What does "coefficient of performance" mean? Efficiency of an internal combustion engine - we know the efficiency in comparison

Coefficient of performance (COP) - a term that can be applied, perhaps, to every system and device. Even a person has an efficiency, though, probably, there is 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 efficiency of a particular system in relation to the return or conversion of energy. Efficiency is a measureless value 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 the efficiency is written as follows:

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

The efficiency factor, unfortunately, is always less than one or equal to it, since, according to the law of conservation of energy, we cannot get more work than the energy spent. In addition, the efficiency, in fact, is extremely rarely equal to one, since useful work is always accompanied by 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 source, T2 is the temperature of the cold source.

Electric motor efficiency

An electric motor is a device that converts electrical energy into mechanical energy, so the efficiency in this case is the efficiency ratio of the device in relation to the conversion of 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 is found as the ratio of work to unit time (P=A/t)

transformer efficiency

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

The efficiency of the transformer is found by the formula:

• Ƞ=1/1+(P0+PL*n2)/(P2*n), where P0 - no-load losses, PL - load losses, P2 - active power delivered to the load, n - relative degree of loading.

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 find descriptions of the type - efficiency of the order of 130%, however, in this case, you need to understand that the term is not used quite correctly, and, most likely, the author or the manufacturer understands a slightly different characteristic by this abbreviation.

For example, heat pumps are distinguished by the fact that they can give off more heat than they consume. Thus, the refrigerating machine can remove more heat from the cooled object than is spent in energy equivalent for the organization of the removal. The efficiency indicator of a refrigerating machine is called the coefficient of performance, denoted by the letter Ɛ and is 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 coefficient of performance is also called the efficiency of the refrigeration machine.

It is also interesting that the efficiency of boilers running on fossil fuels is usually calculated on the basis of the lower calorific value, while it can turn out to be more than one. However, it is still traditionally referred to as efficiency. It is possible to determine the efficiency of the boiler by the gross calorific value, and then it will always be less than one, but in this case it will be inconvenient to compare the performance of the boilers with the data of other installations.

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.

A bit of history

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.

heat engine

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%.

Efficiency calculation

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:

• Efficiency cannot exceed 1 (or 100%);
• to maximize this value, either an increase in the energy received from the heater or a decrease in the energy given to the refrigerator is necessary;
• an increase in the energy of the heater is achieved by changing the quality of the fuel;
• reducing the energy given to the refrigerator, make it possible to achieve the design features of the engines.

Ideal heat engine

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 of problem solving

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.

Real conditions

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.

Other heat engines

Real engines operate on different cycles:

• Otto cycle: the process at a constant volume changes adiabatically, creating a closed cycle;
• Diesel cycle: isobar, adiabat, isochor, adiabat;
• the process occurring at constant pressure is replaced by an adiabatic one, closing the cycle.

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.

Ways to change efficiency

When comparing ideal and real heat engines, it is worth noting that the temperature of the refrigerator of the latter cannot be any. Usually the atmosphere is considered 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.

Motor efficiency values

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.

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, there are common features in the principle of operation of various heat engines. 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.

It is known that a perpetual motion machine is impossible. This is due to the fact that for any mechanism the statement is true: the total work done with the help of this mechanism (including heating the mechanism and the environment, to overcome the friction force) is always more useful work.

For example, more than half of the work of an internal combustion engine is wasted on heating the components of the engine; some heat is carried away by the exhaust gases.

It is often necessary to evaluate the effectiveness of the mechanism, the feasibility of its use. Therefore, in order to calculate what part of the work done is wasted and what part is useful, a special physical quantity is introduced that shows the efficiency of the mechanism.

This value is called the efficiency of the mechanism

The efficiency of a mechanism is equal to the ratio of useful work to total work. Obviously, the efficiency is always less than unity. This value is often expressed as a percentage. Usually it is denoted by the Greek letter η (read "this"). Efficiency is abbreviated as efficiency.

η \u003d (A_full / A_useful) * 100%,

where η efficiency, A_full full work, A_useful useful work.

Among engines, the electric motor has the highest efficiency (up to 98%). Efficiency of internal combustion engines 20% - 40%, steam turbine about 30%.

Note that for increasing the efficiency of the mechanism often try to reduce the force of friction. This can be done using various lubricants or ball bearings in which sliding friction is replaced by rolling friction.

Efficiency calculation examples

Consider an example. A cyclist with a mass of 55 kg climbs a hill with a mass of 5 kg, the height of which is 10 m, while doing 8 kJ of work. Find the efficiency of the bike. The rolling friction of the wheels on the road is not taken into account.

Solution. Find the total mass of the bicycle and the cyclist:

m = 55 kg + 5 kg = 60 kg

Let's find their total weight:

P = mg = 60 kg * 10 N/kg = 600 N

Find the work done on lifting the bike and the cyclist:

Auseful \u003d PS \u003d 600 N * 10 m \u003d 6 kJ

Let's find the efficiency of the bike:

A_full / A_useful * 100% = 6 kJ / 8 kJ * 100% = 75%

Answer: Bicycle efficiency is 75%.

Let's consider one more example. A body of mass m is suspended from the end of the lever arm. A downward force F is applied to the other arm, and its end is lowered by h. Find how much the body has risen if the efficiency of the lever is η%.

Solution. Find the work done by the force F:

η % of this work is done to lift a body of mass m. Therefore, Fhη / 100 was spent on lifting the body. Since the weight of the body is equal to mg, the body has risen to a height of Fhη / 100 / mg.

Efficiency is a characteristic of the efficiency of a device or machine. Efficiency is defined as the ratio of useful energy at the output of the system to the total amount of energy supplied to the system. Efficiency is dimensionless and is often expressed as a percentage.

Formula 1 - efficiency

Where- A useful work

—Q the total work that was spent

Any system that performs any work must receive energy from the outside, with the help of which the work will be done. Take, for example, a voltage transformer. A mains voltage of 220 volts is applied to the input, 12 volts are removed from the output to power, for example, an incandescent lamp. So the transformer converts the energy at the input to the required value at which the lamp will work.

But not all the energy taken from the network will go to the lamp, since there are losses in the transformer. For example, the loss of magnetic energy in the core of a transformer. Or losses in the active resistance of the windings. Where electrical energy will be converted into heat without reaching the consumer. This thermal energy in this system is useless.

Since power losses cannot be avoided in any system, the efficiency is always below unity.

Efficiency can be considered as for the whole system, consisting of many separate parts. So to determine the efficiency for each part separately, then the total efficiency will be equal to the product of the efficiency of all its elements.

In conclusion, we can say that the efficiency determines the level of perfection of any device in the sense of transferring or converting energy. It also indicates how much energy supplied to the system is spent on useful work.