Thermal engine. Heat engine efficiency. What is efficiency

Efficiency factor (efficiency) is a term that can be applied to, perhaps, every system and device. Even a person has an efficiency factor, although there is probably no objective formula for finding it yet. In this article we will explain in detail what efficiency is and how it can be calculated for various systems.

Efficiency definition

Efficiency is an indicator that characterizes the effectiveness of a system in terms of energy output or conversion. Efficiency is an immeasurable quantity and is represented either as a numerical value in the range from 0 to 1, or as a percentage.

General formula

Efficiency is indicated by the symbol Ƞ.

The general mathematical formula for finding efficiency is written as follows:

Ƞ=A/Q, where A is the useful energy/work performed by the system, and Q is the energy consumed by this system to organize the process of obtaining useful output.

The efficiency factor, unfortunately, is always less than or equal to unity, since, according to the law of conservation of energy, we cannot obtain more work than the energy expended. In addition, the efficiency, in fact, is extremely rarely equal to unity, since useful work is always accompanied by the presence of losses, for example, for heating the mechanism.

Heat engine efficiency

A heat engine is a device that converts thermal energy into mechanical energy. In a heat engine, work is determined by the difference between the amount of heat received from the heater and the amount of heat given to the cooler, and therefore the efficiency is determined by the formula:

Ƞ=Qн-Qх/Qн, where Qн is the amount of heat received from the heater, and Qх is the amount of heat given to the cooler.

It is believed that the highest efficiency is provided by engines operating on the Carnot cycle. In this case, the efficiency is determined by the formula:

Ƞ=T1-T2/T1, where T1 is the temperature of the hot spring, T2 is the temperature of the cold spring.

Electric motor efficiency

An electric motor is a device that converts electrical energy into mechanical energy, so efficiency in this case is the efficiency ratio of the device in converting electrical energy into mechanical energy. The formula for finding the efficiency of an electric motor looks like this:

Ƞ=P2/P1, where P1 is the supplied electrical power, P2 is the useful mechanical power generated by the engine.

Electrical power is found as the product of system current and voltage (P=UI), and mechanical power as the ratio of work per unit time (P=A/t)

Transformer efficiency

A transformer is a device that converts alternating current of one voltage to alternating current of another voltage, maintaining the frequency. In addition, transformers can also convert alternating current into direct current.

The efficiency of the transformer is found by the formula:

Ƞ=1/1+(P0+PL*n2)/(P2*n), where P0 is the no-load loss, PL is the load loss, P2 is the active power supplied to the load, n is the relative degree of load.

Efficiency or not efficiency?

It is worth noting that in addition to efficiency, there are a number of indicators that characterize the efficiency of energy processes, and sometimes we can come across descriptions like - efficiency of the order of 130%, however in this case we need to understand that the term is not used entirely correctly, and, most likely, the author or the manufacturer understands this abbreviation to mean a slightly different characteristic.

For example, heat pumps are distinguished by the fact that they can release more heat than they consume. Thus, a refrigeration machine can remove more heat from the object being cooled than was expended in energy equivalent to organize the removal. The efficiency indicator of a refrigeration machine is called the refrigeration coefficient, denoted by the letter Ɛ and determined by the formula: Ɛ=Qx/A, where Qx is the heat removed from the cold end, A is the work expended on the removal process. However, sometimes the refrigeration coefficient is also called the efficiency of the refrigeration machine.

It is also interesting that the efficiency of boilers operating on organic fuel is usually calculated based on the lower calorific value, and it can be greater than unity. However, it is still traditionally called efficiency. It is possible to determine the efficiency of a boiler by the higher calorific value, and then it will always be less than one, but in this case it will be inconvenient to compare the performance of boilers with data from other installations.

The concept of coefficient of performance (efficiency) can be applied to a wide variety of types of devices and mechanisms, the operation of which is based on the use of any resources. So, if we consider the energy used to operate the system as such a resource, then the result of this should be considered the amount of useful work performed on this energy.

In general, the efficiency formula can be written as follows: n = A*100%/Q. In this formula, the symbol n is used to denote efficiency, the symbol A represents the amount of work done, and Q is the amount of energy expended. It is worth emphasizing that the unit of measurement for efficiency is percentage. Theoretically, the maximum value of this coefficient is 100%, but in practice it is almost impossible to achieve such an indicator, since in the operation of each mechanism there are certain energy losses.

Engine efficiency

The internal combustion engine (ICE), which is one of the key components of the mechanism of a modern car, is also a variant of a system based on the use of a resource - gasoline or diesel fuel. Therefore, the efficiency value can be calculated for it.

Despite all the technical achievements of the automotive industry, the standard efficiency of internal combustion engines remains quite low: depending on the technologies used in the design of the engine, it can range from 25% to 60%. This is due to the fact that the operation of such an engine is associated with significant energy losses.

Thus, the greatest loss in the efficiency of the internal combustion engine occurs in the operation of the cooling system, which takes up to 40% of the energy generated by the engine. A significant part of the energy - up to 25% - is lost in the process of exhaust gas removal, that is, it is simply carried away into the atmosphere. Finally, approximately 10% of the energy generated by the engine is spent on overcoming friction between the various parts of the internal combustion engine.

Therefore, technologists and engineers involved in the automotive industry are making significant efforts to increase the efficiency of engines by reducing losses in all of the listed items. Thus, the main direction of design developments aimed at reducing losses related to the operation of the cooling system is associated with attempts to reduce the size of the surfaces through which heat transfer occurs. Reducing losses in the gas exchange process is carried out mainly using a turbocharging system, and reducing losses associated with friction is done through the use of more technologically advanced and modern materials when designing the engine. According to experts, the use of these and other technologies can raise the efficiency of internal combustion engines to 80% and higher.

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 that exceeds 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 strictly.

Let us first consider a heat engine operating in a reversible cycle with a real gas. The cycle can be anything, 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 operate with a common heater and a common refrigerator. Let the Carnot machine operate in a reverse cycle (like a refrigeration machine), and let the other machine operate in a forward cycle (Fig. 5.18). The heat engine performs work equal to, according to formulas (5.12.3) and (5.12.5):

A 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 done on it

(5.12.12)

Since by condition η" > η , That A" > A. Therefore, a heat engine can drive a refrigeration machine, and there will still be an excess of work left. This excess work is done due to heat taken from one source. After all, heat is not transferred to the refrigerator when two machines operate 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 a Carnot machine in a forward cycle. We will again come to a contradiction with the second law of thermodynamics. Consequently, two machines operating on reversible cycles have the same efficiency: η " = η .

It’s a different matter if the second machine operates on an irreversible cycle. If we assume η " > η , then we will again come to a contradiction with the second law of thermodynamics. However, the assumption t|"< 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 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 does η = 1.

But the temperature of the refrigerator practically cannot be much 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. 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 efficiency value is:

The actual efficiency value due to various types of energy losses is approximately 40%. The maximum efficiency - about 44% - is achieved by 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.

Physics is a science that studies processes occurring in nature. This science is very interesting and curious, because each of us wants to satisfy ourselves mentally by gaining knowledge and understanding of how and what works in our world. Physics, the laws of which have been deduced over centuries and by dozens of scientists, helps us with this task, and we should only rejoice and absorb the knowledge provided.

But at the same time, physics is a far from simple science, like, in fact, nature itself, but it would be very interesting to understand it. Today we will talk about efficiency. We will learn what efficiency is and why it is needed. Let's look at everything clearly and interestingly.

Explanation of the abbreviation - efficiency. However, even this interpretation may not be particularly clear the first time. This coefficient characterizes the efficiency of a system or any individual body, and more often, a mechanism. Efficiency is characterized by the output or conversion of energy.

This coefficient applies to almost everything that surrounds us, and even to ourselves, and to a greater extent. After all, we do useful work all the time, but how often and how important it is is another question, and the term “efficiency” is used with it.

It is important to consider that this coefficient is an unlimited value, it usually represents either mathematical values, for example, 0 and 1, or, as is more often the case, as a percentage.

In physics, this coefficient is denoted by the letter Ƞ, or, as it is commonly called, Eta.

Useful work

When using any mechanisms or devices, we necessarily perform work. As a rule, it is always greater than what we need to complete the task. Based on these facts, two types of work are distinguished: expended, which is denoted by a capital letter, A with a small z (Az), and useful - A with the letter p (An). For example, let's take this case: we have a task to lift a cobblestone with a certain mass to a certain height. In this case, work characterizes only overcoming the force of gravity, which, in turn, acts on the load.

In the case when any device other than the gravity of the cobblestone is used for lifting, it is also important to take into account gravity of the parts of this device. And besides all this, it is important to remember that while we win in strength, we will always lose along the way. All these facts lead to one conclusion that the work expended in any case will be more useful, Az > An, the question is how much more it is, because you can reduce this difference as much as possible and thereby increase the efficiency, ours or our device.

Useful work is the portion of expended work that we do using a mechanism. And efficiency is precisely the physical quantity that shows what part of the useful work is from the total work expended.

Result:

The expended work Az is always greater than the useful work Ap.
The greater the ratio of useful to expended, the higher the coefficient, and vice versa.
Ap is found by multiplying the mass by the acceleration of gravity and the height of ascent.

There is a certain formula for finding efficiency. It goes like this: to find efficiency in physics, you need to divide the amount of energy by the work done by the system. That is, efficiency is the ratio of energy expended to work performed. From this we can draw a simple conclusion that the better and more efficient the system or body is, the less energy is spent on doing the work.

The formula itself looks short and very simple: it will equal A/Q. That is, Ƞ = A/Q. This brief formula captures the elements we need for the calculation. That is, A in this case is the used energy that is consumed by the system during operation, and the capital letter Q, in turn, will be the spent A, or again the spent energy.

Ideally, the efficiency is equal to unity. But, as usually happens, he is smaller than her. This happens because of physics and because, of course, the law of conservation of energy.

The thing is that the law of conservation of energy suggests that more A cannot be obtained than energy received. And even this coefficient will be equal to one extremely rarely, since energy is always wasted. And work is accompanied by losses: for example, in an engine, the loss lies in its excessive heating.

So, the efficiency formula:

Ƞ=A/Q, Where

A is the useful work the system performs.
Q is the energy consumed by the system.

Application in various fields of physics

It is noteworthy that efficiency does not exist as a neutral concept, each process has its own efficiency, it is not a friction force, it cannot exist on its own.

Let's look at a few examples of processes with efficiency.

For example, let's take an electric motor. The job of an electric motor is to convert electrical energy into mechanical energy. In this case, the coefficient will be the efficiency of the engine in terms of converting electrical energy into mechanical energy. There is also a formula for this case, and it looks like this: Ƞ=P2/P1. Here P1 is the power in the general version, and P2 is the useful power that the engine itself produces.

It is not difficult to guess that the structure of the coefficient formula is always preserved; only the data that needs to be substituted in it changes. They depend on the specific case, if it is an engine, as in the case above, then it is necessary to operate with the power expended, if it is a job, then the initial formula will be different.

Now we know the definition of efficiency and we have an idea about this physical concept, as well as about its individual elements and nuances. Physics is one of the largest sciences, but it can be broken down into small pieces to understand it. Today we examined one of these pieces.

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The coefficient of efficiency (efficiency) is a value that expresses, as a percentage, the efficiency of a particular mechanism (engine, system) in converting the received energy into useful work.

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Why is diesel efficiency higher?

The efficiency indicator for different engines can vary greatly and depends on a number of factors. have a relatively low efficiency due to the large number of mechanical and thermal losses that arise during the operation of a power unit of this type.

The second factor is friction that occurs during the interaction of mating parts. Most of the useful energy consumption is driven by the movement of the engine pistons, as well as the rotation of parts inside the motor, which are structurally fixed to bearings. About 60% of the combustion energy of gasoline is spent only to ensure the operation of these units.

Additional losses are caused by the operation of other mechanisms, systems and attachments. The percentage of resistance losses at the moment of admission of the next charge of fuel and air, and then the release of exhaust gases from the internal combustion engine cylinder, is also taken into account.

If we compare a diesel unit and a gasoline engine, a diesel engine has a noticeably higher efficiency compared to a gasoline unit. Gasoline power units have an efficiency of about 25-30% of the total amount of energy received.

In other words, out of 10 liters of gasoline spent on engine operation, only 3 liters are used to perform useful work. The rest of the energy from fuel combustion was lost.

With the same displacement, the power of a naturally aspirated gasoline engine is higher, but is achieved at higher speeds. The engine needs to be “turned”, losses increase, fuel consumption increases. It is also necessary to mention torque, which literally means the force that is transmitted from the engine to the wheels and moves the car. Gasoline internal combustion engines achieve maximum torque at higher speeds.

A similar naturally-aspirated diesel engine reaches peak torque at low speeds, while using less diesel fuel to do useful work, which means higher efficiency and fuel economy.

Diesel fuel generates more heat compared to gasoline, the combustion temperature of diesel fuel is higher, and the detonation resistance index is higher. It turns out that a diesel internal combustion engine produces more useful work on a certain amount of fuel.

Energy value of diesel fuel and gasoline

Diesel fuel consists of heavier hydrocarbons than gasoline. The lower efficiency of a gasoline unit compared to a diesel engine also lies in the energy component of gasoline and the characteristics of its combustion. Complete combustion of equal amounts of diesel fuel and gasoline will produce more heat in the first case. Heat in a diesel internal combustion engine is more fully converted into useful mechanical energy. It turns out that when burning the same amount of fuel per unit of time, it is the diesel engine that will do more work.

It is also worth taking into account the features of injection and the creation of proper conditions for complete combustion of the mixture. In a diesel engine, fuel is supplied separately from the air; it is injected not into the intake manifold, but directly into the cylinder at the very end of the compression stroke. The result is a higher temperature and the most complete combustion of a portion of the working fuel-air mixture.

Results

Designers are constantly striving to improve the efficiency of both diesel and gasoline engines. Increasing the number of intake and exhaust valves per cylinder, active use, electronic control of fuel injection, throttle valve and other solutions can significantly increase efficiency. This applies to a greater extent to the diesel engine.

Thanks to these features, a modern diesel engine is able to completely burn a portion of diesel fuel saturated with hydrocarbons in the cylinder and produce high torque at low speeds. Low rpm means less friction loss and resulting drag. For this reason, the diesel engine today is one of the most productive and economical types of internal combustion engines, the efficiency of which often exceeds 50%.