heat engine efficiency. Heat engine efficiency - definition formula

In the theoretical model of a heat engine, three bodies are considered: heater, working body 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 end 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 load received from the heater, amount of heat | Q cool |, given to the refrigerator, and the work done by the working body BUT are related to each other by:

A = Q load – | 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 the engine internal combustion(ICE) combustion products can be considered a heater, and excess air can be considered a working fluid. As a refrigerator, they use the air of the atmosphere or water from natural sources.

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 one 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, the efficiency is determined by the experimental mechanical power N engine and the amount of fuel burned per unit time. So, if in time t mass fuel burned m and specific heat of combustion q, then

For Vehicle the reference characteristic is often the volume V fuel burned 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 a formula for calculating the efficiency:

Second law of thermodynamics

There are several formulations second law of thermodynamics. One of them says that a heat engine is impossible, which would do work only due to a heat source, i.e. without refrigerator. The world ocean could serve for it 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 is impossible in which heat would spontaneously transfer from less heated bodies to more heated bodies.

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 non-equilibrium system occur in such a direction in which the entropy of the system increases; in a state of thermal equilibrium, it is maximum and constant.

Boltzmann's formulation(1877): a closed system of many particles spontaneously passes from a more ordered state to a less ordered one. The spontaneous exit of the system from the equilibrium position is impossible. 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 the working body model is set in heat engine(for example, ideal gas), then it is possible to calculate the change in the thermodynamic parameters of the working fluid during expansion and contraction. This allows you to calculate the efficiency of a heat engine based on the laws of thermodynamics.

The figure shows the cycles for which the efficiency can be calculated if the working fluid is an ideal gas and the parameters are set at the points of transition of one thermodynamic process to another.

Carnot cycle. Efficiency of an ideal heat engine

The highest efficiency at given heater temperatures T heating and refrigerator T cold has a heat engine where the working fluid expands and contracts along 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 the influence of human activity on the Earth's climate, many scientists point out the factors due to which such an influence can occur:

1. The greenhouse effect is an increase in the concentration of carbon dioxide (a product of combustion in the heaters of thermal machines) in the atmosphere. Carbon dioxide transmits visible and ultraviolet radiation from the Sun, but absorbs infrared radiation from the Earth. This leads to an increase in the temperature of the lower layers of the atmosphere, an increase in hurricane winds and global ice melting.
2. Direct impact of toxic exhaust gases on wildlife (carcinogens, smog, acid rain from combustion by-products).
3. Destruction of the ozone layer during aircraft flights and rocket launches. The ozone of the upper atmosphere protects all life on Earth from excess ultraviolet radiation from the Sun.

The way out of the emerging ecological crisis lies in increasing thermal efficiency engines (the efficiency of modern heat engines rarely exceeds 30%); use of serviceable engines and neutralizers of harmful exhaust gases; use of alternative energy sources (solar batteries and heaters) and alternative means of transport (bicycles, etc.).

Efficiency factor (COP) is a measure of the efficiency of a system in terms of energy conversion or transfer, which is determined by the ratio of the energy usefully used to the total energy received by the system.

efficiency- the value is dimensionless, it is usually expressed as a percentage:

The coefficient of performance (COP) of a heat engine is determined by the formula: , where A = Q1Q2. The efficiency of a heat engine is always less than 1.

Carnot cycle- This is a reversible circular gas process, which consists of two consecutive isothermal and two adiabatic processes performed with a working fluid.

The circular cycle, which includes two isotherms and two adiabats, corresponds to the maximum efficiency.

The French engineer Sadi Carnot in 1824 derived a formula for the maximum efficiency of an ideal heat engine, where the working fluid is an ideal gas, the cycle of which consisted of two isotherms and two adiabats, that is, the Carnot cycle. The Carnot cycle is the real working cycle of a heat engine that performs work due to the heat supplied to the working fluid in an isothermal process.

The formula for the efficiency of the Carnot cycle, i.e., the maximum efficiency of a heat engine, is: , where T1 is the absolute temperature of the heater, T2 is the absolute temperature of the refrigerator.

Heat engines- These are structures in which thermal energy is converted into mechanical energy.

Heat engines are diverse both in design and purpose. These include steam engines, steam turbines, internal combustion engines, jet engines.

However, despite the diversity, in principle, the operation of various heat engines is common features. The main components of each heat engine:

• heater;
• working body;
• fridge.

The heater releases thermal energy, while heating the working fluid, which is located in the working chamber of the engine. The working fluid can be steam or gas.

Having accepted the amount of heat, the gas expands, because. its pressure is greater than the external pressure, and moves the piston, producing positive work. At the same time, its pressure drops, and its volume increases.

If we compress the gas, passing through the same states, but in the opposite direction, then we will perform the same absolute value, but negative work. As a result, all the work for the cycle will be equal to zero.

In order for the work of a heat engine to be nonzero, the work of compressing the gas must be less than the work of expansion.

In order for the work of compression to become less than the work of expansion, it is necessary that the compression process take place at a lower temperature, for this the working fluid must be cooled, therefore, a refrigerator is included in the design of the heat engine. The working fluid gives off the amount of heat to the refrigerator when in contact with it.

The main significance of the formula (5.12.2) obtained by Carnot for the efficiency of an ideal machine is that it determines the maximum possible efficiency of any heat engine.

Carnot proved, based on the second law of thermodynamics*, the following theorem: any real heat engine operating with a temperature heaterT 1 and refrigerator temperatureT 2 , cannot have an efficiency 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 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 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: 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 internal combustion engines.

The efficiency of any heat engine cannot exceed the maximum possible value
, where T 1 - absolute temperature of the heater, and T 2 - absolute temperature of the refrigerator.

Increasing the efficiency of heat engines and bringing it closer to the maximum possible- the most important technical challenge.

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 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 special device 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.

Heat engine operation

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.

Carnot engine

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.

Varieties

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.

Other types of heat engines

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.

How can you increase efficiency

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.

The topic of the current lesson will be the consideration of the processes occurring in quite specific, and not abstract, as in previous lessons, devices - heat engines. We will define such machines, describe their main components and the principle of operation. Also during this lesson, the question of finding efficiency - the efficiency of thermal engines, both real and maximum possible, will be considered.

Topic: Fundamentals of thermodynamics
Lesson: The principle of operation of a heat engine

The topic of the last lesson was the first law of thermodynamics, which set the relationship between a certain amount of heat that was transferred to a portion of a gas and the work done by this gas during expansion. And now it's time to say that this formula is of interest not only for some theoretical calculations, but also in quite practical application, because the work of a gas is nothing more than useful work, which we extract when using heat engines.

Definition. heat engine- a device in which the internal energy of the fuel is converted into mechanical work (Fig. 1).

Rice. 1. Various examples of heat engines (), ()

As can be seen from the figure, heat engines are any devices that work according to the above principle, and they range from incredibly simple to very complex in design.

Without exception, all heat engines are functionally divided into three components (see Fig. 2):

• Heater
• working body
• Fridge

Rice. 2. Functional diagram of a heat engine ()

The heater is the process of combustion of fuel, which, during combustion, transfers a large amount of heat to the gas, heating it to high temperatures. Hot gas, which is a working fluid, due to an increase in temperature and, consequently, pressure, expands, doing work. Of course, since there is always heat transfer with the engine casing, ambient air, etc., the work will not numerically equal the heat transferred - some of the energy goes to the refrigerator, which, as a rule, is the environment.

The easiest way is to imagine the process taking place in a simple cylinder under a movable piston (for example, the cylinder of an internal combustion engine). Naturally, for the engine to work and make sense, the process must occur cyclically, and not one-time. That is, after each expansion, the gas must return to its original position (Fig. 3).

Rice. 3. An example of the cyclic operation of a heat engine ()

In order for the gas to return to its initial position, it is necessary to perform some work on it (the work of external forces). And since the work of the gas is equal to the work on the gas with the opposite sign, in order for the gas to perform a total positive work for the entire cycle (otherwise there would be no point in the engine), it is necessary that the work of external forces be less than the work of the gas. That is, the graph of the cyclic process in P-V coordinates should look like: a closed loop with a clockwise bypass. Under this condition, the work of the gas (in the section of the graph where the volume increases) is greater than the work on the gas (in the section where the volume decreases) (Fig. 4).

Rice. 4. An example of a graph of a process occurring in a heat engine

Since we are talking about a certain mechanism, it is imperative to say what its efficiency is.

Definition. Efficiency (coefficient of performance) of a heat engine- the ratio of useful work performed by the working fluid to the amount of heat transferred to the body from the heater.

If we take into account the conservation of energy: the energy that has departed from the heater does not disappear anywhere - part of it is removed in the form of work, the rest goes to the refrigerator:

We get:

This is an expression for efficiency in parts, if you need to get the efficiency value as a percentage, you must multiply the resulting number by 100. The efficiency in the SI measurement system is a dimensionless value and, as can be seen from the formula, cannot be more than one (or 100).

It should also be said that this expression is called the real efficiency or the efficiency of a real heat engine (heat engine). If we assume that we somehow manage to completely get rid of the design flaws of the engine, then we will get an ideal engine, and its efficiency will be calculated according to the formula for the efficiency of an ideal heat engine. This formula was obtained by the French engineer Sadi Carnot (Fig. 5):