What is efficiency and how is it determined. Heat engine

Basic theoretical information

Mechanical work

The energy characteristics of motion are introduced based on the concept mechanical work or force work. Work done by a constant force F, is a physical quantity equal to the product of the force and displacement moduli multiplied by the cosine of the angle between the force vectors F and movements S:

Work is a scalar quantity. It can be either positive (0° ≤ α < 90°), так и отрицательна (90° < α ≤ 180°). At α = 90° the work done by the force is zero. In the SI system, work is measured in joules (J). A joule is equal to the work done by a force of 1 newton to move 1 meter in the direction of the force.

If the force changes over time, then to find the work, build a graph of the force versus displacement and find the area of ​​the figure under the graph - this is the work:

An example of a force whose modulus depends on the coordinate (displacement) is the elastic force of a spring, which obeys Hooke’s law ( F control = kx).

Power

The work done by a force per unit time is called power. Power P(sometimes denoted by the letter N) – physical quantity equal to the work ratio A to a period of time t during which this work was completed:

This formula calculates average power, i.e. power generally characterizing the process. So, work can also be expressed in terms of power: A = Pt(if, of course, the power and time of doing the work are known). The unit of power is called the watt (W) or 1 joule per second. If the motion is uniform, then:

Using this formula we can calculate instant power(power in at the moment time), if instead of speed we substitute the value of instantaneous speed into the formula. How do you know what power to count? If the problem asks for power at a moment in time or at some point in space, then instantaneous is considered. If they ask about power over a certain period of time or part of the route, then look for average power.

Efficiency – coefficient useful action , is equal to the ratio useful work to the amount spent, or useful power to spent:

Which work is useful and which is wasted is determined from the conditions of a specific task through logical reasoning. For example, if a crane does the work of lifting a load to a certain height, then the useful work will be the work of lifting the load (since it is for this purpose that the crane was created), and the expended work will be the work done by the crane’s electric motor.

So, useful and expended power do not have a strict definition, and are found by logical reasoning. In each task, we ourselves must determine what in this task was the goal of doing work (useful work or power), and what was the mechanism or way of doing all the work (expended power or work).

In general, efficiency shows how efficiently a mechanism converts one type of energy into another. If the power changes over time, then the work is found as the area of ​​the figure under the graph of power versus time:

Kinetic energy

A physical quantity equal to half the product of a body’s mass and the square of its speed is called kinetic energy of the body (energy of movement):

That is, if a car weighing 2000 kg moves at a speed of 10 m/s, then it has kinetic energy equal to E k = 100 kJ and is capable of doing 100 kJ of work. This energy can turn into heat (when a car brakes, the tires of the wheels, the road and the brake discs heat up) or can be spent on deforming the car and the body that the car collided with (in an accident). When calculating kinetic energy, it does not matter where the car is moving, since energy, like work, is a scalar quantity.

A body has energy if it can do work. For example, a moving body has kinetic energy, i.e. energy of motion, and is capable of doing work to deform bodies or impart acceleration to bodies with which a collision occurs.

Physical meaning kinetic energy: in order for a body at rest with a mass m began to move at speed v it is necessary to do work equal to the obtained value of kinetic energy. If the body has a mass m moves at speed v, then to stop it it is necessary to do work equal to its initial kinetic energy. When braking, kinetic energy is mainly (except for cases of impact, when the energy goes to deformation) “taken away” by the friction force.

Kinetic energy theorem: the work done by the resultant force is equal to the change in the kinetic energy of the body:

The theorem on kinetic energy is also valid in the general case, when a body moves under the influence of a changing force, the direction of which does not coincide with the direction of movement. It is convenient to apply this theorem in problems involving acceleration and deceleration of a body.

Potential energy

Along with kinetic energy or energy of motion in physics important role plays concept potential energy or energy of interaction of bodies.

Potential energy is determined by the relative position of bodies (for example, the position of the body relative to the surface of the Earth). The concept of potential energy can be introduced only for forces whose work does not depend on the trajectory of the body and is determined only by the initial and final positions (the so-called conservative forces). The work done by such forces on a closed trajectory is zero. This property is possessed by gravity and elastic force. For these forces we can introduce the concept of potential energy.

Potential energy of a body in the Earth's gravity field calculated by the formula:

The physical meaning of the potential energy of a body: potential energy is equal to the work done by gravity when lowering the body to zero level ( h– distance from the center of gravity of the body to the zero level). If a body has potential energy, then it is capable of doing work when this body falls from a height h to zero level. The work done by gravity is equal to the change in the potential energy of the body, taken from opposite sign:

Often in energy problems one has to find the work of lifting (turning over, getting out of a hole) the body. In all these cases, it is necessary to consider the movement not of the body itself, but only of its center of gravity.

The potential energy Ep depends on the choice of the zero level, that is, on the choice of the origin of the OY axis. In each problem, the zero level is chosen for reasons of convenience. What has a physical meaning is not the potential energy itself, but its change when a body moves from one position to another. This change is independent of the choice of zero level.

Potential energy of a stretched spring calculated by the formula:

Where: k– spring stiffness. An extended (or compressed) spring can set a body attached to it in motion, that is, impart kinetic energy to this body. Consequently, such a spring has a reserve of energy. Tension or compression X must be calculated from the undeformed state of the body.

The potential energy of an elastically deformed body is equal to the work done by the elastic force during the transition from this state into a state with zero deformation. If in the initial state the spring was already deformed, and its elongation was equal to x 1, then upon transition to a new state with elongation x 2, the elastic force will do work equal to the change in potential energy, taken with the opposite sign (since the elastic force is always directed against the deformation of the body):

Potential energy during elastic deformation is the energy of interaction of individual parts of the body with each other by elastic forces.

The work of the friction force depends on the path traveled (this type of force, whose work depends on the trajectory and the path traveled is called: dissipative forces). The concept of potential energy for the friction force cannot be introduced.

Efficiency

Efficiency factor (efficiency)– characteristic of the efficiency of a system (device, machine) in relation to the conversion or transmission of energy. It is determined by the ratio of usefully used energy to the total amount of energy received by the system (the formula has already been given above).

Efficiency can be calculated both through work and through power. Useful and expended work (power) are always determined by simple logical reasoning.

IN electric motors Efficiency is the ratio of the performed (useful) mechanical work to the electrical energy received from the source. In heat engines, the ratio of useful mechanical work to the amount of heat expended. In electrical transformers - ratio electromagnetic energy received in the secondary winding to the energy consumed by the primary winding.

Due to its generality, the concept of efficiency makes it possible to compare and evaluate such various systems, How nuclear reactors, electric generators and engines, thermal power plants, semiconductor devices, biological objects, etc.

Due to inevitable energy losses due to friction, heating of surrounding bodies, etc. Efficiency is always less than unity. Accordingly, the efficiency is expressed in shares of the energy expended, that is, in the form proper fraction or as a percentage, and is a dimensionless quantity. Efficiency characterizes how efficiently a machine or mechanism operates. The efficiency of thermal power plants reaches 35–40%, internal combustion engines with supercharging and pre-cooling – 40–50%, dynamos and high-power generators – 95%, transformers – 98%.

A problem in which you need to find the efficiency or it is known, you need to start with logical reasoning - which work is useful and which is wasted.

Law of conservation of mechanical energy

Total mechanical energy is called the sum of kinetic energy (i.e. the energy of motion) and potential (i.e. the energy of interaction of bodies by the forces of gravity and elasticity):

If mechanical energy does not transform into other forms, for example, into internal (thermal) energy, then the sum of kinetic and potential energy remains unchanged. If mechanical energy turns into thermal energy, then the change in mechanical energy is equal to the work of the friction force or energy losses, or the amount of heat released, and so on, in other words, the change in total mechanical energy is equal to the work of external forces:

The sum of the kinetic and potential energy of the bodies that make up closed system(i.e. one in which there are no external forces acting, and their work is correspondingly equal to zero) and the gravitational and elastic forces interacting with each other, remains unchanged:

This statement expresses law of conservation of energy (LEC) in mechanical processes. It is a consequence of Newton's laws. The law of conservation of mechanical energy is satisfied only when bodies in a closed system interact with each other by forces of elasticity and gravity. In all problems on the law of conservation of energy there will always be at least two states of a system of bodies. The law states that the total energy of the first state will be equal to the total energy of the second state.

Algorithm for solving problems on the law of conservation of energy:

1. Find the points of the initial and final position of the body.
2. Write down what or what energies the body has at these points.
3. Equate the initial and final energy of the body.
4. Add other necessary equations from previous physics topics.
5. Solve the resulting equation or system of equations using mathematical methods.

It is important to note that the law of conservation of mechanical energy made it possible to obtain a relationship between the coordinates and velocities of a body in two different points trajectories without analyzing the law of body motion at all intermediate points. The application of the law of conservation of mechanical energy can greatly simplify the solution of many problems.

In real conditions, moving bodies are almost always acted upon, along with gravitational forces, elastic forces and other forces, by frictional forces or environmental resistance forces. The work done by the friction force depends on the length of the path.

If friction forces act between the bodies that make up a closed system, then mechanical energy is not conserved. Part of the mechanical energy is converted into internal energy of bodies (heating). Thus, energy as a whole (i.e., not only mechanical) is conserved in any case.

For any physical interactions energy neither arises nor disappears. It just changes from one form to another. This experimentally established fact expresses a fundamental law of nature - law of conservation and transformation of energy.

One of the consequences of the law of conservation and transformation of energy is the statement about the impossibility of creating a “perpetual motion machine” (perpetuum mobile) - a machine that could do work indefinitely without consuming energy.

Various tasks for work

If the problem requires finding mechanical work, then first select a method for finding it:

1. A job can be found using the formula: A = FS∙cos α . Find the force that does the work and the amount of displacement of the body under the influence of this force in the chosen frame of reference. Note that the angle must be chosen between the force and displacement vectors.
2. The work of an external force can be found as the difference in mechanical energy in the final and initial situations. Mechanical energy is equal to the sum of the kinetic and potential energies of the body.
3. Work on lifting the body with constant speed can be found using the formula: A = mgh, Where h- height to which it rises body center of gravity.
4. Work can be found as the product of power and time, i.e. according to the formula: A = Pt.
5. The work can be found as the area of ​​the figure under the graph of force versus displacement or power versus time.

Law of conservation of energy and dynamics of rotational motion

The problems of this topic are quite complex mathematically, but if you know the approach, they can be solved using a completely standard algorithm. In all problems you will have to consider the rotation of the body in the vertical plane. The solution will come down to the following sequence of actions:

1. You need to determine the point you are interested in (the point at which you need to determine the speed of the body, the tension force of the thread, weight, and so on).
2. Write down Newton’s second law at this point, taking into account that the body rotates, that is, it has centripetal acceleration.
3. Write down the law of conservation of mechanical energy so that it contains the speed of the body at that very interesting point, as well as the characteristics of the state of the body in some state about which something is known.
4. Depending on the condition, express the squared speed from one equation and substitute it into the other.
5. Carry out the remaining necessary mathematical operations to obtain the final result.

When solving problems, you need to remember that:

• The condition for passing the top point when rotating on a thread at a minimum speed is the support reaction force N at the top point is 0. The same condition is met when passing the top point of the dead loop.
• When rotating on a rod, the condition for passing the entire circle is: the minimum speed at the top point is 0.
• The condition for the separation of a body from the surface of the sphere is that the support reaction force at the separation point is zero.

Inelastic collisions

The law of conservation of mechanical energy and the law of conservation of momentum make it possible to find solutions to mechanical problems in cases where unknown active forces. An example of this type of problem is the impact interaction of bodies.

By impact (or collision) It is customary to call a short-term interaction of bodies, as a result of which their speeds experience significant changes. During a collision of bodies, short-term impact forces act between them, the magnitude of which, as a rule, is unknown. Therefore, it is impossible to consider the impact interaction directly using Newton's laws. The application of the laws of conservation of energy and momentum in many cases makes it possible to exclude the collision process itself from consideration and obtain a connection between the velocities of bodies before and after the collision, bypassing all intermediate values ​​of these quantities.

We often have to deal with the impact interaction of bodies in everyday life, in technology and in physics (especially in the physics of the atom and elementary particles). In mechanics, two models of impact interaction are often used - absolutely elastic and absolutely inelastic impacts.

Absolutely inelastic impact called such an impact interaction in which bodies connect (stick together) with each other and move further as one body.

In a completely inelastic collision, mechanical energy is not conserved. It partially or completely turns into the internal energy of bodies (heating). To describe any impacts, you need to write down both the law of conservation of momentum and the law of conservation of mechanical energy, taking into account the heat released (it is highly advisable to make a drawing first).

Absolutely elastic impact

Absolutely elastic impact called a collision in which the mechanical energy of a system of bodies is conserved. In many cases, collisions of atoms, molecules and elementary particles obey the laws of absolutely elastic impact. With an absolutely elastic impact, along with the law of conservation of momentum, the law of conservation of mechanical energy is satisfied. A simple example A perfectly elastic collision can be a central impact of two billiard balls, one of which was at rest before the collision.

Central strike balls is called a collision in which the velocities of the balls before and after the impact are directed along the line of centers. Thus, using the laws of conservation of mechanical energy and momentum, it is possible to determine the velocities of the balls after a collision if their velocities before the collision are known. The central strike is very rarely implemented in practice, especially if we're talking about about collisions of atoms or molecules. In a non-central elastic collision, the velocities of particles (balls) before and after the collision are not directed in one straight line.

A special case of an off-central elastic impact can be the collision of two billiard balls of the same mass, one of which was motionless before the collision, and the speed of the second was not directed along the line of the centers of the balls. In this case, the velocity vectors of the balls after an elastic collision are always directed perpendicular to each other.

Conservation laws. Complex tasks

Multiple bodies

In some problems on the law of conservation of energy, the cables with which certain objects are moved can have mass (that is, not be weightless, as you might already be used to). In this case, the work of moving such cables (namely their centers of gravity) also needs to be taken into account.

If two bodies connected by a weightless rod rotate in a vertical plane, then:

1. choose a zero level to calculate potential energy, for example at the level of the axis of rotation or at the level of the lowest point of one of the weights and be sure to make a drawing;
2. write down the law of conservation of mechanical energy, in which on the left side we write the sum of the kinetic and potential energy of both bodies in the initial situation, and on the right side we write the sum of the kinetic and potential energy of both bodies in the final situation;
3. take into account that angular velocities bodies are the same, then linear speeds bodies are proportional to the radii of rotation;
4. if necessary, write down Newton's second law for each of the bodies separately.

Shell burst

When a projectile explodes, explosive energy is released. To find this energy, it is necessary to subtract the mechanical energy of the projectile before the explosion from the sum of the mechanical energies of the fragments after the explosion. We will also use the law of conservation of momentum, written in the form of the cosine theorem (vector method) or in the form of projections onto selected axes.

Collisions with a heavy plate

Let us meet a heavy plate that moves at speed v, a light ball of mass is moving m at speed u n. Since the momentum of the ball is much less than the momentum of the plate, after the impact the speed of the plate will not change, and it will continue to move at the same speed and in the same direction. As a result of the elastic impact, the ball will fly away from the plate. It is important to understand here that the speed of the ball relative to the plate will not change. In this case, for the final speed of the ball we obtain:

Thus, the speed of the ball after impact increases by twice the speed of the wall. Similar reasoning for the case when before the impact the ball and the plate were moving in the same direction leads to the result that the speed of the ball decreases by twice the speed of the wall:

In physics and mathematics, among other things, three essential conditions must be met:

1. Study all topics and complete all tests and assignments given in the educational materials on this site. To do this, you need nothing at all, namely: devote three to four hours every day to preparing for the CT in physics and mathematics, studying theory and solving problems. The fact is that CT is an exam where it is not enough just to know physics or mathematics, you also need to be able to solve quickly and without failures large number tasks for different topics and of varying complexity. The latter can only be learned by solving thousands of problems.
2. Learn all the formulas and laws in physics, and formulas and methods in mathematics. In fact, this is also very simple to do; there are only about 200 necessary formulas in physics, and even a little less in mathematics. Each of these items contains about a dozen standard methods solving problems of a basic level of complexity, which can also be learned, and thus completely automatically and without difficulty solved in right moment most of the DH. After this, you will only have to think about the most difficult tasks.
3. Attend all three stages of rehearsal testing in physics and mathematics. Each RT can be visited twice to decide on both options. Again, on the CT, in addition to the ability to quickly and efficiently solve problems, and knowledge of formulas and methods, you must also be able to properly plan time, distribute forces, and most importantly, correctly fill out the answer form, without confusing the numbers of answers and problems, or your own last name. Also, during RT, it is important to get used to the style of asking questions in problems, which may seem to an unprepared person very unusual.

Successful, diligent and responsible implementation of these three points will allow you to show an excellent result at the CT, the maximum of what you are capable of.

Found a mistake?

If you think you have found an error in educational materials, then please write about it by email. You can also report a bug to social network(). In the letter, indicate the subject (physics or mathematics), the name or number of the topic or test, the number of the problem, or the place in the text (page) where, in your opinion, there is an error. Also describe what the suspected error is. Your letter will not go unnoticed, the error will either be corrected, or you will be explained why it is not an error.

EFFICIENCY COEFFICIENT (efficiency) is a characteristic of the efficiency of a system (device, machine) in relation to energy conversion; is determined by the ratio of usefully used energy (converted into work during a cyclic process) to the total amount of energy transferred to the system.

Efficiency

(efficiency), a characteristic of the efficiency of a system (device, machine) in relation to the conversion or transmission of energy; determined by the ratio of usefully used energy to the total amount of energy received by the system; usually denoted by h = Wpol/Wcym.

In electric motors, efficiency is the ratio of the (useful) mechanical work performed to the electrical energy received from the source; in heat engines ≈ the ratio of useful mechanical work to the amount of heat expended; in electrical transformers, the ratio of the electromagnetic energy received in the secondary winding to the energy consumed by the primary winding. To calculate efficiency different types energy and mechanical work expressed in identical units based on the mechanical equivalent of heat, and other similar relationships. Due to its generality, the concept of efficiency allows us to compare and evaluate from a unified point of view such different systems as nuclear reactors, electric generators and engines, thermal power plants, semiconductor devices, biological objects, etc.

Due to the inevitable energy losses due to friction, heating of surrounding bodies, etc., the efficiency is always less than unity. Accordingly, efficiency is expressed as a fraction of the energy expended, i.e., as a proper fraction or as a percentage, and is a dimensionless quantity. The efficiency of thermal power plants reaches 35-40%, internal combustion engines ≈ 40-50%, dynamos and high-power generators ≈95%, transformers ≈98%. The efficiency of the photosynthesis process is usually 6≈8%; in chlorella it reaches 20≈25%. For heat engines, due to the second law of thermodynamics, the efficiency has an upper limit determined by the characteristics of the thermodynamic cycle (circular process) that the working substance undergoes. The Carnot cycle has the highest efficiency.

There is a distinction between the efficiency of an individual element (stage) of a machine or device and the efficiency that characterizes the entire chain of energy transformations in the system. The efficiency of the first type, in accordance with the nature of energy conversion, can be mechanical, thermal, etc. The second type includes general, economic, technical and other types of efficiency. The overall efficiency of the system is equal to the product of the partial efficiencies, or stage efficiencies.

In technical literature, efficiency is sometimes defined in such a way that it may be greater than unity. Similar situation arises if efficiency is determined by the ratio Wpol/Wcost, where Wpol ≈ the used energy received at the “output” of the system, Wcost ≈ not all the energy entering the system, but only that part of it for which real costs are incurred. For example, when operating semiconductor thermoelectric heaters (heat pumps), the energy consumption is less than the amount of heat generated by the thermoelement. Excess energy is drawn from environment. In this case, although the true efficiency of the installation is less than unity, the considered efficiency h = Wpol/Wloss may turn out to be greater than unity.

Lit.: Artobolevsky I.I., Theory of Mechanisms and Machines, 2nd ed., M.≈L., 1952; General heat engineering, ed. S. Ya. Kornitsky and Ya. M. Rubinshtein, 2nd ed., M.≈L., 1952; General electrical engineering, M.≈L., 1951; Vukalovich M.P., Novikov I.I., Technical thermodynamics, 4th ed., M., 1968.

Wikipedia

Efficiency

Efficiency (Efficiency) - characteristic of the efficiency of the system in relation to the conversion or transmission of energy. It is determined by the ratio of usefully used energy to the total amount of energy received by the system; usually denoted by η. Efficiency is a dimensionless quantity and is often measured as a percentage.

Probably everyone has wondered about the efficiency (Coefficient of Efficiency) of an internal combustion engine. After all, the higher this indicator, the more efficiently the power unit operates. The most efficient type at the moment is considered to be the electric type, its efficiency can reach up to 90 - 95%, but for internal combustion engines, be it diesel or gasoline, it is, to put it mildly, far from ideal...

To be honest, modern engine options are much more efficient than their counterparts that were released 10 years ago, and there are many reasons for this. Think for yourself before, the 1.6 liter version produced only 60 - 70 hp. And now this value can reach 130 - 150 hp. This painstaking work on increasing efficiency, in which each “step” is given by trial and error. However, let's start with a definition.

- this is the value of the ratio of two quantities, the power that is supplied to the engine crankshaft to the power received by the piston, due to the pressure of the gases that were formed by igniting the fuel.

In simple terms, this is the conversion of thermal or heat energy that appears during the combustion of a fuel mixture (air and gasoline) into mechanical energy. It should be noted that this has already happened, for example, with steam power plants - also the fuel, under the influence of temperature, pushed the pistons of the units. However, the installations there were many times larger, and the fuel itself was solid (usually coal or firewood), which made it difficult to transport and operate; it was constantly necessary to “feed” it into the furnace with shovels. Internal combustion engines are much more compact and lighter than “steam” ones, and the fuel is much easier to store and transport.

More about losses

Looking ahead, we can confidently say that the efficiency of a gasoline engine ranges from 20 to 25%. And there are many reasons for this. If we take the incoming fuel and convert it into percentages, then we seem to get “100% of the energy” that is transferred to the engine, and then there are losses:

1)Fuel efficiency . Not all the fuel is burned, a small part of it goes with the exhaust gases, at this level we already lose up to 25% efficiency. Of course, now fuel systems are improving, an injector has appeared, but it is also far from ideal.

2) The second is thermal lossesAnd . The engine warms itself and many other elements, such as radiators, its body, and the liquid that circulates in it. Also, some of the heat leaves with exhaust gases. All this results in up to 35% loss of efficiency.

3) The third is mechanical losses . ON all kinds of pistons, connecting rods, rings - all places where there is friction. This can also include losses from the load of the generator, for example, the more electricity the generator generates, the more it slows down the rotation of the crankshaft. Of course, lubricants have also made progress, but again, no one has yet been able to completely overcome friction - losses are still 20%.

Thus, the bottom line is that the efficiency is about 20%! Of course, among the gasoline options, there are standout options in which this figure is increased to 25%, but there are not many of them.

That is, if your car consumes fuel 10 liters per 100 km, then only 2 liters of them will go directly to work, and the rest are losses!

Of course, you can increase the power, for example, by boring the head, watch a short video.

If you remember the formula, it turns out:

Which engine has the highest efficiency?

Now I want to talk about gasoline and diesel options, and find out which of them is the most efficient.

To put it in simple language and without getting into the weeds of technical terms, if you compare the two efficiency factors, the more efficient of them is, of course, diesel and here’s why:

1) Gasoline engine converts only 25% of energy into mechanical energy, but diesel about 40%.

2) If you equip a diesel type with turbocharging, you can achieve an efficiency of 50-53%, and this is very significant.

So why is it so effective? It's simple - despite the similar type of work (both are internal combustion units), diesel does its job much more efficiently. It has greater compression, and the fuel ignites using a different principle. It heats up less, which means there is a saving on cooling, it has fewer valves (saving on friction), and it also does not have the usual ignition coils and spark plugs, which means it does not require additional energy costs from the generator. It operates at lower speeds, there is no need to frantically spin the crankshaft - all this makes the diesel version a champion in terms of efficiency.

About diesel fuel efficiency

FROM more high value efficiency - fuel efficiency follows. So, for example, a 1.6-liter engine can consume only 3–5 liters in the city, in contrast to the gasoline type, where the consumption is 7–12 liters. A diesel engine is much more efficient; the engine itself is often more compact and lighter, and also lately and more environmentally friendly. All these positive points, are achieved thanks to higher value, there is a direct relationship between efficiency and compression, look at the small plate.

However, despite all the advantages, it also has many disadvantages.

As it becomes clear, the efficiency of an internal combustion engine is far from ideal, so the future clearly belongs to electric options - all that remains is to find efficient batteries that are not afraid of frost and hold a charge for a long time.

Efficiency (Efficiency) - characteristic of the efficiency of a system (device, machine) in relation to the conversion or transmission of energy. Determined by the ratio of usefully used energy to the total amount of energy received by the system; usually denoted η (“this”). η = Wpol/Wcym. Efficiency is a dimensionless quantity and is often measured as a percentage. Mathematically determination of efficiency can be written as:

X 100%,

Where A- useful work, and Q- energy expended.

Due to the law of conservation of energy, efficiency is always less than or equal to unity, that is, it is impossible to obtain more useful work than the energy expended.

Heat engine efficiency- the ratio of the complete useful work of the engine to the energy received from the heater. Efficiency heat engine can be calculated using the following formula

,

where is the amount of heat received from the heater, is the amount of heat given to the refrigerator. Highest efficiency among cyclic machines operating at given hot source temperatures T 1 and cold T 2, have heat engines operating on the Carnot cycle; this marginal efficiency is equal to

.

Not all indicators characterizing efficiency energy processes, correspond to the above description. Even if they are traditionally or erroneously called "efficiency", they can have other properties, in particular, exceed 100%.

Boiler efficiency

Main article: Boiler heat balance

The efficiency of fossil fuel boilers is traditionally calculated based on the lower calorific value; it is assumed that the moisture of the combustion products leaves the boiler in the form of superheated steam. In condensing boilers, this moisture is condensed, and the heat of condensation is usefully used. When calculating efficiency according to lower heat combustion, it may eventually turn out to be greater than unity. IN in this case it would be more correct to calculate it by the higher calorific value, which takes into account the heat of condensation of steam; however, the performance of such a boiler is difficult to compare with data on other installations.

Heat pumps and chillers

The advantage of heat pumps as heating equipment is the ability to sometimes receive more heat than the energy consumed for their operation; similarly, a refrigeration machine can remove more heat from the cooled end than is expended in organizing the process.

The efficiency of such heat engines is characterized by coefficient of performance(for refrigeration machines) or transformation ratio(for heat pumps)

,

where is the heat taken from the cold end (in refrigeration machines) or transferred to the hot end (in heat pumps); - the work (or electricity) spent on this process. The reverse Carnot cycle has the best performance indicators for such machines: it has a coefficient of performance

,

where , are the temperatures of the hot and cold ends, . This value, obviously, can be arbitrarily large; Although it is difficult to approach practically, the coefficient of performance can still exceed unity. This does not contradict the first law of thermodynamics, since, in addition to the energy taken into account A(e.g. electric), to heat Q There is also energy taken from the cold source.

Literature

• Peryshkin A.V. Physics. 8th grade. - Bustard, 2005. - 191 p. - 50,000 copies. - ISBN 5-7107-9459-7.

Notes

Wikimedia Foundation. 2010.

Synonyms:

See what “Efficiency factor” is in other dictionaries:

efficiency- Ratio of supplied power to consumed active power. [OST 45.55 99] efficiency factor efficiency actions A quantity characterizing the perfection of the processes of transformation, transformation or transfer of energy, which is the ratio of useful... ... Technical Translator's Guide

Or return coefficient (Efficiency) is a characteristic of the quality of operation of any machine or apparatus in terms of its efficiency. By efficiency is meant the ratio of the amount of work received from a machine or energy from the apparatus to the amount ... ... Marine Dictionary

- (efficiency), an indicator of the efficiency of a mechanism, defined as the ratio of the work performed by the mechanism to the work spent on its operation. Efficiency usually expressed as a percentage. An ideal mechanism would have efficiency =... ... Scientific and technical encyclopedic dictionary

Modern encyclopedia

- (efficiency) characteristic of the efficiency of a system (device, machine) in relation to energy conversion; is determined by the ratio of usefully used energy (converted into work during a cyclic process) to the total amount of energy,... ... Big Encyclopedic Dictionary

- (efficiency), characteristic of the efficiency of a system (device, machine) in relation to the conversion or transmission of energy; is determined by the ratio m) of usefully used energy (Wtotal) to the total amount of energy (Wtotal) received by the system; h=Wfloor… … Physical encyclopedia

- (efficiency) ratio of usefully used energy W p, for example. in the form of work, to the total amount of energy W received by the system (machine or engine), W p/W. Due to inevitable energy losses due to friction and other nonequilibrium processes for real systems... ... Physical encyclopedia

The ratio of useful work expended or energy received to all work expended or, respectively, energy consumed. For example, the efficiency of an electric motor is the ratio of mechanical. the power it gives out to the electricity supplied to it. power; TO.… … Technical railway dictionary

Noun, number of synonyms: 8 efficiency (4) return (27) fruitfulness (10) ... Dictionary of synonyms

Efficiency- is a quantity characterizing the perfection of any system in relation to any process of transformation or transfer of energy occurring in it, defined as the ratio of useful work to the work spent on actuation.... ... Encyclopedia of terms, definitions and explanations of building materials

Efficiency- (efficiency), a numerical characteristic of the energy efficiency of any device or machine (including a heat engine). Efficiency is determined by the ratio of usefully used energy (i.e. converted into work) to the total amount of energy... ... Illustrated Encyclopedic Dictionary

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's consider first heat engine, operating in a reversible cycle with 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 work according to reverse cycle(like a refrigeration machine), and the other machine - in a direct 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. 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:

Real efficiency value Due to various types of energy losses, it 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.