The efficiency of a heat engine is called. How heat engines are designed and how they work. Previously, nature threatened man, but now man threatens nature.
Heat engine – a device that converts the internal energy of burned fuel into mechanical energy. Types of heat engines : 1) internal combustion engines: a) diesel, b) carburetor; 2) steam engines; 3) turbines: a) gas, b) steam.
All named heat engines have a different design, but consist of three main parts : heater, working fluid and refrigerator. Heater provides heat to the engine. Working fluid converts part of the received heat into mechanical work. Fridge takes away some of the heat from the working fluid.
T 1– heater temperature;
T 2– refrigerator temperature;
Q 1– heat received
from the heater;
Q 2- heat given
refrigerator;
A"- work done
engine.
The operation of any heat engine consists of repeating cyclic processes - cycles. Cycle is a sequence of thermodynamic processes as a result of which the system returns to its initial state.
Efficiency factor (efficiency)
of a heat engine is the ratio of the work performed by the engine to the amount of heat received from the heater: 
.
French engineer Sadi Carnot considered ideal heat engine
with an ideal gas as a working fluid. He found the optimal ideal cycle of a heat engine, consisting of two isothermal and two adiabatic reversible processes - Carnot cycle
. The efficiency of such a heat engine with a heater at temperature and a refrigerator at temperature: 
. Regardless of the design, choice of working fluid and type of processes in a heat engine, its efficiency cannot be greater than the efficiency of a heat engine operating according to the Carnot cycle and having the same heater and refrigerator temperatures as the given heat engine.
The efficiency of heat engines is low, so the most important technical task is to increase it. Heat engines have two significant disadvantages. First, most heat engines use fossil fuels, the extraction of which is rapidly depleting the planet's resources. Secondly, as a result of fuel combustion, a huge amount of harmful substances is released into the environment, which creates significant environmental problems.
The study of the question of the maximum efficiency of heat engines is associated with the discovery in 1850 by the German physicist R. Clasius second law of thermodynamics : a process in which heat would spontaneously transfer from colder bodies to hotter bodies is impossible.
Physical quantities and their units of measurement:
| Name value | Designation | Unit | Formula |
| Relative molecular weight | M r(um er) | dimensionless quantity | |
| Mass of one molecule (atom) | m 0 | kg | |
| Weight | m | kg | |
| Molar mass | M |  |
|
| Quantity of substance | ν (nude) | mole(mol) | ; |
| Number of particles | N(en) | dimensionless quantity | |
| Pressure | p(peh) | Pa(pascal) | |
| Concentration | n(en) | ||
| Volume | V(ve) | ||
| Average kinetic energy forward movement molecules | J(joule) | ||
| Temperature in Celsius | t | °C | |
| Kelvin temperature | T | TO(kelvin) | |
| Mean square speed of molecules | |||
| Surface tension | σ (sigma) | ||
| Absolute humidity | ρ (ro) | ||
| Relative humidity | φ (fi) | % | |
| Internal energy | U(y) | J(joule) | |
| Job | A(A) | J(joule) | |
| Quantity of heat | Q(ku) | J(joule) |
Since ancient times, people have tried to convert energy into mechanical work. They transformed kinetic energy wind, potential energy of water, etc. Beginning in the 18th century, machines began to appear that converted the internal energy of fuel into work. Such machines worked thanks to heat engines.
A heat engine is a device that converts thermal energy into mechanical work due to expansion (most often of gases) due to high temperature.
Any heat engines have the following components:
- A heating element. Body with high temperature relatively environment.
- Working fluid. Since expansion provides the work, this element should expand well. Typically gas or steam is used.
- Cooler. Body with low temperature.
The working fluid receives thermal energy from the heater. As a result, it begins to expand and do work. In order for the system to perform work again, it must be returned to its original state. Therefore, the working fluid is cooled, that is, excess thermal energy, as if dumped into the cooling element. And the system returns to its original state, then the process repeats again.
Efficiency calculation
To calculate the efficiency, we introduce the following notation:
Q 1 – Amount of heat received from the heating element
A’– Work done by the working fluid
Q 2 – Amount of heat received by the working fluid from the cooler
During the cooling process, the body transfers heat, so Q 2< 0.
The operation of such a device is a cyclical process. This means that after committing full cycle, the internal energy will return to its original state. Then, according to the first law of thermodynamics, the work done by the working fluid will be equal to the difference in the amount of heat received from the heater and the heat received from the cooler:
Q 2 is a negative value, so it is taken modulo
Efficiency is expressed as the ratio of useful work to the total work performed by the system. In this case, the total work will be equal to the amount of heat that is spent on heating the working fluid. All energy expended is expressed through Q 1.
Modern realities assume widespread use of heat engines. Numerous attempts to replace them with electric motors have so far failed. Problems associated with the accumulation of electricity in autonomous systems are difficult to solve.
The problems of manufacturing technology for electric power batteries, taking into account their long-term use, are still relevant. The speed characteristics of electric vehicles are far from those of cars with internal combustion engines.
The first steps to create hybrid engines can significantly reduce harmful emissions in megacities, solving environmental problems.
A little history
The possibility of converting steam energy into motion energy was known in ancient times. 130 BC: The philosopher Heron of Alexandria presented a steam toy - aeolipile - to the audience. The sphere filled with steam began to rotate under the influence of the jets emanating from it. This prototype of modern steam turbines was not used in those days.
For many years and centuries, the philosopher's developments were considered just a fun toy. In 1629, the Italian D. Branchi created an active turbine. The steam drove a disk equipped with blades.
From that moment on, the rapid development of steam engines began.
Heat engine
The conversion of fuel into the energy of movement of machine parts and mechanisms is used in heat engines.
The main parts of the machines: heater (system for obtaining energy from the outside), working fluid (performs a useful action), refrigerator.
The heater is designed to ensure that the working fluid accumulates a sufficient supply of internal energy to perform useful work. The refrigerator removes excess energy.
The main characteristic of efficiency is called the efficiency of heat engines. This value shows how much of the energy spent on heating is spent on doing useful work. The higher the efficiency, the more profitable the operation of the machine, but this value cannot exceed 100%.
Efficiency calculation
Let the heater acquire from the outside energy equal to Q 1 . The working fluid performed work A, while the energy given to the refrigerator amounted to Q 2.
Based on the definition, we calculate the efficiency value:
η= A / Q 1 . Let's take into account that A = Q 1 - Q 2.
Hence, the efficiency of the heat engine, the formula of which is η = (Q 1 - Q 2) / Q 1 = 1 - Q 2 / Q 1, allows us to draw the following conclusions:
- Efficiency cannot exceed 1 (or 100%);
- For maximum magnification this value requires either an increase in the energy received from the heater, or a decrease in the energy given to the refrigerator;
- increasing the heater energy is achieved by changing the quality of the fuel;
- The design features of the engines can reduce the energy given to the refrigerator.
Ideal heat engine
Is it possible to create an engine whose efficiency would be maximum (ideally equal to 100%)? The French theoretical physicist and talented engineer Sadi Carnot tried to find the answer to this question. In 1824, his theoretical calculations about processes occurring in gases were made public.
The main idea inherent in the ideal machine can be considered to carry out reversible processes with an ideal gas. We start by expanding the gas isothermally at temperature T 1 . The amount of heat required for this is Q 1. Afterwards, the gas expands without heat exchange. Having reached the temperature T 2, the gas compresses isothermally, transferring energy Q 2 to the refrigerator. The gas returns to its original state adiabatically.
The efficiency of an ideal Carnot heat engine, when accurately calculated, is equal to the ratio of the temperature difference between the heating and cooling devices to the temperature of the heater. It looks like this: η=(T 1 - T 2)/ T 1.
The possible efficiency of a heat engine, the formula of which is: η = 1 - T 2 / T 1, depends only on the temperatures of the heater and cooler and cannot be more than 100%.
Moreover, this relationship allows us to prove that the efficiency of heat engines can be equal to unity only when the refrigerator reaches temperatures. As is known, this value is unattainable.
Carnot's theoretical calculations make it possible to determine the maximum efficiency of a heat engine of any design.
The theorem proved by Carnot is as follows. Under no circumstances can an arbitrary heat engine have an efficiency greater than the same efficiency value of an ideal heat engine.
Example of problem solving
Example 1. What is the efficiency of an ideal heat engine if the heater temperature is 800 o C and the refrigerator temperature is 500 o C lower?
T 1 = 800 o C = 1073 K, ∆T = 500 o C = 500 K, η - ?
By definition: η=(T 1 - T 2)/ T 1.
We are not given the temperature of the refrigerator, but ∆T= (T 1 - T 2), hence:
η= ∆T / T 1 = 500 K/1073 K = 0.46.
Answer: Efficiency = 46%.
Example 2. Determine the efficiency of an ideal heat engine if, due to the acquired one kilojoule of heater energy, useful work of 650 J is performed. What is the temperature of the heater of the heat engine if the cooler temperature is 400 K?
Q 1 = 1 kJ = 1000 J, A = 650 J, T 2 = 400 K, η - ?, T 1 = ?
In this problem we are talking about a thermal installation, the efficiency of which can be calculated using the formula:
To determine the heater temperature, we use the formula for the efficiency of an ideal heat engine:
η = (T 1 - T 2)/ T 1 = 1 - T 2 / T 1.
After performing mathematical transformations, we get:
T 1 = T 2 /(1- η).
T 1 = T 2 /(1- A / Q 1).
Let's calculate:
η= 650 J/ 1000 J = 0.65.
T 1 = 400 K / (1 - 650 J / 1000 J) = 1142.8 K.
Answer: η= 65%, T 1 = 1142.8 K.
Real conditions
An ideal heat engine is designed with ideal processes in mind. Work is performed only in isothermal processes; its value is determined as the area limited by the graph of the Carnot cycle.
In reality, it is impossible to create conditions for the process of changing the state of a gas to occur without accompanying temperature changes. There are no materials that would exclude heat exchange with surrounding objects. The adiabatic process becomes impossible to carry out. In the case of heat exchange, the gas temperature must necessarily change.
The efficiency of heat engines created in real conditions differs significantly from the efficiency of ideal engines. Note that the processes in real engines occur so quickly that the variation in the internal thermal energy of the working substance in the process of changing its volume cannot be compensated by the influx of heat from the heater and transfer to the refrigerator.
Other heat engines
Real engines operate on different cycles:
- Otto cycle: a process with a constant volume changes adiabatically, creating a closed cycle;
- Diesel cycle: isobar, adiabatic, isochore, adiabatic;
- the process occurring at constant pressure is replaced by an adiabatic one, closing the cycle.
Create equilibrium processes in real engines (to bring them closer to ideal ones) under conditions modern technology does not seem possible. The efficiency of heat engines is significantly lower, even taking into account the same temperature conditions as in an ideal thermal installation.
But the role of the efficiency calculation formula should not be reduced, since it is precisely this that becomes the starting point in the process of working to increase the efficiency of real engines.
Ways to change efficiency
When comparing ideal and real heat engines, it is worth noting that the temperature of the refrigerator of the latter cannot be any. Usually the atmosphere is considered a refrigerator. The temperature of the atmosphere can only be accepted in approximate calculations. Experience shows that the temperature of the coolant is equal to the temperature of the exhaust gases in the engines, as is the case in internal combustion engines (abbreviated as ICE).
ICE is the most common heat engine in our world. The efficiency of the heat engine in this case depends on the temperature created by the burning fuel. A significant difference between internal combustion engines and steam engines is the merging of the functions of the heater and the working fluid of the device in the air-fuel mixture. As the mixture burns, it creates pressure on the moving parts of the engine.
An increase in the temperature of the working gases is achieved, significantly changing the properties of the fuel. Unfortunately, this cannot be done indefinitely. Any material from which the combustion chamber of an engine is made has its own melting point. The heat resistance of such materials is the main characteristic of the engine, as well as the ability to significantly affect efficiency.
Motor efficiency values
If we consider the temperature of the working steam at the inlet of which is 800 K, and the exhaust gas - 300 K, then the efficiency of this machine is 62%. In reality, this value does not exceed 40%. This decrease occurs due to heat losses when heating the turbine casing.
The highest value of internal combustion does not exceed 44%. Increasing this value is a matter of the near future. Changing the properties of materials and fuel is a problem that the best minds of humanity are working on.
In the theoretical model of a heat engine, three bodies are considered: heater, working fluid And fridge.
Heater – a thermal reservoir (large body), the temperature of which is constant.
In each cycle of engine operation, the working fluid receives a certain amount of heat from the heater, expands and performs mechanical work. The transfer of part of the energy received from the heater to the refrigerator is necessary to return the working fluid to its original state.
Since the model assumes that the temperature of the heater and refrigerator does not change during the operation of the heat engine, then at the completion of the cycle: heating-expansion-cooling-compression of the working fluid, it is considered that the machine returns to its original state.
For each cycle, based on the first law of thermodynamics, we can write that the amount of heat Q heat received from the heater, amount of heat | Q cold| given to the refrigerator, and the work done by the working body A are related to each other by the relation:
A = Q heat – | Q cold|.
In real technical devices, which are called heat engines, the working fluid is heated by the heat released during the combustion of fuel. So, in a steam turbine of a power plant, the heater is a furnace with hot coal. In an internal combustion engine (ICE), combustion products can be considered a heater, and excess air can be considered a working fluid. They use atmospheric air or water from natural sources as a refrigerator.
Efficiency of a heat engine (machine)
Heat engine efficiency (efficiency) is the ratio of the work done by the engine to the amount of heat received from the heater:
The efficiency of any heat engine is less than unity and is expressed as a percentage. The impossibility of converting the entire amount of heat received from the heater into mechanical work is the price to pay for the need to organize a cyclic process and follows from the second law of thermodynamics.
In real heat engines, efficiency is determined by experimental mechanical power N engine and the amount of fuel burned per unit time. So, if in time t mass of fuel burned m and specific heat of combustion q, That
For vehicles, the reference characteristic is often the volume V burned fuel on the way s at mechanical engine power N and at speed. In this case, taking into account the density r of the fuel, we can write the formula for calculating the efficiency:
Second law of thermodynamics
There are several formulations second law of thermodynamics. One of them says that it is impossible to have a heat engine that would do work only due to a heat source, i.e. no refrigerator. The world's oceans could serve for him as a practically inexhaustible source of internal energy (Wilhelm Friedrich Ostwald, 1901).
Other formulations of the second law of thermodynamics are equivalent to this one.
Clausius formulation(1850): a process in which heat would spontaneously transfer from less heated bodies to more heated bodies is impossible.
Thomson's formulation(1851): a circular process is impossible, the only result of which would be the production of work by reducing the internal energy of the thermal reservoir.
Clausius formulation(1865): all spontaneous processes in a closed nonequilibrium system occur in a direction in which the entropy of the system increases; in a state of thermal equilibrium it is maximum and constant.
Boltzmann formulation(1877): a closed system of many particles spontaneously passes from a more ordered state to a less ordered one. The system cannot spontaneously leave its equilibrium position. Boltzmann introduced a quantitative measure of disorder in a system consisting of many bodies - entropy.
Efficiency of a heat engine with an ideal gas as a working fluid
If a model of the working fluid in a heat engine is given (for example, an ideal gas), then it is possible to calculate the change in the thermodynamic parameters of the working fluid during expansion and compression. This allows the efficiency of a heat engine to be calculated based on the laws of thermodynamics.
The figure shows cycles for which the efficiency can be calculated if the working fluid is an ideal gas and the parameters are specified at the transition points of one thermodynamic process to another.
|
|
Isobaric-isochoric |
|
Isochoric-adiabatic |
|
Isobaric-adiabatic |
|
Isobaric-isochoric-isothermal |
|
|
Isobaric-isochoric-linear |
Carnot cycle. Efficiency of an ideal heat engine
Highest efficiency at given heater temperatures T heater and refrigerator T hall has a heat engine, where the working fluid expands and contracts according to Carnot cycle(Fig. 2), the graph of which consists of two isotherms (2–3 and 4–1) and two adiabats (3–4 and 1–2).
Carnot's theorem proves that the efficiency of such an engine does not depend on the working fluid used, so it can be calculated using the thermodynamic relations for an ideal gas:
Environmental consequences of heat engines
The intensive use of heat engines in transport and energy (thermal and nuclear power plants) significantly affects the Earth's biosphere. Although there are scientific disputes about the mechanisms of influence of human activity on the Earth's climate, many scientists note the factors due to which such an influence can occur:
- The greenhouse effect is an increase in the concentration of carbon dioxide (a product of combustion in heaters of heat engines) in the atmosphere. Carbon dioxide transmits visible and ultraviolet radiation from the Sun, but absorbs infrared radiation going into space from the Earth. This leads to an increase in the temperature of the lower layers of the atmosphere, increased hurricane winds and global melting of ice.
- Direct impact of toxic exhaust gases on wildlife (carcinogens, smog, acid rain from combustion by-products).
- Destruction of the ozone layer during airplane flights and rocket launches. Ozone in the upper atmosphere protects all life on Earth from excess ultraviolet radiation from the Sun.
The way out of the emerging environmental crisis lies in increasing the efficiency of heat engines (the efficiency of modern heat engines rarely exceeds 30%); using serviceable engines and harmful exhaust gas neutralizers; the use of alternative energy sources (solar panels and heaters) and alternative means of transport (bicycles, etc.).
>>Physics: The principle of operation of heat engines. Coefficient of performance (efficiency) of heat engines
Internal energy reserves in 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, and to rotate the rotors of generators electric current etc. Humanity needs engines - devices capable of doing work. Most of engines on Earth are heat engines. Heat engines are devices that convert the internal energy of fuel into mechanical energy.
Operating principles 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 of the 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 T1. 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 heater temperature."
The role of the refrigerator. As work is done, the gas loses energy and inevitably cools to a certain temperature. T 2, 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 atmospheric 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 is lost.
A heat engine performs work using the internal energy of the working fluid. Moreover, in this process, heat is transferred from hotter bodies (heater) to colder ones (refrigerator).
Schematic diagram heat engine is shown in Figure 13.11.
The working fluid of the engine receives heat from the heater during fuel combustion Q 1 does work A´ and transfers the amount of heat to the refrigerator Q 2 .
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.
According to the law of conservation of energy, the work done by the engine is equal to:
Where Q 1- the amount of heat received from the heater, and Q 2- the amount of heat transferred to the refrigerator.
Coefficient of performance (efficiency) of a heat engine called work attitude 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.
The efficiency of a heat engine is proportional to the temperature difference between the heater and the refrigerator. At T 1 -T 2=0 The motor cannot run.
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 having a temperature T 1, and a refrigerator with a temperature T 2. This was first done 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. First, a vessel with gas is brought into contact with a heater, the gas expands isothermally, performing positive work, at a temperature T1, at the same time he receives the 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 transfers an amount of heat to the refrigerator Q 2, shrinking to volume V 4
Carnot obtained the following expression for the efficiency of this machine:
As one would expect, 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 any real heat engine operating with a heater having a temperature T1, and a refrigerator with a temperature T 2, cannot have an efficiency exceeding that of an ideal heat engine.
Formula (13.19) 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, η
=1.
But the temperature of the refrigerator practically cannot be 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:
Increasing the efficiency of heat engines and bringing it closer to the maximum possible is the most important technical task.
Heat engines perform work due to the difference in gas pressure on the surfaces of the pistons or turbine blades. This pressure difference is created by a temperature difference. The maximum possible efficiency is proportional to this temperature difference and inversely proportional to the absolute temperature of the heater.
A heat engine cannot operate without a refrigerator, the role of which is usually played by the atmosphere.
???
1. What device is called a heat engine?
2. What is the role of the heater, cooler and working fluid in a heat engine?
3. What is the efficiency of the engine?
4. What is the maximum efficiency value of a heat engine?
G.Ya.Myakishev, B.B.Bukhovtsev, N.N.Sotsky, Physics 10th grade
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