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Temperature efficiency. Efficiency of heat engines

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:

The coefficient of performance (efficiency) 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 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 an 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 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, and jet engines.

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

heater;
working fluid;
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 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.

The operation of many types of machines is characterized by such an important indicator as the efficiency of the heat engine. Every year engineers strive to create more advanced equipment that, with lower fuel consumption, would give the maximum result from its use.

Heat engine device

Before understanding what efficiency is, it is necessary to understand how this mechanism works. Without knowing the principles of its action, it is impossible to find out the essence of this indicator. A heat engine is a device that performs work using internal energy. Any heat engine that converts thermal energy into mechanical energy uses the thermal expansion of substances as the temperature increases. In solid-state engines, it is possible not only to change the volume of a substance, but also the shape of the body. The action of such an engine is subject to the laws of thermodynamics.

Operating principle

In order to understand how a heat engine works, it is necessary to consider the basics of its design. For the operation of the device, two bodies are needed: hot (heater) and cold (refrigerator, cooler). The operating principle of heat engines (heat engine efficiency) depends on their type. Often the refrigerator is a steam condenser, and the heater is any type of fuel that burns in the firebox. The efficiency of an ideal heat engine is found by the following formula:

Efficiency = (Theat - Cool) / Theat. x 100%.

In this case, the efficiency of a real engine can never exceed the value obtained according to this formula. Also, this figure will never exceed the above-mentioned value. To increase efficiency, most often the heater temperature is increased and the refrigerator temperature is decreased. Both of these processes will be limited by the actual operating conditions of the equipment.

When a heat engine operates, work is done, as the gas begins to lose energy and cools to a certain temperature. The latter is usually several degrees higher than the surrounding atmosphere. This is the temperature of the refrigerator. This special device is designed for cooling and subsequent condensation of exhaust steam. Where condensers are present, the temperature of the refrigerator is sometimes lower than the ambient temperature.

In a heat engine, when a body heats up and expands, it is not able to give up all its internal energy to do work. Some of the heat will be transferred to the refrigerator along with exhaust gases or steam. This part of the thermal internal energy is inevitably lost. During fuel combustion, the working fluid receives a certain amount of heat Q 1 from the heater. At the same time, it still performs work A, during which it transfers part of the thermal energy to the refrigerator: Q 2

Efficiency characterizes the efficiency of the engine in the field of energy conversion and transmission. This indicator is often measured as a percentage. Efficiency formula:

η*A/Qx100%, where Q is the energy expended, A is the useful work.

Based on the law of conservation of energy, we can conclude that the efficiency will always be less than unity. In other words, there will never be more useful work than the energy expended on it.

Engine efficiency is the ratio of useful work to the energy supplied by the heater. It can be represented in the form of the following formula:

η = (Q 1 -Q 2)/ Q 1, where Q 1 is the heat received from the heater, and Q 2 is given to the refrigerator.

Heat engine operation

The work done by a heat engine is calculated using the following formula:

A = |Q H | - |Q X |, where A is work, Q H is the amount of heat received from the heater, Q X is the amount of heat given to the cooler.

|Q H | - |Q X |)/|Q H | = 1 - |Q X |/|Q H |

It is equal to the ratio of the work done by the engine to the amount of heat received. Part of the thermal energy is lost during this transfer.

Carnot engine

The maximum efficiency of a heat engine is observed in the Carnot device. This is due to the fact that in this system it depends only on the absolute temperature of the heater (Tn) and cooler (Tx). The efficiency of a heat engine operating according to the Carnot cycle is determined by the following formula:

(Tn - Tx)/ Tn = - Tx - Tn.

The laws of thermodynamics made it possible to calculate the maximum efficiency that is possible. This indicator was first calculated by the French scientist and engineer Sadi Carnot. He invented a heat engine that operated on an ideal gas. It works in a cycle of 2 isotherms and 2 adiabats. The principle of its operation is quite simple: a heater is connected to a vessel with gas, as a result of which the working fluid expands isothermally. At the same time, it functions and receives a certain amount of heat. Afterwards the vessel is thermally insulated. Despite this, the gas continues to expand, but adiabatically (without heat exchange with the environment). At this time, its temperature drops to that of a refrigerator. At this moment, the gas comes into contact with the refrigerator, as a result of which it gives off a certain amount of heat during isometric compression. Then the vessel is thermally insulated again. In this case, the gas is adiabatically compressed to its original volume and state.

Varieties

Nowadays, there are many types of heat engines that operate on different principles and on different fuels. They all have their own efficiency. These include the following:

An internal combustion engine (piston), which is a mechanism where part of the chemical energy of burning fuel is converted into mechanical energy. Such devices can be gas and liquid. There are 2-stroke and 4-stroke engines. They can have a continuous duty cycle. According to the method of preparing the fuel mixture, such engines are carburetor (with external mixture formation) and diesel (with internal). Based on the type of energy converter, they are divided into piston, jet, turbine, and combined. The efficiency of such machines does not exceed 0.5.

A Stirling engine is a device in which the working fluid is located in a confined space. It is a type of external combustion engine. The principle of its operation is based on periodic cooling/heating of the body with the production of energy due to changes in its volume. This is one of the most efficient engines.

Turbine (rotary) engine with external combustion of fuel. Such installations are most often found at thermal power plants.

Turbine (rotary) internal combustion engines are used at thermal power plants in peak mode. Not as widespread as others.

A turbine engine generates some of its thrust through its propeller. It gets the rest from exhaust gases. Its design is a rotary engine (gas turbine), on the shaft of which a propeller is mounted.

Other types of heat engines

Rocket, turbojet and jet engines that obtain thrust from exhaust gases.

Solid state engines use solid matter as fuel. During operation, it is not its volume that changes, but its shape. When operating the equipment, an extremely small temperature difference is used.

How can you increase efficiency

Is it possible to increase the efficiency of a heat engine? The answer must be sought in thermodynamics. She studies the mutual transformations of different types of energy. It has been established that it is impossible to convert all available thermal energy into electrical, mechanical, etc. However, their conversion into thermal energy occurs without any restrictions. This is possible due to the fact that the nature of thermal energy is based on the disordered (chaotic) movement of particles.

The more a body heats up, the faster its constituent molecules will move. The movement of particles will become even more erratic. Along with this, everyone knows that order can easily be turned into chaos, which is very difficult to order.

The main significance of the formula (5.12.2) obtained by Carnot for the efficiency of an ideal machine is that it determines the maximum possible efficiency of any heat engine.

Carnot proved, based on the second law of thermodynamics*, the following theorem: any real heat engine operating with a temperature heaterT 1 and refrigerator temperatureT 2 , cannot have an efficiency that exceeds the efficiency of an ideal heat engine.

* Carnot actually established the second law of thermodynamics before Clausius and Kelvin, when the first law of thermodynamics had not yet been formulated strictly.

Let us first consider a heat engine operating in a reversible cycle with a real gas. The cycle can be anything, it is only important that the temperatures of the heater and refrigerator are T 1 And T 2 .

Let us assume that the efficiency of another heat engine (not operating according to the Carnot cycle) η ’ > η . The machines operate with a common heater and a common refrigerator. Let the Carnot machine operate in a reverse cycle (like a refrigeration machine), and let the other machine operate in a forward cycle (Fig. 5.18). The heat engine performs work equal to, according to formulas (5.12.3) and (5.12.5):

A refrigeration machine can always be designed so that it takes the amount of heat from the refrigerator Q 2 = ||

Then, according to formula (5.12.7), work will be done on it

(5.12.12)

Since by condition η" > η , That A" > A. Therefore, a heat engine can drive a refrigeration machine, and there will still be an excess of work left. This excess work is done by 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:

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

The efficiency of any heat engine cannot exceed the maximum possible value
, where T 1 - absolute temperature of the heater, and T 2 - absolute temperature of the refrigerator.

Increasing the efficiency of heat engines and bringing it closer to the maximum possible- the most important technical challenge.

How to find the efficiency factor. Formula for efficiency through power

How to find efficiency

Efficiency shows the ratio of the usable work 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 mechanical work performed by the mechanism as suitable work. 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 detect the efficiency, any heat engine (internal combustion engine, steam engine, turbine, etc.), where work is performed by gas, has an efficiency index equal to the difference in heat given off by the heater Q1 and received by the refrigerator Q2, find the difference 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 temperature of the heater 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 complete 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 is the height to which the load was raised, and the expended work Az=P?t, where P is the power of the motor, t is the 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 performance indicator (efficiency) is an indicator of the performance of any system, be it a car engine, machine or other mechanism. It shows how effectively a given system uses the energy it receives. Calculating efficiency is very easy.

Instructions

1. Most of the time, 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? (“this”) 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, you 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: Efficiency cannot be greater than one; during operation of any system, energy losses inevitably occur.

Associated transportation is a type of transport transportation that consists of loading a vehicle that is making an idle run. Situations when transport is forced to move without cargo occur quite often, both before and later after the planned transport order has been completed. 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 in reality 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 completion 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 your vehicle's cargo space is unoccupied.

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 selected direction on 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.

Useful 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 find the indicator of the suitable operation of any engine, it is necessary to divide the suitable work by the expended and multiply by 100 percent. For a heat engine, find this value by the ratio of the power multiplied by the duration of operation to the heat released during combustion of the fuel. Theoretically, the efficiency of a heat engine is 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. Determining the efficiency of an internal combustion engine Find its power in the technical documentation of a given engine. 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. Using a stopwatch, record the operating time of the 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. To determine the efficiency, multiply the maximum power by the operating time of the 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 the efficiency from the number 1, subtract the ratio of the temperatures of the refrigerator and the heater (fuel combustion temperature) Efficiency = (1-Tcol/Tnag) 100%. This option for calculating efficiency does not consider mechanical friction and heat exchange with the external environment.

3. Determining the efficiency of an electric motor Find out the rated power of the electric motor, according to the 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. To determine the 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 determine overall coefficients. 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. Please note that the overall indicator is a relative indicator. 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 types of 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, put an unconditional indicator corresponding to the desired relative one. 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 useful 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 wish 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 - single pensioners, disabled people or single mothers who have the entire ruble in their account probably live in an apartment building. 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 the education of 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.

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 actual moisture indicator, and the symbol R indicates 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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Efficiency

Let's say we are relaxing at the dacha, and we need to fetch water from the well. We lower the bucket into it, scoop up the water and begin to lift it. Have you forgotten what our goal is? That's right: get some water. But look: we are lifting not only the water, but also the bucket itself, as well as the heavy chain on which it hangs. This is symbolized by a two-color arrow: the weight of the load we lift is the sum of the weight of the water and the weight of the bucket and chain.

Considering the situation qualitatively, we will say: along with the useful work of raising water, we also perform other work - lifting the bucket and chain. Of course, without the chain and bucket we would not be able to draw water, but from the point of view of the ultimate goal, their weight “harms” us. If this weight were less, then the total work done would also be less (with the same useful work).

Now let's move on to a quantitative study of these works and introduce a physical quantity called efficiency.

Task. The loader pours the apples selected for processing from the baskets into the truck. The mass of an empty basket is 2 kg, and the apples in it are 18 kg. What is the share of the loader's useful work from his total work?

Solution. The full job is moving apples in baskets. This work consists of lifting apples and lifting baskets. Important: lifting apples is useful work, but lifting baskets is “useless”, because the purpose of the loader’s work is to move only the apples.

Let us introduce the notation: Fя is the force with which the hands lift only apples up, and Fк is the force with which the hands lift only the basket up. Each of these forces is equal to the corresponding force of gravity: F=mg.

Using the formula A = ±(F||· l) , we “write out” the work of these two forces:

Auseful = +Fя · lя = mя g · h and Аuseless = +Fк · lк = mк g · h

The total work consists of two works, that is, it is equal to their sum:

Afull = Auseful + Auseless = mя g h + mк g h = (mя + mк) · g h

In the problem we are asked to calculate the share of the loader's useful work from his total work. Let's do this by dividing the useful work by the total:

In physics, such shares are usually expressed as percentages and denoted by the Greek letter “η” (read: “this”). As a result we get:

η = 0.9 or η = 0.9 100% = 90%, which is the same.

This number shows that out of 100% of the loader's total work, the share of his useful work is 90%. The problem is solved.

A physical quantity equal to the ratio of useful work to total work done has its own name in physics - efficiency - efficiency factor:

After calculating the efficiency using this formula, it is usually multiplied by 100%. And vice versa: to substitute efficiency into this formula, its value must be converted from percent to decimal fraction, dividing by 100%.

questions-physics.ru

Heat engine efficiency. Heat engine efficiency

Heat engine device

Operating principle

Efficiency = (Theat - Cool) / Theat. x 100%.

In a heat engine, when a body heats up and expands, it is not able to give up all its internal energy to do work. Some of the heat will be transferred to the refrigerator along with exhaust gases or steam. This part of the thermal internal energy is inevitably lost. During fuel combustion, the working fluid receives a certain amount of heat Q1 from the heater. At the same time, it still performs work A, during which it transfers part of the thermal energy to the refrigerator: Q2

Efficiency characterizes the efficiency of the engine in the field of energy conversion and transmission. This indicator is often measured as a percentage. Efficiency formula:

η*A/Qx100%, where Q is the energy expended, A is the useful work.

Based on the law of conservation of energy, we can conclude that the efficiency will always be less than unity. In other words, there will never be more useful work than the energy expended on it.

Engine efficiency is the ratio of useful work to the energy supplied by the heater. It can be represented in the form of the following formula:

η = (Q1-Q2)/ Q1, where Q1 is the heat received from the heater, and Q2 is the heat given to the refrigerator.

Heat engine operation

The work done by a heat engine is calculated using the following formula:

A = |QH| - |QX|, where A is work, QH is the amount of heat received from the heater, QX is the amount of heat given to the cooler.

|QH| - |QX|)/|QH| = 1 - |QX|/|QH|

It is equal to the ratio of the work done by the engine to the amount of heat received. Part of the thermal energy is lost during this transfer.

Carnot engine

(Tn - Tx)/ Tn = - Tx - Tn.

Varieties

Nowadays, there are many types of heat engines that operate on different principles and on different fuels. They all have their own efficiency. These include the following:

Turbine (rotary) engine with external combustion of fuel. Such installations are most often found at thermal power plants.

Turbine (rotary) internal combustion engines are used at thermal power plants in peak mode. Not as widespread as others.

A turbine engine generates some of its thrust through its propeller. It gets the rest from exhaust gases. Its design is a rotary engine (gas turbine), on the shaft of which a propeller is mounted.

Other types of heat engines

Rocket, turbojet and jet engines that obtain thrust from exhaust gases.

Solid state engines use solid matter as fuel. During operation, it is not its volume that changes, but its shape. When operating the equipment, an extremely small temperature difference is used.

How can you increase efficiency

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« Physics - 10th grade"

To solve problems, you need to use known expressions for determining the efficiency of heat engines and keep in mind that expression (13.17) is valid only for an ideal heat engine.

Task 1.

In the boiler of a steam engine the temperature is 160 °C, and the temperature of the refrigerator is 10 °C.
What is the maximum work that a machine can theoretically perform if coal weighing 200 kg with a specific heat of combustion of 2.9 10 7 J/kg is burned in a furnace with an efficiency of 60%?

Solution.

The maximum work can be done by an ideal heat engine operating according to the Carnot cycle, the efficiency of which is η = (T 1 - T 2)/T 1, where T 1 and T 2 are the absolute temperatures of the heater and refrigerator. For any heat engine, the efficiency is determined by the formula η = A/Q 1, where A is the work performed by the heat engine, Q 1 is the amount of heat received by the machine from the heater.
From the conditions of the problem it is clear that Q 1 is part of the amount of heat released during fuel combustion: Q 1 = η 1 mq.

Then where does A = η 1 mq(1 - T 2 /T 1) = 1.2 10 9 J.

Task 2.

A steam engine with a power of N = 14.7 kW consumes fuel weighing m = 8.1 kg per 1 hour of operation, with a specific heat of combustion q = 3.3 10 7 J/kg.
Boiler temperature 200 °C, refrigerator 58 °C.
Determine the efficiency of this machine and compare it with the efficiency of an ideal heat engine.

Solution.

The efficiency of a heat engine is equal to the ratio of the completed mechanical work A to the expended amount of heat Qlt released during fuel combustion.
Amount of heat Q 1 = mq.

Work done during the same time A = Nt.

Thus, η = A/Q 1 = Nt/qm = 0.198, or η ≈ 20%.

For an ideal heat engine η < η ид.

Task 3.

An ideal heat engine with efficiency η operates in a reverse cycle (Fig. 13.15).

What is the maximum amount of heat that can be taken from the refrigerator by performing mechanical work A?

Since the refrigeration machine operates in a reverse cycle, in order for heat to transfer from a less heated body to a more heated one, it is necessary for external forces to do positive work.
Schematic diagram of a refrigeration machine: a quantity of heat Q 2 is taken from the refrigerator, work is done by external forces and a quantity of heat Q 1 is transferred to the heater.
Hence, Q 2 = Q 1 (1 - η), Q 1 = A/η.