To perform work by burning fuel in a device called a heater, you can use a cylinder in which gas is heated and expanded and moves a piston.<Appendix 3 > The gas whose expansion 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 operate continuously, it is necessary that the piston, after expanding the gas, returns to its original position each time, compressing the gas to its original state. Compression of a gas can only occur under the influence of an external force, which in this case does work (the gas pressure force in this case does negative work). After this, gas expansion and compression processes can occur again. This means that the operation of a heat engine must consist of periodically repeating processes (cycles) of expansion and compression.
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 gas during compression is negative (since A.F.< 0
) and is numerically equal to the area of the figure CDEF. The useful work for this cycle is numerically equal to the difference in the areas under the curves AB And CD(shaded in the picture).
The presence of a heater, working fluid and 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 part of this amount of heat, equal in modulus |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.
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 equal to V 1.
Let's bring the cylinder into contact with the heater (Figure 2) and give the gas the opportunity to expand isothermally and do work . The gas receives a certain amount of heat from the heater Q 1. This process is graphically represented by an isotherm (curve AB).
When the volume of gas becomes equal to a certain value V 1'< V 2 ,
the bottom of the cylinder is isolated from the heater ,
After this, the gas expands adiabatically to the volume V 2, corresponding to the maximum possible stroke of the piston in the cylinder (adiabatic Sun). In this case, the gas is cooled to a temperature T 2< 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 a refrigerator ,
and compress the gas by 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 a certain intermediate volume V 2 '>V 1(isotherm CD). In this case, the gas gives off some heat to the refrigerator Q2, equal to the work of compression performed on it. After this, the gas is compressed adiabatically to a volume V 1, at the same time its temperature rises to T 1(adiabatic D.A.). Now the gas has returned to its original state, in which its volume is equal to V 1, temperature - T1, pressure - p 1, and the cycle can be repeated again.
So, on the site ABC gas does work (A > 0), and on the site CDA work done on the gas (A< 0).
At the sites Sun And AD work is done only by changing the internal energy of the gas. Since the change in internal energy UBC = –UDA, then the work during adiabatic processes is equal: ABC = –ADA. Consequently, the total work done per cycle is determined by the difference in work done during isothermal processes (sections AB And CD). Numerically, this work is equal to the area of the 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, 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 refrigerators):
The formula shows that the higher the heater temperature and the lower the refrigerator temperature, the greater the engine efficiency.
Problem No. 703
The engine operates according to the Carnot cycle. How will the efficiency of a heat engine change if, at a constant refrigerator temperature of 17 o C, the heater temperature is increased from 127 to 447 o C?
Problem No. 525
Determine the efficiency of a tractor engine, which required 1.5 kg of fuel with a specific heat of combustion of 4.2 · 107 J/kg to perform work of 1.9 × 107 J.
Taking a computer test on the topic.<Appendix 4 > Working with a heat engine model.
« Physics - 10th grade"
To solve problems, you need to use known expressions for determining the efficiency of heat engines and keep in mind that expression (13.17) is valid only for an ideal heat engine.
Task 1.
In the boiler of a steam engine the temperature is 160 °C, and the temperature of the refrigerator is 10 °C.
What is the maximum work that a machine can theoretically perform if coal weighing 200 kg with a specific heat of combustion of 2.9 10 7 J/kg is burned in a furnace with an efficiency of 60%?
Solution.
The maximum work can be done by an ideal heat engine operating according to the Carnot cycle, the efficiency of which is η = (T 1 - T 2)/T 1, where T 1 and T 2 are the absolute temperatures of the heater and refrigerator. For any heat engine, the efficiency is determined by the formula η = A/Q 1, where A is the work performed by the heat engine, Q 1 is the amount of heat received by the machine from the heater.
From the conditions of the problem it is clear that Q 1 is part of the amount of heat released during fuel combustion: Q 1 = η 1 mq.
Then where does A = η 1 mq(1 - T 2 /T 1) = 1.2 10 9 J.
Task 2.
A steam engine with a power of N = 14.7 kW consumes fuel weighing m = 8.1 kg per 1 hour of operation, with a specific heat of combustion q = 3.3 10 7 J/kg.
Boiler temperature 200 °C, refrigerator 58 °C.
Determine the efficiency of this machine and compare it with the efficiency of an ideal heat engine.
Solution.
The efficiency of a heat engine is equal to the ratio of the completed mechanical work A to the expended amount of heat Qlt released during fuel combustion.
Amount of heat Q 1 = mq.
Work done during the same time A = Nt.
Thus, η = A/Q 1 = Nt/qm = 0.198, or η ≈ 20%.
For an ideal heat engine 
η < η ид.
Task 3.
An ideal heat engine with efficiency η operates in a reverse cycle (Fig. 13.15).
What is the maximum amount of heat that can be taken from the refrigerator by performing mechanical work A?
Since the refrigeration machine operates in a reverse cycle, in order for heat to transfer from a less heated body to a more heated one, it is necessary for external forces to do positive work.
Schematic diagram of a refrigeration machine: a quantity of heat Q 2 is taken from the refrigerator, work is done by external forces and a quantity of heat Q 1 is transferred to the heater.
Hence, 
Q 2 = Q 1 (1 - η), Q 1 = A/η.
Finally, Q 2 = (A/η)(1 - η).
Source: “Physics - 10th grade”, 2014, textbook Myakishev, Bukhovtsev, Sotsky
Fundamentals of thermodynamics. Thermal phenomena - Physics, textbook for grade 10 - Classroom physics
« 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 and solar powered vehicles are already being produced.
