The operation of many types of machines is characterized by such an important indicator as the efficiency of a heat engine. Every year, engineers strive to create more advanced equipment, which, with less, would give the maximum result from its use.
Heat engine device
Before understanding what it is, it is necessary to understand how this mechanism works. Without knowing the principles of its action, it is impossible to find out the essence of this indicator. A heat engine is a device that does work by using internal energy. Any heat engine that turns into a mechanical one uses the thermal expansion of substances with increasing temperature. In solid-state engines, it is possible not only to change the volume of matter, but also the shape of the body. The operation of such an engine is subject to the laws of thermodynamics.
Operating principle
In order to understand how a heat engine works, it is necessary to consider the basics of its design. For the operation of the device, two bodies are needed: hot (heater) and cold (refrigerator, cooler). The principle of operation of heat engines (the efficiency of heat engines) depends on their type. Often, the steam condenser acts as a refrigerator, and any type of fuel that burns in the furnace acts as a heater. The efficiency of an ideal heat engine is found by the following formula:
Efficiency = (Theating - Tcold.) / Theating. x 100%.
At the same time, the efficiency of a real engine can never exceed the value obtained according to this formula. Also, this indicator will never exceed the above value. To increase the efficiency, most often increase the temperature of the heater and reduce the temperature of the refrigerator. Both of these processes will be limited by the actual operating conditions of the equipment.
During the operation of a heat engine, work is done, as the gas begins to lose energy and cools to a certain temperature. The latter is usually a few degrees above the surrounding atmosphere. This is the refrigerator temperature. Such a special device is designed for cooling with subsequent condensation of the exhaust steam. Where condensers are present, the temperature of the refrigerator is sometimes lower than the ambient temperature.
In a heat engine, the body, when heated and expanded, is not able to give all its internal energy to do work. Some of the heat will be transferred to the refrigerator along with or steam. This part of the thermal is inevitably lost. During the combustion of fuel, the working fluid receives a certain amount of heat Q 1 from the heater. At the same time, it still does work A, during which it transfers part of the thermal energy to the refrigerator: Q 2 Efficiency characterizes the efficiency of the engine in the field of energy conversion and transmission. This indicator is often measured as a percentage. Efficiency formula: η*A/Qx100%, where Q is the expended energy, A is useful work. Based on the law of conservation of energy, we can conclude that the efficiency will always be less than unity. In other words, there will never be more useful work than the energy expended on it. Engine efficiency is the ratio of useful work to the energy supplied by the heater. It can be represented as the following formula: η \u003d (Q 1 -Q 2) / Q 1, where Q 1 is the heat received from the heater, and Q 2 is given to the refrigerator. The work done by a heat engine is calculated by the following formula: A = |Q H | - |Q X |, where A is work, Q H is the amount of heat received from the heater, Q X is the amount of heat given to the cooler. |Q H | - |Q X |)/|Q H | = 1 - |Q X |/|Q H | It is equal to the ratio of the work done by the engine to the amount of heat received. Part of the thermal energy is lost during this transfer. The maximum efficiency of a heat engine is noted for the Carnot device. This is due to the fact that in this system it depends only on the absolute temperature of the heater (Тн) and cooler (Тх). The efficiency of a heat engine operating on is determined by the following formula: (Tn - Tx) / Tn = - Tx - Tn. The laws of thermodynamics made it possible to calculate the maximum efficiency that is possible. For the first time this indicator was calculated by the French scientist and engineer Sadi Carnot. He invented a heat engine that ran on ideal gas. It works on a cycle of 2 isotherms and 2 adiabats. The principle of its operation is quite simple: a heater contact is brought to the vessel with gas, as a result of which the working fluid expands isothermally. At the same time, it functions and receives a certain amount of heat. After the vessel is thermally insulated. Despite this, the gas continues to expand, but already adiabatically (without heat exchange with the environment). At this time, its temperature drops to the refrigerator. At this moment, the gas is in contact with the refrigerator, as a result of which it gives it a certain amount of heat during isometric compression. Then the vessel is again thermally insulated. In this case, the gas is adiabatically compressed to its original volume and state. Nowadays, there are many types of heat engines that operate on different principles and on different fuels. They all have their own efficiency. These include the following: An internal combustion engine (piston), which is a mechanism where part of the chemical energy of the burning fuel is converted into mechanical energy. Such devices can be gas and liquid. There are 2-stroke and 4-stroke engines. They may have a continuous duty cycle. According to the method of preparing a mixture of fuel, such engines are carburetor (with external mixture formation) and diesel (with internal). According to the types of energy converter, they are divided into piston, jet, turbine, combined. The efficiency of such machines does not exceed 0.5. Stirling engine - a device in which the working fluid is in a closed space. It is a kind of external combustion engine. The principle of its operation is based on periodic cooling/heating of the body with the production of energy due to a change in its volume. This is one of the most efficient engines. Turbine (rotary) engine with external combustion of fuel. Such installations are most often found in thermal power plants. Turbine (rotary) internal combustion engines are used at thermal power plants in peak mode. Not as common as others. A turboprop engine generates some of the thrust due to the propeller. The rest comes from exhaust gases. Its design is a rotary engine on the shaft of which a propeller is mounted. Rocket, turbojet and which receive thrust due to the return of exhaust gases. Solid state engines use a solid body as fuel. When working, it is not its volume that changes, but its shape. During operation of the equipment, an extremely small temperature difference is used. Is it possible to increase the efficiency of a heat engine? The answer must be sought in thermodynamics. It studies the mutual transformations of different types of energy. It has been established that all available mechanical, etc., is impossible. At the same time, their conversion into thermal energy occurs without any restrictions. This is possible due to the fact that the nature of thermal energy is based on the disordered (chaotic) movement of particles. The more the body heats up, the faster the molecules that make it up will move. Particle motion will become even more erratic. Along with this, everyone knows that order can be easily turned into chaos, which is very difficult to order. Since ancient times, people have tried to convert energy into mechanical work. They converted the kinetic energy of the wind, the potential energy of water, etc. Starting from the 18th century, machines began to appear that convert 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 gases) from high temperature. Any heat engines have components: 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 is, as it were, discharged into the cooling element. And the system comes to its original state, then the process repeats again. To calculate the efficiency, we introduce the following notation: Q 1 - The amount of heat received from the heating element A’– Work done by the working body Q 2 - The amount of heat received by the working fluid from the cooler In the process of cooling, the body transfers heat, so Q 2< 0. The operation of such a device is a cyclic process. This means that after a complete 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 between 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 that the system has performed. In this case, the total work will be equal to the amount of heat that is spent on heating the working fluid. All expended energy is expressed through Q 1 . Therefore, the efficiency factor is defined as. heat engine efficiency. According to the law of conservation of energy, the work done by the engine is: where is the heat received from the heater, is the heat given to the refrigerator. The efficiency of a heat engine is the ratio of the work done by the engine to the amount of heat received from the heater: Since in all engines a certain amount of heat is transferred to the refrigerator, in all cases The maximum value of the efficiency of heat engines. The French engineer and scientist Sadi Carnot (1796 1832) in his work “Reflection on the driving force of fire” (1824) set the goal: to find out under what conditions the operation of a heat engine would be most efficient, that is, under what conditions the engine would have maximum efficiency. Carnot came up with an ideal heat engine with an ideal gas as the working fluid. He calculated the efficiency of this machine operating with a temperature heater and a temperature refrigerator The main significance of this formula is, as Carnot proved, based on the second law of thermodynamics, that any real heat engine operating with a temperature heater and a temperature refrigerator cannot have an efficiency exceeding the efficiency of an ideal heat engine. Formula (4.18) gives the theoretical limit for the maximum efficiency of heat engines. It shows that the heat engine is more efficient, the higher the temperature of the heater and the lower the temperature of the refrigerator. Only when the temperature of the refrigerator is equal to absolute zero, 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 are still large here. So, for a steam turbine, the initial and final steam temperatures are approximately as follows: At these temperatures, the maximum efficiency value is: The actual value of the efficiency due to various kinds of energy losses is equal to: Increasing the efficiency of heat engines, bringing it closer to the maximum possible is the most important technical challenge. Thermal engines and nature conservation. The widespread use of heat engines in order to obtain energy that is convenient for use to the greatest extent, in comparison with all other types of production processes are associated with environmental impacts. According to the second law of thermodynamics, the production of electrical and mechanical energy, in principle, cannot be carried out without significant amounts of heat being removed to the environment. This cannot but lead to a gradual increase in the average temperature on Earth. Now the power consumption is about 1010 kW. When this power is reached, the average temperature will rise in a noticeable way (by about one degree). A further rise in temperature could pose a threat of melting glaciers and a catastrophic rise in global sea levels. But this far from exhausts the negative consequences of the use of heat engines. Furnaces of thermal power plants, internal combustion engines of automobiles, etc. continuously emit substances harmful to plants, animals and humans into the atmosphere: sulfur compounds (during the combustion of coal), nitrogen oxides, hydrocarbons, carbon monoxide (CO), etc. Special danger in this respect represent motor vehicles, the number of which is growing alarmingly, and the purification of exhaust gases is difficult. Nuclear power plants face the problem of hazardous radioactive waste disposal. In addition, the use of steam turbines at power plants requires large areas for ponds to cool the exhaust steam. With an increase in the capacity of power plants, the need for water increases sharply. In 1980, about 35% of the water supply of all sectors of the economy was required for these purposes in our country. All this poses a number of serious problems for society. Along with the most important task of increasing the efficiency of heat engines, it is necessary to carry out a number of measures to protect the environment. It is necessary to improve the efficiency of structures that prevent the emission of harmful substances into the atmosphere; achieve more complete combustion of fuel in automobile engines. Already, cars with a high content of CO in the exhaust gases are not allowed to operate. The possibility of creating electric vehicles that can compete with conventional ones and the possibility of using fuel without harmful substances in exhaust gases, for example, in engines running on a mixture of hydrogen and oxygen, are discussed. In order to save space and water resources, it is expedient to build entire complexes of power plants, primarily nuclear ones, with a closed water supply cycle. Another direction of the efforts being made is to increase the efficiency of energy use, the struggle for its savings. Solving the problems listed above is vital for humanity. And these problems with maximum success can be solved in a socialist society with a planned development of the economy on a national scale. But the organization of environmental protection requires efforts on a global scale. 1. What processes are called irreversible? 2. Name the most typical irreversible processes. 3. Give examples of irreversible processes not mentioned in the text. 4. Formulate the second law of thermodynamics. 5. If the rivers flowed backwards, would this mean a violation of the law of conservation of energy? 6. What device is called a heat engine? 7. What is the role of the heater, refrigerator and working fluid of a heat engine? 8. Why is it impossible to use the internal energy of the ocean as an energy source in heat engines? 9. What is called the efficiency of a heat engine? 10. What is the maximum possible value of the efficiency of a heat engine? Historically, the emergence of thermodynamics as a science was associated with the practical task of creating an efficient heat 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: 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: 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: 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 $Q_2$. 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. Let's reverse the cycle shown in Fig. 1. 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: $\tau =\frac(Q_2)(A")=\frac(Q_2)(Q_1-Q_2)\left (5\right).$ 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: 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 expansion of the gas 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 gas work 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. Modern realities involve the widespread operation of heat engines. Numerous attempts to replace them with electric motors have so far failed. The problems associated with the accumulation of electricity in autonomous systems are solved with great difficulty. Still relevant are the problems of technology for the manufacture of electric power accumulators, taking into account their long-term use. The speed characteristics of electric vehicles are far from those of cars on internal combustion engines. The first steps towards the creation of hybrid engines can significantly reduce harmful emissions in megacities, solving environmental problems. The possibility of converting steam energy into motion energy was known in antiquity. 130 BC: Philosopher Heron of Alexandria presented to the audience a steam toy - aeolipil. A sphere filled with steam began to rotate under the action of jets emanating from it. This prototype of modern steam turbines did not find application in those days. For many years and centuries, the development of the philosopher was considered only a fun toy. In 1629, the Italian D. Branchi created an active turbine. Steam set in motion a disk equipped with blades. From that moment began the rapid development of steam engines. The conversion of fuel into energy for the movement of parts of machines and mechanisms is used in heat engines. The main parts of machines: a heater (a system for obtaining energy from outside), a working fluid (performs a useful action), a refrigerator. The heater is designed to ensure that the working fluid has accumulated 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 what part 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%. Let the heater acquire from outside the energy equal to Q 1 . The working fluid did work A, while the energy given to the refrigerator was Q 2 . Based on the definition, we calculate the efficiency: η= A / Q 1 . We take into account that A \u003d Q 1 - Q 2. From here, the efficiency of the heat engine, the formula of which has the form η = (Q 1 - Q 2) / Q 1 = 1 - Q 2 / Q 1, allows us to draw the following conclusions: Is it possible to create such an engine, the efficiency of which 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 the processes occurring in gases were made public. The main idea behind an ideal machine is to carry out reversible processes with an ideal gas. We start with the expansion of the gas isothermally at a temperature T 1 . The amount of heat required for this is Q 1. After the gas expands without heat exchange. Having reached the temperature T 2, the gas is compressed isothermally, transferring the energy Q 2 to the refrigerator. The return of the gas to its original state is adiabatic. 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 that the heater has. 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 temperature of the heater and cooler and cannot be more than 100%. Moreover, this ratio allows us to prove that the efficiency of heat engines can be equal to unity only when the refrigerator reaches temperatures. As you know, 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. An arbitrary heat engine under no circumstances is capable of having a coefficient of efficiency greater than the similar value of the efficiency of an ideal heat engine. Example 1 What is the efficiency of an ideal heat engine if the heater temperature is 800°C and the refrigerator temperature is 500°C lower? T 1 \u003d 800 o C \u003d 1073 K, ∆T \u003d 500 o C \u003d 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), from here: η \u003d ∆T / T 1 \u003d 500 K / 1073 K \u003d 0.46. Answer: efficiency = 46%. Example 2 Determine the efficiency of an ideal heat engine if 650 J of useful work is performed due to the acquired one kilojoule of heater energy. What is the temperature of the heat engine heater if the coolant temperature is 400 K? Q 1 \u003d 1 kJ \u003d 1000 J, A \u003d 650 J, T 2 \u003d 400 K, η -?, T 1 \u003d? In this problem, we are talking about a thermal installation, the efficiency of which can be calculated by the formula: To determine the temperature of the heater, we use the formula for the efficiency of an ideal heat engine: η \u003d (T 1 - T 2) / T 1 \u003d 1 - T 2 / T 1. After performing mathematical transformations, we get: T 1 \u003d T 2 / (1- η). T 1 \u003d T 2 / (1- A / Q 1). Let's calculate: η= 650 J / 1000 J = 0.65. T 1 \u003d 400 K / (1- 650 J / 1000 J) \u003d 1142.8 K. Answer: η \u003d 65%, T 1 \u003d 1142.8 K. The ideal heat engine is designed with ideal processes in mind. Work is done only in isothermal processes, its value is defined as the area bounded by the Carnot cycle graph. In fact, it is impossible to create conditions for the process of changing the state of a gas without accompanying changes in temperature. There are no materials that would exclude heat exchange with surrounding objects. The adiabatic process is no longer possible. In the case of heat transfer, the temperature of the gas must necessarily change. The efficiency of heat engines created in real conditions differ significantly from the efficiency of ideal engines. Note that the processes in real engines are so fast 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 return to the cooler. Real engines operate on different cycles: It is not possible to create equilibrium processes in real engines (to bring them closer to ideal ones) under the conditions of modern technology. The efficiency of thermal engines is much lower, even taking into account the same temperature regimes as in an ideal thermal installation. But you should not reduce the role of the efficiency calculation formula, since it is it that becomes the starting point in the process of working to increase the efficiency of real engines. 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 to be a refrigerator. The temperature of the atmosphere can be taken only 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 internal combustion engines). ICE is the most common heat engine in our world. The efficiency of a heat engine in this case depends on the temperature created by the burning fuel. An essential difference between an internal combustion engine and steam engines is the merging of the functions of the heater and the working fluid of the device in the air-fuel mixture. Burning, the mixture creates pressure on the moving parts of the engine. An increase in the temperature of the working gases is achieved by significantly changing the properties of the fuel. Unfortunately, it is not possible to do this 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 the efficiency. If we consider the temperature of the working steam at the inlet of which is 800 K, and the exhaust gas is 300 K, then the efficiency of this machine is 62%. In reality, this value does not exceed 40%. Such a decrease occurs due to heat losses during heating of 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, fuels is a problem that the best minds of mankind are working on.Heat engine operation
Carnot engine
Varieties
Other types of heat engines
How can you increase efficiency
Efficiency calculation
heat engine
heat engine efficiency
Chiller efficiency
Efficiency of reversible and irreversible heat engine
A bit of history
heat engine
Efficiency calculation
Ideal heat engine
Example of problem solving
Real conditions
Other heat engines
Ways to change efficiency
Motor efficiency values
