What is efficiency in physics formula. The topic of efficiency and fuel efficiency

Not a single action performed occurs without losses - they always exist. The result obtained is always less than the effort that has to be expended to achieve it. The coefficient indicates how large the losses are when performing work. useful action(efficiency).

What is hidden behind this abbreviation? In essence, this is the efficiency coefficient of the mechanism or indicator rational use energy. The efficiency value does not have any units of measurement; it is expressed as a percentage. This coefficient is determined as the ratio of the useful work of the device to the work expended on its operation. To calculate the efficiency, the calculation formula will look like this:

Efficiency =100* (useful work done/work expended)

Various devices use to calculate this ratio. different meanings. For electric motors Efficiency will look like the ratio of useful work performed to electrical energy received from the network. For will be defined as the ratio of the useful work performed to the amount of heat expended.

For determination of efficiency It is necessary that everyone is different and the work is expressed in the same units. It will then be possible to compare any objects, such as electricity generators and biological objects, in terms of efficiency.

As already noted, due to inevitable losses during the operation of mechanisms, the efficiency factor is always less than 1. Thus, the efficiency of thermal stations reaches 90%, the efficiency of internal combustion engines is less than 30%, and the efficiency of an electric transformer is 98%. The concept of efficiency can be applied both to the mechanism as a whole and to its individual components. At overall assessment efficiency of the mechanism as a whole (its efficiency) is taken as the product of the efficiency of individual components this device.

Problem effective use fuel did not appear today. With the continuous increase in the cost of energy resources, the issue of increasing the efficiency of mechanisms turns from a purely theoretical into a practical issue. If the efficiency of a regular car does not exceed 30%, then we simply throw away 70% of our money spent on refueling the car.

Consideration of the efficiency of the internal combustion engine (ICE) shows that losses occur at all stages of its operation. Thus, only 75% of the incoming fuel is burned in the engine cylinders, and 25% is released into the atmosphere. Of all the burned fuel, only 30-35% of the released heat is used to perform useful work; the rest of the heat is either lost in the exhaust gases or remains in the car’s cooling system. From the received power to useful work about 80% is used, the rest of the power is spent on overcoming friction forces and is used auxiliary mechanisms car.

Even on this simple example analysis of the efficiency of the mechanism allows us to determine the directions in which work should be carried out to reduce losses. Thus, one of the priority areas is to ensure complete combustion of fuel. This is achieved by additional atomization of fuel and increased pressure, which is why engines with direct injection and turbocharging are becoming so popular. The heat removed from the engine is used to heat the fuel for better vaporization, and mechanical losses are reduced through the use of modern grades

Here we have considered such a concept, as described, what it is and what it affects. Using the example of an internal combustion engine, the efficiency of its operation is considered and directions and ways to increase the capabilities of this device, and, consequently, efficiency are determined.

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

Formula 1 - efficiency

Where- A useful work

—Q total work that was spent

Any system that does any work must receive energy from outside, with the help of which the work will be done. Take, for example, a voltage transformer. The input is supplied mains voltage 220 volts, 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 operate.

But not all the energy taken from the network will reach the lamp, since there are losses in the transformer. For example, losses of magnetic energy in the core of a transformer. Or losses in the active resistance of the windings. Where electrical energy will turn into heat before reaching the consumer. This thermal energy is useless in this system.

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

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

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

As is known, on at the moment mechanisms have not yet been created that would completely convert one type of energy into another. During operation, any man-made device spends part of the energy on resisting forces or wastes it in vain. environment. The same thing happens in a closed electrical circuit. When charges flow through conductors, there is total resistance and payload electricity work. To compare their ratios, you will need to calculate the coefficient of performance (efficiency).

Why do you need to calculate efficiency?

The efficiency of an electrical circuit is the ratio of useful heat to total heat.

For clarity, let's give an example. By finding the efficiency of a motor, it is possible to determine whether its primary operating function justifies the cost of electricity consumed. That is, its calculation will give a clear picture of how well the device converts the received energy.

Pay attention! As a rule, efficiency does not have a value, but is a percentage or a numerical equivalent from 0 to 1.

Efficiency is found by general formula calculations for all devices in general. But to get its result in an electrical circuit, you first need to find the force of electricity.

Finding the current in a complete circuit

It is known from physics that any current generator has its own resistance, which is also called internal power. Apart from this meaning, the source of electricity also has its own power.

Let's give values ​​to each element of the chain:

• resistance – r;
• current strength – E;

So, to find the current strength, the designation of which will be - I, and the voltage across the resistor - U, it will take time - t, with the passage of charge q = lt.

Due to the fact that the power of electricity is constant, the work of the generator is entirely converted into heat released to R and r. This amount can be calculated using the Joule-Lenz law:

Q = I2 + I2 rt = I2 (R + r) t.

Then the right sides of the formula are equated:

EIt = I2 (R + r) t.

Having carried out the reduction, the calculation is obtained:

By rearranging the formula, the result is:

This final value will be the electrical force in this device.

Having made a preliminary calculation in this way, the efficiency can now be determined.

Calculation of electrical circuit efficiency

The power received from the current source is called consumed, its definition is written - P1. If this physical quantity passes from the generator into the complete circuit, it is considered useful and is written down - P2.

To determine the efficiency of a circuit, it is necessary to recall the law of conservation of energy. In accordance with it, the power of the receiver P2 will always be less than the power consumption of P1. This is explained by the fact that during operation in the receiver there is always an inevitable waste of converted energy, which is spent on heating the wires, their sheath, eddy currents, etc.

To find an assessment of the properties of energy conversion, an efficiency is required, which will be equal to the ratio of the powers P2 and P1.

So, knowing all the values ​​of the indicators that make up the electrical circuit, we find its useful and complete operation:

• And useful. = qU = IUt =I2Rt;
• And total = qE = IEt = I2(R+r)t.

In accordance with these values, we find the power of the current source:

• P2 = A useful /t = IU = I2 R;
• P1 = A total /t = IE = I2 (R + r).

Having performed all the steps, we obtain the efficiency formula:

n = A useful / A total = P2 / P1 =U / E = R / (R +r).

This formula turns out that R is above infinity, and n is above 1, but with all this, the current in the circuit remains in a low position, and its useful power is small.

Everyone wants to find increased efficiency. To do this, it is necessary to find conditions under which P2 will be maximum. The optimal values ​​will be:

• P2 = I2 R = (E / R + r)2 R;
• dP2 / dR = (E2 (R + r)2 - 2 (r + R) E2 R) / (R + r)4 = 0;
• E2 ((R + r) -2R) = 0.

In this expression, E and (R + r) are not equal to 0, therefore, the expression in brackets is equal to it, that is, (r = R). Then it turns out that the power has a maximum value, and the efficiency = 50%.

It is known that electrical energy is transmitted over long distances at voltages exceeding the level used by consumers. The use of transformers is necessary in order to convert voltages to the required values, increase the quality of the electricity transmission process, and also reduce the resulting losses.

Description and principle of operation of the transformer

A transformer is a device used to lower or increase voltage, change the number of phases and, in rare cases, change the frequency of alternating current.

The following device types exist:

• power;
• measuring;
• low power;
• pulse;
• peak transformers.

A static device consists of the following main structural elements: two (or more) windings and a magnetic circuit, which is also called a core. In transformers, voltage is supplied to the primary winding and removed from the secondary in a converted form. The windings are connected inductively, through magnetic field in the core.

Along with other converters, transformers have an efficiency factor (abbreviated as Efficiency), With symbol. This coefficient represents the ratio of energy effectively used to energy consumed from the system. It can also be expressed as the ratio of the power consumed by the load to the power consumed by the device from the network. Efficiency is one of the primary parameters characterizing the efficiency of the work performed by a transformer.

Types of losses in a transformer

The process of transferring electricity from the primary winding to the secondary is accompanied by losses. For this reason, not all energy is transferred, but most of it.

The design of the device does not include rotating parts, unlike other electrical machines. This explains the absence of mechanical losses in it.

So, the device contains the following losses:

• electrical, in copper windings;
• magnetic, in steel core.

Energy diagram and the Law of Conservation of Energy

The principle of operation of the device can be schematically presented in the form of an energy diagram, as shown in Image 1. The diagram reflects the process of energy transfer, during which electrical and magnetic losses are generated .

According to the diagram, the formula for determining the effective power P 2 is as follows:

P 2 =P 1 -ΔP el1 -ΔP el2 -ΔP m (1)

where, P 2 is useful, and P 1 is the power consumed by the device from the network.

Denoting the total losses ΔP, the law of conservation of energy will look like: P 1 =ΔP+P 2 (2)

From this formula it is clear that P 1 is spent on P 2, as well as on the total losses ΔP. Hence, the efficiency of the transformer is obtained in the form of the ratio of the supplied (useful) power to the consumed power (the ratio of P 2 and P 1).

Determination of efficiency

With the required accuracy for calculating the device, the previously derived efficiency values ​​can be taken from Table No. 1:

As shown in the table, the value of the parameter directly depends on the total power.

Determination of efficiency by direct measurements

The formula for calculating efficiency can be presented in several versions:

This expression clearly reflects that the efficiency value of the transformer is not more than one, and is also not equal to it.

The following expression determines the net power value:

P 2 =U 2 *J 2 *cosφ 2 , (4)

where U 2 and J 2 are the secondary voltage and current of the load, and cosφ 2 is the power factor, the value of which depends on the type of load.

Since P 1 =ΔP+P 2, formula (3) takes on the following form:

Electrical losses of the primary winding ΔP el1n depend on the square of the current flowing in it. Therefore, they should be defined this way:

(6)

In turn:

(7)

where r mp is the active winding resistance.

Since the operation of an electromagnetic device is not limited to the rated mode, determining the degree of current load requires the use of a load factor, which is equal to:

β=J 2 /J 2н, (8)

where J 2n is the rated current of the secondary winding.

From here, we write down expressions for determining the secondary winding current:

J 2 =β*J 2n (9)

If we substitute this equality into formula (5), we get the following expression:

Note that determining the efficiency value using the last expression is recommended by GOST.

Summarizing the information presented, we note that the efficiency of a transformer can be determined by the power values ​​of the primary and secondary windings of the device at rated mode.

Determination of efficiency by indirect method

Due to the large efficiency values, which can be equal to 96% or more, as well as the uneconomical nature of the direct measurement method, it is not possible to calculate the parameter with a high degree of accuracy. Therefore, its determination is usually carried out by an indirect method.

Summarizing all the obtained expressions, we obtain the following formula for calculating the efficiency:

η=(P 2 /P 1)+ΔP m +ΔP el1 +ΔP el2, (11)

To summarize, it should be noted that a high efficiency indicator indicates the efficient operation of the electromagnetic device. Losses in the windings and core steel, according to GOST, are determined by experience or a short circuit, and measures aimed at reducing them will help achieve the highest possible efficiency values, which is what we need to strive for.

Efficiency factor (efficiency) is a characteristic of the system's performance in relation to the conversion or transfer of energy, which is determined by the ratio of the useful energy used to the total energy received by the system.

Efficiency- a dimensionless quantity, usually expressed as a percentage:

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

Carnot cycle is a reversible circular gas process, which consists of sequentially standing two isothermal and two adiabatic processes performed with the working fluid.

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

The French engineer Sadi Carnot in 1824 derived the formula for the maximum efficiency of an ideal heat engine, where the working fluid is ideal gas, the cycle of which consisted of two isotherms and two adiabats, i.e. 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, has the form: , where T1 - absolute temperature 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, and jet engines.

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

• heater;
• working fluid;
• fridge.

The heater emits 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 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, going through the same states, but in the opposite direction, then we will do the same absolute value, but negative work. As a result, all work per cycle will be zero.

In order for the work of a heat engine to be different from zero, the work of gas compression 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, which is why a refrigerator is included in the design of the heat engine. The working fluid transfers heat to the refrigerator when it comes into contact with it.