Mathematically, the definition of efficiency can be written as:

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

If efficiency is expressed as a percentage, then it is calculated by the formula:

Where Q X (\displaystyle Q_(\mathrm (X) ))- heat taken from the cold end (in refrigeration machines, cooling capacity); A (\displaystyle A)

The term used for heat pumps is transformation ratio

Where Q Γ (\displaystyle Q_(\Gamma ))- condensation heat transferred to the coolant; A (\displaystyle A)- the work (or electricity) spent on this process.

In the perfect car Q Γ = Q X + A (\displaystyle Q_(\Gamma )=Q_(\mathrm (X) )+A), from here to the ideal car ε Γ = ε X + 1 (\displaystyle \varepsilon _(\Gamma )=\varepsilon _(\mathrm (X) )+1)

Coefficient useful action shows the ratio of suitable work that is performed by a mechanism or device to the work expended. Often, work expended is the amount of energy that a device consumes in order to perform work.

You will need

• - automobile;
• – thermometer;
• - calculator.

Instructions

2. When calculating the efficiency of a heat motor, consider the eligible work to be the mechanical work performed by the mechanism. For the work expended, take the number of heat released by the burned fuel, which is the source of energy for the engine.

3. Example. The average traction force of a car engine is 882 N. It consumes 7 kg of gasoline per 100 km of travel. Determine the efficiency of its motor. Find suitable work first. It is equal to the product of force F and the distance S covered by the body under its influence Аn=F?S. Determine the amount of heat that will be released when burning 7 kg of gasoline, this will be the work expended Az = Q = q? m, where q is the specific heat of combustion of the fuel, for gasoline it is equal to 42? 10^6 J/kg, and m is the mass this fuel. The motor efficiency will be equal to efficiency=(F?S)/(q?m)?100%= (882?100000)/(42?10^6?7)?100%=30%.

4. In general, in order to determine the efficiency, every heat engine (internal combustion engine, steam engine, turbine, etc.), where work is performed by gas, has an indicator useful action equal to the difference in heat given off by the heater Q1 and received by the refrigerator Q2, find the difference in the heat of the heater and refrigerator, and divide by the heat of the heater efficiency = (Q1-Q2)/Q1. Here, efficiency is measured in submultiple units from 0 to 1; to convert the result into percentages, multiply it by 100.

5. In order to obtain the efficiency of an impeccable heat engine (Carnot machine), find the ratio of the temperature difference between the heater T1 and the refrigerator T2 to the heater temperature efficiency = (T1-T2)/T1. This is the maximum permissible efficiency for a certain type of heat engine with given temperatures of the heater and refrigerator.

6. For an electric motor, find the work expended as the product of the power and the time it takes to do it. Let's say, if a crane electric motor with a power of 3.2 kW lifts a load weighing 800 kg to a height of 3.6 m in 10 s, then its efficiency is equal to the ratio of suitable work Аp=m?g?h, where m is the mass of the load, g?10 m /With? acceleration of free fall, h – height to which the load was raised, and expended work Az=P?t, where P – motor power, t – time of its operation. Get the formula for determining the efficiency=Ap/Az?100%=(m?g?h)/(P?t)?100%=%=(800?10?3.6)/(3200?10)?100% =90%.

The efficiency index (efficiency index) is an indicator of the performance of any system, be it a car engine, a machine or another mechanism. It shows how effectively a given system uses the energy it receives. Calculating efficiency is very easy.

Instructions

1. Most of the time, the efficiency is calculated from the ratio of the energy usable by the system to each total energy received in a certain time interval. It is worth noting that efficiency does not have specific units of measurement. However, in the school curriculum this value is measured as a percentage. This indicator, based on the above data, is calculated using the formula:? = (A/Q)*100%, where? (“eta”) is the desired efficiency, A is the usable performance of the system, Q is the total energy consumption, A and Q are measured in Joules.

2. The above method for calculating efficiency is not exclusive, because the usable work of the system (A) is calculated by the formula: A = Po-Pi, where Po is the energy supplied to the system from the outside, Pi is the energy loss during system operation. Having expanded the numerator of the above formula, it can be written in the following form:? = ((Po-Pi)/Po)*100%.

3. To make the calculation of efficiency more clear and visual, we can look at examples. Example 1: The useful operation of the system is 75 J, the amount of energy expended for its operation is 100 J, it is necessary to determine the efficiency of this system. To solve this problem, use the very first formula:? = 75/100 = 0.75 or 75%Answer: The efficiency of the proposed system is 75%.

4. Example 2: The energy supplied to operate the motor is 100 J, the energy loss during operation of this motor is 25 J, the efficiency needs to be calculated. To solve the proposed problem, use the 2nd formula for calculating the desired indicator:? = (100-25)/100 = 0.75 or 75%. The results in both examples were identical; in the second case, the numerator data was analyzed in more detail.

Note!
Many types of modern engines (say, a rocket engine or a turbo-air engine) have several stages of their operation, and for the entire stage there is its own efficiency, which is calculated using each of the above formulas. But in order to find a universal indicator, you will need to multiply all the famous efficiencies at all stages of operation of a given motor: = ?1*?2*?3*…*?.

Helpful advice
The efficiency cannot be greater than unity; during operation of any system, energy losses inevitably occur.

Associated transportation is a type of transport transportation consisting of load a vehicle running idle. Situations when transport is forced to move without cargo occur quite often, both before and later after the completion of the intended transport order. For an enterprise, the likelihood of taking on additional cargo means, at a minimum, a reduction in financial losses.

Instructions

1. Evaluate the effectiveness of using associated cargo transportation for your enterprise. A significant point that should be understood is the fact that associated cargo can be transported at a time when transport is forced to move empty after the implementation of the primary (core) transport request. If such situations occur regularly in the activities of your enterprise, boldly choose this method of optimizing transportation.

2. Estimate what associated cargo your vehicle can transport in terms of weight and dimensions. Passing cargo can be economically advantageous even if part of the cargo space of your vehicle is not occupied.

3. Consider from which points of the main route you will be able to take passing cargo. It is more comfortable for everyone if you can receive such cargo at the final point of the planned route and transport it to the place where your transport enterprise is located. But such a situation may not always occur. Therefore, also consider the likelihood of some deviation from the route, calculating, of course, the economic rationality of such a metamorphosis.

4. Find out whether the company to which you are making scheduled cargo transportation requires return transportation of cargo. In this case, it is much easier to agree on the price of the issue and ensure the security of additional mutually beneficial cooperation.

5. Find several specialized Internet portals that provide information services in the field of cargo transportation. As usual, the websites of such companies have corresponding sections that allow you to find associated cargo along your route and leave a corresponding request. In most cases, the use of such a probability requires, at a minimum, registration on the site. It will be perfect if the information source has built-in probabilities for a logistical review of counteroffers.

6. Do not neglect consolidated transportation when small cargo from different clients is transported in the chosen direction using one type of transport. In this case, transport must make shuttle routes in selected directions.

Note!
Detecting passing cargo is absolutely not difficult! The main task of our service is to search for different downloads, something that users can do not only with maximum convenience, but also for free. With the help of our system, the operation of which is based on the use of modern information technologies, cargo can be detected very easily.

Helpful advice
Apparently, you have decided to buy or rent a huge truck, with the help of which you intend to earn money by transporting goods throughout Russia, the CIS and Europe. It doesn’t matter whether you hire a driver or drive one yourself, you will need customers, that is, cargo for transportation. Then you will definitely think or have already thought about where and how to find cargo for your truck?

In order to discover the indicator of the suitable action of any engine, you need to divide the suitable work by the expended and multiply by 100 percent. For thermal engine discover this value by the ratio of power multiplied by the duration of operation to the heat released during fuel combustion. In theory Efficiency thermal engine determined by the ratio of the temperatures of the refrigerator and heater. For electric motors, find the ratio of its power to the power of the current consumed.

You will need

• internal combustion engine (ICE) passport, thermometer, tester

Instructions

1. Definition Efficiency ICE Find in the technical documentation of this specific engine its power. Fill its tank with a certain amount of fuel and start the engine so that it runs for some time at full cycles, developing the maximum power indicated in the passport. Use a stopwatch to track your working time. engine, expressing it in seconds. After a while, stop the engine and drain the remaining fuel. By subtracting the final volume from the initial volume of fuel poured, find the volume of fuel consumed. Using the table, find its density and multiply by volume, obtaining the mass of fuel consumed m =? V. Express the mass in kilograms. Depending on the type of fuel (gasoline or diesel), determine its specific heat of combustion from the table. For determining Efficiency multiply maximum power by operating time engine and by 100%, and divide the result stepwise by its mass and specific heat of combustion Efficiency=P t 100%/(q m).

2. For a perfect heat engine, it is possible to apply Carnot's formula. To do this, find out the combustion temperature of the fuel and measure the temperature of the refrigerator (exhaust gases) with a special thermometer. Convert the temperature measured in degrees Celsius to an unconditional scale by adding the number 273 to the value. To determine Efficiency from the number 1, subtract the temperature ratio of the refrigerator and heater (fuel combustion temperature) Efficiency=(1-Thol/Tnag) 100%. This calculation option Efficiency does not consider mechanical friction and heat exchange with the external environment.

3. Definition Efficiency electro engine Find out the rated power of the electric engine, according to technical documentation. Connect it to a current source, achieving maximum shaft cycles, and with the help of a tester, measure the voltage on it and the current in the circuit. For determining Efficiency divide the power stated in the documentation by the product of current and voltage, multiply the total by 100% Efficiency=P 100%/(I U).

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Note!
In all calculations, the efficiency should be less than 100%.

To review normal population dynamics, sociologists need to identify general odds. The main ones are indicators of fertility, mortality, marriage and natural income. Based on them, it is possible to draw up a demographic picture at a given point in time.

Instructions

1. Note that the overall rate is a relative rate. Thus, the number of births in a certain period, say, in a year, will differ from the general fertility rate. This is due to the fact that when finding it, data on the total population is taken into account. This makes it possible to compare the current research results with the results of previous years.

2. Determine the billing period. For example, in order to find the marriage rate, you need to determine over what time period the number of marriages concerns you. Thus, data for the last six months will differ significantly from those that you will receive when determining a five-year time period. Consider that the calculation period when calculating the overall indicator is specified in years.

3. Determine the total population. Similar data can be obtained by referring to population census data. To determine the general indicators of fertility, mortality, marriage and divorce rates, you will need to find the product of the total population and the calculation period. Write the resulting number into the denominator.

4. In place of the numerator, replace the unconditional indicator with the desired relative indicator. Let's say, if you are faced with the task of determining the universal birth rate, then in the place of the numerator there should be a number that reflects the total number of children born during the period that concerns you. If your goal is to determine the tier of mortality or marriage rate, then in place of the numerator put the number of people who died in the calculation period or the number of people who got married, respectively.

5. Multiply the resulting number by 1000. This will be the overall indicator you desire. If you are faced with the task of finding a general income indicator, then subtract the mortality rate from the birth rate.

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The word “work” refers to every action that gives a person a means of subsistence. In other words, he receives physical reward for it. Nevertheless, people are ready, in their free time, either for free or for a purely symbolic fee, to also participate in socially beneficial work aimed at supporting those in need, improving courtyards and streets, landscaping, etc. The number of such volunteers would probably still be enormous, but they often do not know where their services may be needed.

Instructions

1. One of the most famous types of socially beneficial work is charity. It includes assistance to needy, socially vulnerable groups of the population: the disabled, the elderly, the homeless. In a word, to every one who, for some reason, finds himself in a difficult life situation.

2. Volunteers who want to take part in providing such assistance should contact the nearest philanthropic organizations or public assistance departments. You can make inquiries at the nearest church - the clergyman probably knows which of his flock is in particular need of support.

3. You can also take the initiative literally at your place of residence - in an apartment building there probably live lonely pensioners, disabled people or single mothers who have the entire ruble in their account. Give them all possible help. It does not necessarily have to consist of a monetary donation - it is permissible, say, from time to time to go to the grocery store or to the pharmacy to buy medicine.

4. Many people want to take part in the improvement of their hometown. They should contact the relevant structures of the local municipality, say, those that are responsible for cleaning the territories and landscaping. There will probably be work. In addition, it is allowed, say, on one’s own initiative to make a flower bed under the windows of the house and plant flowers.

5. There are people who really love animals and want to help stray dogs and cats. If you fall into this category, contact local animal rights organizations or animal shelter owners. Well, if you live in a huge city where there are zoos, ask the administration if assistants are needed to care for the animals. As usual, such offers of help are greeted with gratitude.

6. It is impossible to forget about educating the younger generation. If an enthusiastic volunteer is able to, say, teach classes in some school club or cultural and creative center, he will bring enormous benefit. In a word, there is a lot of socially suitable work for caring people, for every taste and probability. There would be a desire.

Tip 7: What is moisture index and how to calculate it

Humidity indicator is an indicator used to determine microclimate parameters. It can be calculated if you have information about precipitation in the region over a fairly long period.

Humidity index

The humidification coefficient is a special indicator developed by experts in the field of meteorology to assess the degree of microclimate humidity in a particular region. It was taken into account that microclimate represents a long-term response to weather conditions in a given area. Consequently, it was also decided to consider the moisture indicator over a long time frame: as usual, this indicator is calculated on the basis of data collected during the year. Thus, the moisture indicator shows how huge the amount of precipitation falling during this period is in the region under consideration. This, in turn, is one of the main factors determining the prevailing type of vegetation in this area.

Calculation of moisture index

The formula for calculating the moisture indicator is as follows: K = R / E. In this formula, the symbol K denotes the moisture indicator itself, and the symbol R denotes the amount of precipitation that fell in a given area during the year, expressed in millimeters. Finally, the symbol E represents the amount of precipitation that evaporated from the earth's surface during the same period of time. The stated amount of precipitation, which is also expressed in millimeters, depends on the type of soil, the temperature in a given region at a certain time and other factors. Consequently, despite the apparent simplicity of the given formula, the calculation of the moisture indicator requires a large number of advance measurements using precision instruments and can only be carried out by a fairly large team of meteorologists. In turn, the value of the moisture indicator in a certain territory, considering all these indicators, as usual , allows us to determine with a high degree of reliability which type of vegetation is predominant in this region. Thus, if the humidity index exceeds 1, this indicates a high level of humidity in the given area, which entails the advantage of such types of vegetation as taiga, tundra or forest-tundra. A satisfactory moisture level corresponds to a moisture index of 1, and, as usual, is characterized by the predominance of mixed or broad-leaved forests. Humidity index ranging from 0.6 to 1 is typical for forest-steppe areas, from 0.3 to 0.6 – for steppes, from 0.1 to 0.3 – for semi-desert areas, and from 0 to 0.1 – for deserts .

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Electric motors appeared quite a long time ago, but great interest in them arose when they began to represent an alternative to internal combustion engines. Of particular interest is the issue of electric motor efficiency, which is one of its main characteristics.

Each system has something that characterizes the effectiveness of its operation as a whole. That is, it determines how well a system or device delivers or converts energy. Efficiency has no value, and most often it is presented as a percentage or a number from zero to one.

Efficiency parameters in electric motors

The main task of an electric motor is to convert electrical energy into mechanical energy. Efficiency determines the effectiveness of a given function. The formula for electric motor efficiency is as follows:

• n = p2/p1

In this formula, p1 is the supplied electrical power, p2 is the useful mechanical power that is generated directly by the engine. Electrical power is determined by the formula: p1=UI (voltage multiplied by current), and the value of mechanical power by the formula P=A/t (ratio of work per unit time). This is how the calculation of the efficiency of an electric motor looks like. However, this is the simplest part of it. Depending on the purpose of the engine and the scope of its application, the calculation will differ and take into account many other parameters. In fact, the formula for electric motor efficiency includes many more variables. The simplest example was given above.

Decrease in efficiency

The mechanical efficiency of an electric motor must be taken into account when choosing a motor. Losses that are associated with heating the engine and reducing currents play a very important role. Most often, a drop in efficiency is associated with the release of heat, which naturally occurs during engine operation. The reasons for the release of heat can be different: the engine can heat up due to friction, as well as for electrical and even magnetic reasons. As the simplest example, we can cite a situation where 1,000 rubles were spent on electrical energy, and work was done for 700 rubles. In this case, the efficiency will be equal to 70%.

To cool electric motors, fans are used that drive air through the gaps created. Depending on the class of engines, heating can be carried out to a certain temperature. For example, class A engines can heat up to 85-90 degrees, class B - up to 110 degrees. In the case when the temperature exceeds the permissible limit, this may indicate a short circuit in the stator.

Average efficiency of electric motors

It is worth noting that the efficiency of a DC electric motor (and alternating current too) varies depending on the load:

1. At idle, the efficiency is 0%.
2. At a load of 25%, the efficiency is 83%.
3. At 50% load the efficiency is 87%.
4. At 75% load the efficiency is 88%.
5. At 100% load the efficiency is 87%.

One of the reasons for the drop in efficiency is current asymmetry, when a different voltage is applied to each of the three phases. If, for example, the first phase has a voltage of 410 V, the second - 403 V, and the third - 390 V, then the average value will be equal to 401 V. The asymmetry in this case will be equal to the difference between the maximum and minimum voltage on the phases (410 -390), that is, 20 V. The formula for the efficiency of an electric motor for calculating losses will look like this in our situation: 20/401*100 = 4.98%. This means that we lose 5% efficiency during operation due to the voltage difference between the phases.

General losses and drop in efficiency

There are a lot of negative factors that influence a decrease in the efficiency of an electric motor. There are certain techniques that allow you to determine them. For example, you can determine whether there is a gap through which power is partially transferred from the network to the stator and then to the rotor.

Starter losses also occur and they consist of several values. First of all, these may be losses related to eddy currents and magnetization reversal of the stator cores.

If the motor is asynchronous, then additional losses occur due to teeth in the rotor and stator. Eddy currents can also occur in individual engine components. All this in total reduces the efficiency of the electric motor by 0.5%. In asynchronous motors, all losses that may occur during operation are taken into account. Therefore, the range can vary from 80 to 90%.

Car engines

The history of the development of electric motors begins with the discovery. According to him, induced current always moves in such a way as to counteract the cause that causes it. It was this theory that formed the basis for the creation of the first electric motor.

Modern models are based on the same principle, but are radically different from the first copies. Electric motors have become much more powerful, more compact, but most importantly, their efficiency has increased significantly. We have already written above about the efficiency of an electric motor, and compared to an internal combustion engine this is an amazing result. For example, the maximum efficiency of an internal combustion engine reaches 45%.

Advantages of an electric motor

High efficiency is the main advantage of such a motor. And if an internal combustion engine spends more than 50% of energy on heating, then in an electric motor a small part of the energy is spent on heating.

The second advantage is light weight and compact dimensions. For example, Yasa Motors has created a motor that weighs only 25 kg. It is capable of producing 650 Nm, which is a very decent result. Also, such motors are durable and do not require a gearbox. Many electric car owners talk about the efficiency of electric engines, which is logical to some extent. After all, during operation, the electric motor does not emit any combustion products. However, many drivers forget that coal, gas or enriched uranium must be used to produce electricity. All these elements pollute the environment, so the environmental friendliness of electric motors is a very controversial issue. Yes, they do not pollute the air during operation. Power plants do this for them when producing electricity.

Increasing the efficiency of electric motors

Electric motors have some disadvantages that have a negative impact on operating efficiency. These are a weak starting torque, a high starting current and a mismatch between the mechanical torque of the shaft and the mechanical load. This leads to the device's efficiency decreasing.

To increase efficiency, they try to ensure the engine load is up to 75% or higher and increase power factors. There are also special devices for regulating the frequency of the supplied current and voltage, which also leads to increased efficiency and increased efficiency.

One of the most popular devices for increasing the efficiency of an electric motor is a soft starter, which limits the rate of increase in the starting current. It is also appropriate to use changes in the motor rotation speed by changing the voltage frequency. This results in reduced power consumption and ensures smooth, high-precision adjustment. The starting torque also increases, and under variable load the rotation speed is stabilized. As a result, the efficiency of the electric motor increases.

Maximum motor efficiency

Depending on the type of design, the efficiency of electric motors can vary from 10 to 99%. It all depends on what kind of engine it will be. For example, the efficiency of a piston-type pump electric motor is 70-90%. The final result depends on the manufacturer, the structure of the device, etc. The same can be said about the efficiency of the electric motor of a crane. If it is equal to 90%, then this means that 90% of the electricity consumed will be used to perform mechanical work, the remaining 10% will be used to heat the parts. Still, there are the most successful models of electric motors, the efficiency of which approaches 100%, but is not equal to this value.

Is efficiency above 100% possible?

It's no secret that electric motors whose efficiency exceeds 100% cannot exist in nature, since this contradicts the basic law of conservation of energy. The fact is that energy cannot come from nowhere and disappear in the same way. Any engine needs an energy source: gasoline, electricity. However, gasoline does not last forever, just like electricity, because their reserves have to be replenished. But if there was an energy source that did not need replenishment, then it would be quite possible to create a motor with an efficiency of over 100%. Russian inventor Vladimir Chernyshov showed a description of a motor that is based on a permanent magnet, and its efficiency, as the inventor himself assures, is more than 100%.

Hydroelectric power station as an example of a perpetual motion machine

For example, let's take a hydroelectric power station, where energy is generated by falling water from a great height. Water turns a turbine, which produces electricity. The fall of water is carried out under the influence of Earth's gravity. And although the work to produce electricity is done, the Earth's gravity does not become weaker, that is, the force of attraction does not decrease. Then the water evaporates under the influence of sunlight and returns to the reservoir. This completes the cycle. As a result, electricity has been generated and costs for its production have been resumed.

Of course, we can say that the Sun is not eternal, this is true, but it will last a couple of billion years. As for gravity, it constantly does work, pulling moisture from the atmosphere. To broadly generalize, a hydroelectric power plant is an engine that converts mechanical energy into electrical energy, and its efficiency is more than 100%. This makes it clear that we should not stop looking for ways to create an electric motor whose efficiency can be more than 100%. After all, not only gravity can be used as an inexhaustible source of energy.

Permanent magnets as energy sources for motors

The second interesting source is a permanent magnet, which does not receive energy from anywhere, and the magnetic field is not consumed even when doing work. For example, if a magnet attracts something to itself, it will do the work, and its magnetic field will not become weaker. They have tried to use this property more than once to create a so-called perpetual motion machine, but so far nothing more or less normal has come of it. Any mechanism will wear out sooner or later, but the source itself, which is a permanent magnet, is practically eternal.

However, there are experts who claim that over time, permanent magnets lose their strength as a result of aging. This is not true, but even if it were true, it could be brought back to life with just one electromagnetic pulse. An engine that would require recharging once every 10-20 years, although it cannot claim to be eternal, comes very close to this.

There have already been many attempts to create a perpetual motion machine based on permanent magnets. So far there have been no successful solutions, unfortunately. But given the fact that there is a demand for such engines (it simply cannot but exist), it is quite possible that in the near future we will see something that comes very close to the model of a perpetual motor that will run on renewable energy.

Conclusion

Electric motor efficiency is the most important parameter that determines the operating efficiency of a particular motor. The higher the efficiency, the better the motor. In an engine with an efficiency of 95%, almost all the energy expended is spent on doing work and only 5% is spent for other purposes (for example, heating spare parts). Modern diesel engines can achieve an efficiency value of 45%, and this is considered a great result. The efficiency of gasoline engines is even less.

Encyclopedic YouTube

• 1 / 5

  Mathematically, the definition of efficiency can be written as:

  η = A Q , (\displaystyle \eta =(\frac (A)(Q)),)

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

  If efficiency is expressed as a percentage, then it is calculated by the formula:

  η = A Q × 100% (\displaystyle \eta =(\frac (A)(Q))\times 100\%) ε X = Q X / A (\displaystyle \varepsilon _(\mathrm (X) )=Q_(\mathrm (X) )/A),

  Where Q X (\displaystyle Q_(\mathrm (X) ))- heat taken from the cold end (in refrigeration machines, cooling capacity); A (\displaystyle A)

  The term used for heat pumps is transformation ratio

  ε Γ = Q Γ / A (\displaystyle \varepsilon _(\Gamma )=Q_(\Gamma )/A),

  Where Q Γ (\displaystyle Q_(\Gamma ))- condensation heat transferred to the coolant; A (\displaystyle A)- the work (or electricity) spent on this process.

  In the perfect car Q Γ = Q X + A (\displaystyle Q_(\Gamma )=Q_(\mathrm (X) )+A), from here to the ideal car ε Γ = ε X + 1 (\displaystyle \varepsilon _(\Gamma )=\varepsilon _(\mathrm (X) )+1)

  The reverse Carnot cycle has the best performance indicators for refrigeration machines: it has a coefficient of performance

  ε = T X T Γ − T X (\displaystyle \varepsilon =(T_(\mathrm (X) ) \over (T_(\Gamma )-T_(\mathrm (X)))), because, in addition to the energy taken into account A(e.g. electric), in heat Q There is also energy taken from the cold source.

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

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

  It is often necessary to evaluate the effectiveness of the mechanism and 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 one. This value is often expressed as a percentage. It is usually denoted by the Greek letter η (read “this”). The efficiency factor is abbreviated as efficiency.

  η = (A_full /A_useful) * 100%,

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

  Among engines, the electric motor has the highest efficiency (up to 98%). The efficiency of internal combustion engines is 20% - 40%, and that of a steam turbine is approximately 30%.

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

  Examples of efficiency calculations

  Let's look at an example. A cyclist weighing 55 kg rode a bicycle weighing 5 kg up a hill 10 m high, doing 8 kJ of work. Find the efficiency of the bicycle. Do not take into account the rolling friction of the wheels on the road.

  Solution. Let's 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

  Let's find the work done to lift the bicycle and the cyclist:

  Auseful = PS = 600 N * 10 m = 6 kJ

  Let's find the efficiency of the bicycle:

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

  Answer: The efficiency of the bicycle is 75%.

  Let's look at another 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 rose if the efficiency of the lever is η%.

  Solution. Let's find the work done by force F:

  η% of this work is done to lift a body of mass m. Consequently, Fhη / 100 was spent on raising the body. Since the weight of the body is equal to mg, the body rose to a height of Fhη / 100 / mg.