Algorithm for solving problems to determine the efficiency. thermal cycle according to the plot of pressure versus volume
Modern realities involve the widespread operation of heat engines. Numerous attempts to replace them with electric motors have so far failed. The problems associated with the accumulation of electricity in autonomous systems are solved with great difficulty.
Still relevant are the problems of technology for the manufacture of electric power accumulators, taking into account their long-term use. The speed characteristics of electric vehicles are far from those of cars on internal combustion engines.
The first steps towards the creation of hybrid engines can significantly reduce harmful emissions in megacities, solving environmental problems.
A bit of history
The possibility of converting steam energy into motion energy was known in antiquity. 130 BC: The philosopher Heron of Alexandria presented to the audience a steam toy - aeolipil. A sphere filled with steam began to rotate under the action of jets emanating from it. This prototype of modern steam turbines did not find application in those days.
For many years and centuries, the development of the philosopher was considered only a fun toy. In 1629, the Italian D. Branchi created an active turbine. Steam set in motion a disk equipped with blades.
From that moment began the rapid development of steam engines.
heat engine
The conversion of fuel into energy for the movement of parts of machines and mechanisms is used in heat engines.
The main parts of machines: a heater (a system for obtaining energy from outside), a working fluid (performs a useful action), a refrigerator.
The heater is designed to ensure that the working fluid has accumulated a sufficient supply of internal energy to perform useful work. The refrigerator removes excess energy.
The main characteristic of efficiency is called the efficiency of thermal engines. This value shows what part of the energy spent on heating is spent on doing useful work. The higher the efficiency, the more profitable the operation of the machine, but this value cannot exceed 100%.
Efficiency calculation
Let the heater acquire from outside the energy equal to Q 1 . The working fluid did work A, while the energy given to the refrigerator was Q 2 .
Based on the definition, we calculate the efficiency:
η= A / Q 1 . We take into account that A \u003d Q 1 - Q 2.
From here, the efficiency of the heat engine, the formula of which has the form η = (Q 1 - Q 2) / Q 1 = 1 - Q 2 / Q 1, allows us to draw the following conclusions:
- Efficiency cannot exceed 1 (or 100%);
- to maximize this value, either an increase in the energy received from the heater or a decrease in the energy given to the refrigerator is necessary;
- an increase in the energy of the heater is achieved by changing the quality of the fuel;
- reducing the energy given to the refrigerator, make it possible to achieve the design features of the engines.
Ideal heat engine
Is it possible to create such an engine, the efficiency of which would be maximum (ideally, equal to 100%)? The French theoretical physicist and talented engineer Sadi Carnot tried to find the answer to this question. In 1824, his theoretical calculations about the processes occurring in gases were made public.
The main idea behind an ideal machine is to carry out reversible processes with an ideal gas. We start with the expansion of the gas isothermally at a temperature T 1 . The amount of heat required for this is Q 1. After the gas expands without heat exchange. Having reached the temperature T 2, the gas is compressed isothermally, transferring the energy Q 2 to the refrigerator. The return of the gas to its original state is adiabatic.
The efficiency of an ideal Carnot heat engine, when accurately calculated, is equal to the ratio of the temperature difference between the heating and cooling devices to the temperature that the heater has. It looks like this: η=(T 1 - T 2)/ T 1.
The possible efficiency of a heat engine, the formula of which is: η= 1 - T 2 / T 1 , depends only on the temperature of the heater and cooler and cannot be more than 100%.
Moreover, this ratio allows us to prove that the efficiency of heat engines can be equal to unity only when the refrigerator reaches temperatures. As you know, this value is unattainable.
Carnot's theoretical calculations make it possible to determine the maximum efficiency of a heat engine of any design.
The theorem proved by Carnot is as follows. An arbitrary heat engine under no circumstances is capable of having a coefficient of efficiency greater than the similar value of the efficiency of an ideal heat engine.
Example of problem solving
Example 1 What is the efficiency of an ideal heat engine if the heater temperature is 800°C and the refrigerator temperature is 500°C lower?
T 1 \u003d 800 o C \u003d 1073 K, ∆T \u003d 500 o C \u003d 500 K, η -?
By definition: η=(T 1 - T 2)/ T 1.
We are not given the temperature of the refrigerator, but ∆T = (T 1 - T 2), from here:
η \u003d ∆T / T 1 \u003d 500 K / 1073 K \u003d 0.46.
Answer: efficiency = 46%.
Example 2 Determine the efficiency of an ideal heat engine if 650 J of useful work is performed due to the acquired one kilojoule of heater energy. What is the temperature of the heat engine heater if the coolant temperature is 400 K?
Q 1 \u003d 1 kJ \u003d 1000 J, A \u003d 650 J, T 2 \u003d 400 K, η -?, T 1 \u003d?
In this problem, we are talking about a thermal installation, the efficiency of which can be calculated by the formula:
To determine the temperature of the heater, we use the formula for the efficiency of an ideal heat engine:
η \u003d (T 1 - T 2) / T 1 \u003d 1 - T 2 / T 1.
After performing mathematical transformations, we get:
T 1 \u003d T 2 / (1- η).
T 1 \u003d T 2 / (1- A / Q 1).
Let's calculate:
η= 650 J / 1000 J = 0.65.
T 1 \u003d 400 K / (1- 650 J / 1000 J) \u003d 1142.8 K.
Answer: η \u003d 65%, T 1 \u003d 1142.8 K.
Real conditions
The ideal heat engine is designed with ideal processes in mind. Work is done only in isothermal processes, its value is defined as the area bounded by the Carnot cycle graph.
In fact, it is impossible to create conditions for the process of changing the state of a gas without accompanying changes in temperature. There are no materials that would exclude heat exchange with surrounding objects. The adiabatic process is no longer possible. In the case of heat transfer, the temperature of the gas must necessarily change.
The efficiency of heat engines created in real conditions differ significantly from the efficiency of ideal engines. Note that the processes in real engines are so fast that the variation in the internal thermal energy of the working substance in the process of changing its volume cannot be compensated by the influx of heat from the heater and return to the cooler.
Other heat engines
Real engines operate on different cycles:
- Otto cycle: the process at a constant volume changes adiabatically, creating a closed cycle;
- Diesel cycle: isobar, adiabat, isochor, adiabat;
- the process occurring at constant pressure is replaced by an adiabatic one, closing the cycle.
It is not possible to create equilibrium processes in real engines (to bring them closer to ideal ones) under the conditions of modern technology. The efficiency of thermal engines is much lower, even taking into account the same temperature regimes as in an ideal thermal installation.
But you should not reduce the role of the efficiency calculation formula, since it is it that becomes the starting point in the process of working to increase the efficiency of real engines.
Ways to change efficiency
When comparing ideal and real heat engines, it is worth noting that the temperature of the refrigerator of the latter cannot be any. Usually the atmosphere is considered to be a refrigerator. The temperature of the atmosphere can be taken only in approximate calculations. Experience shows that the temperature of the coolant is equal to the temperature of the exhaust gases in the engines, as is the case in internal combustion engines (abbreviated internal combustion engines).
ICE is the most common heat engine in our world. The efficiency of a heat engine in this case depends on the temperature created by the burning fuel. An essential difference between an internal combustion engine and steam engines is the merging of the functions of the heater and the working fluid of the device in the air-fuel mixture. Burning, the mixture creates pressure on the moving parts of the engine.
An increase in the temperature of the working gases is achieved by significantly changing the properties of the fuel. Unfortunately, it is not possible to do this indefinitely. Any material from which the combustion chamber of an engine is made has its own melting point. The heat resistance of such materials is the main characteristic of the engine, as well as the ability to significantly affect the efficiency.
Motor efficiency values
If we consider the temperature of the working steam at the inlet of which is 800 K, and the exhaust gas is 300 K, then the efficiency of this machine is 62%. In reality, this value does not exceed 40%. Such a decrease occurs due to heat losses during heating of the turbine housing.
The highest value of internal combustion does not exceed 44%. Increasing this value is a matter of the near future. Changing the properties of materials, fuels is a problem that the best minds of mankind are working on.
How to find the efficiency factor. The formula for efficiency in terms of power
How to find the efficiency factor
The coefficient of efficiency shows the ratio of the useful work that is performed by a mechanism or device to the expended. Often, work expended is taken as the amount of energy that a device consumes in order to perform work.
You will need
- - automobile;
- - thermometer;
- - calculator.
Instruction
2. When calculating the efficiency of a heat engine, consider the mechanical work performed by the mechanism as suitable work. For the work expended, take the amount of heat released by the burnt fuel, which is the source of energy for the motor.
3. Example. The average traction force of a car engine is 882 N. It consumes 7 kg of gasoline per 100 km. Determine the efficiency of his motor. Find a suitable job first. It is equal to the product of the force F by the distance S, overcome by the body under its influence Ап=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 42 × 10^6 J / kg, and m is the mass this fuel. The efficiency of the motor will be equal to efficiency=(F?S)/(q?m)?100%= (882?100000)/(42?10^6?7)?100%=30%.
4. In the general case, in order to find the efficiency, any heat engine (internal combustion engine, steam engine, turbine, etc.), where the work is done by gas, has an efficiency indicator 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 the efficiency is measured in submultiple units from 0 to 1, in order to convert the result into a percentage, 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 refrigerator T2 to the temperature of the heater COP=(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 was performed. Say, if a crane electric motor with a power of 3.2 kW lifts a load of 800 kg to a height of 3.6 m in 10 s, then its efficiency is equal to the ratio of suitable work Ap \u003d m?g?h, where m is the weight of the load, g?10 m /With? acceleration of free fall, h - the height to which the load was raised, and the expended work Az \u003d P? t, where P is the power of the motor, t is the time of its operation. Get the formula for determining efficiency = Ap / Az? 100% = (m? G? H) / (P? t)? 100% =% = (800? 10? 3.6) / (3200? 10)? 100% =90%.
The usable action index (COP) is an indicator of the performance of a system, whether it be a car engine, machine or other mechanism. It shows how effectively the given system uses the received energy. Calculating the efficiency is very easy.
Instruction
1. More often than not, the efficiency is calculated from the ratio of the energy suitably applied by the system to each total energy received in a certain time interval. It is worth noting that the efficiency has no 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 by the formula:? = (A/Q)*100%, where? ("this") is the desired efficiency, A is the usable work of the system, Q is the summed energy costs, A and Q are measured in Joules.
2. The above method for calculating the efficiency is not exclusive, because the usable operation 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. Expanding the numerator of the above formula, it can be written in the following form:? = ((Po-Pi)/Po)*100%.
3. In order to make the calculation of the efficiency more intelligible and illustrative, it is allowed to see 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 required to find the efficiency of this system. To solve this problem, apply 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 for the operation of the motor is 100 J, the energy loss during operation of this motor is 25 J, you need to calculate the efficiency. 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, tea in the second case, the numerator data were analyzed in more detail.
Note! Many types of modern engines (say, a rocket engine or a turbo-air engine) have several stages of their work, and for the entire stage there is its own efficiency, the one that is calculated using any of the above formulas. But in order to find a general indicator, you will need to multiply all the famous efficiency at all stages of the operation of this motor:? = ?1*?2*?3*…*?.
Useful advice Efficiency cannot be greater than unity, tea during the operation of any system, energy losses inevitably appear.
Passing transportation is a kind of transportation, consisting in the loading of a vehicle that performs an idle run. Situations when transport is forced to move without cargo are quite common, both before and after the execution of the planned transport order. For an enterprise, the probability of taking additional cargo means, at a minimum, a reduction in financial losses.
Instruction
1. Evaluate the effectiveness of the use of passing cargo transportation realistically for your company. A significant point that should be understood is the fact that a passing cargo can be transported at a time when the 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, courageously choose this method of optimizing transportation.
2. Assess what kind of passing cargo in terms of weight and dimensions your vehicle can carry. Passage cargo can be economically advantageous even if part of the cargo space of your car is not occupied.
3. Think over from which points of the main route you will be able to take a passing cargo. It is more comfortable for everyone if you can receive such cargo at the final point of the planned route and take it to the place where your transport company is located. But such a situation may not always occur. Consequently, consider also the probability of some deviation from the route, having calculated, of course, the economic rationality of such a metamorphosis.
4. Find out if a return shipment is required by the company to which you are making a scheduled shipment. 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 the appropriate sections that allow you to find a passing cargo on your route and leave a corresponding application. 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 the logistical review of counteroffers.
6. Do not neglect groupage transportation, when small-sized cargo from different clients is transported in the same direction on the same mode of transport. At the same time, transport should make shuttle routes in selected directions.
Note! Finding a passing cargo is absolutely easy! The main task of our service is to search for various downloads, one that users can carry out not only = with maximum convenience for themselves, but also with an ideal gift. With the help of our system, which is based on the use of modern information technology, it is possible to detect cargo very easily.
Useful advice It seems that you have decided to buy or rent a huge truck, with the help of which you intend to earn money by transporting goods across Russia, the CIS and Europe. It doesn't matter whether you hire a driver or drive it yourself, you will need customers, that is, goods for transportation. Then you will definitely think or think more closely about where and how to find cargo for your truck?
In order to find the indicator of the useful action of any engine, it is necessary to divide the useful work by the expended and multiply by 100 percent. For a heat engine, find this value by the ratio of power multiplied by the duration of operation to the heat released during the combustion of fuel. Theoretically, the efficiency of a heat engine is determined by the ratio of 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
- passport of the internal combustion engine (ICE), thermometer, tester
Instruction
1. Determining the efficiency of the internal combustion engine Find its power in the technical documentation of this particular engine. Pour a certain amount of fuel into its tank and start the engine so that it runs for some time at full cycles, developing the maximum power indicated in the passport. With the help of a stopwatch, note the time the engine is running, expressing it in seconds. After a while, stop the engine and drain the remaining fuel. Subtracting the final volume from the initial volume of filled fuel, find the volume of fuel consumed. Using the table, find its density and multiply by volume to get the mass of fuel used m=? V. Express the mass in kilograms. Depending on the type of fuel (gasoline or diesel fuel), 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 in steps by its mass and specific heat of combustion Efficiency = P t 100% / (q m).
2. For a perfect heat engine, it is allowed to apply the Carnot 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, for which add the number 273 to the value. To determine the efficiency, subtract the ratio of the refrigerator and heater temperatures (fuel combustion temperature) from the number 1 Efficiency \u003d (1-Thol / Tnag) 100%. This option for calculating the efficiency does not consider mechanical friction and heat exchange with the external environment.
3. Determining the efficiency of the electric motor Find out the rated power of the electric motor, according to the technical documentation. Connect it to a current source, having achieved maximum shaft cycles, and with the help of a tester, measure the voltage value on it and the current strength in the circuit. To determine the efficiency, divide the power declared in the documentation by the product of current strength and voltage, multiply the total by 100% efficiency = P 100% / (I U).
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Note! In all calculations, the efficiency must be less than 100%.
In order to survey ordinary population dynamics, sociologists need to determine the overall coefficients. The main ones are indicators of birth rate, death rate, marriage rate and in-kind income. Based on them, it is possible to draw up a demographic picture at a given point in time.
Instruction
1. Please note that the overall rate is a relative rate. Thus, the number of births for a certain period, say, for a year, will differ from the general birth rate. This is due to the fact that when it is found, data on the total number of the population are taken into account. This makes it possible to compare the current survey results with the results of previous years.
2. Determine the billing period. Say, in order to find the marriage rate, you need to determine for what time period the number of marriages you care about. So, the data for the last six months will be significantly different from those that you get when determining the five-year time period. Consider that the calculation period when calculating the overall indicator is indicated in years.
3. Determine the total population. Similar data can be obtained by referring to the population census data. To determine the total birth rate, death rate, marriage rate, and divorce rate, you need to find the product of the total population and the reference period. Write the resulting number in the denominator.
4. Replace the numerator with an unconditional indicator corresponding to the desired relative. Say, if you are faced with the task of determining the universal fertility rate, then in place of the numerator there should be a number that reflects the total number of children born for the period that concerns you. If your goal is to determine the tier of mortality or marriage, then put the number of deceased in the calculation period or the number of those who got married, respectively, in place of the numerator.
5. Multiply the resulting number by 1000. This will be your desired overall indicator. If your task is to find the total birth rate, then subtract the death rate from the birth rate.
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Under the word "work" is perceived before each action, which gives a person a livelihood. In other words, he receives a 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 useful work aimed at supporting the needy, landscaping yards and streets, landscaping, etc. The number of such volunteers would probably still be huge, but they often do not know where their services may be needed.
Instruction
1. One of the most famous types of socially useful work is charity. It includes assistance to needy, socially unprotected 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 wishing to take part in the provision of such assistance should contact the nearest philanthropic organizations or departments of public assistance. You can make inquiries at the nearest church - the clergyman probably knows which of his flock is in extreme need of support.
3. You can also take the initiative verbatim at the place of residence - lonely pensioners, disabled people or single mothers who have the whole ruble in their account probably live in an apartment building. Give them all the help you can. It does not at all strictly consist in a monetary donation - it is allowed, say, from time to time to go to the grocery store or to the pharmacy for medicines.
4. Many people want to take part in the improvement of their native city. They should contact the relevant structures of the local municipality, for example, those responsible for cleaning the territories, landscaping. There will probably be work. In addition, it is allowed, say, on your own initiative to break a flower bed under the windows of the house, plant flowers.
5. There are people who are very fond of animals, who want to help neglected dogs and cats. If you are in this category, contact your local animal rights organizations or animal sanctuaries. Well, if you live in a huge city where there are zoos, ask the administration if animal care assistants are needed. As usual, such offers of help are greeted with gratitude.
6. It is impossible to forget about the upbringing of the younger generation. If an enthusiastic volunteer can, say, lead classes in some school circle or center of culture and creativity, he will bring great benefits. In a word, there is a lot of socially useful work for caring people, for every taste and probability. There would be a desire.
Moisture indicator - an indicator used to determine the parameters of the microclimate. It is possible to calculate it, having information about precipitation in the region for a rather long period.
Moisture index
Humidity coefficient is a special indicator developed by experts in the field of meteorology to assess the degree of humidity of the microclimate in a particular region. At the same time, it was taken into account that the microclimate is a long-term recall of weather conditions in a given area. Consequently, it was also decided to consider the moisture index in a long time frame: as usual, this indicator is calculated on the basis of data collected during the year. Thus, the moisture index shows how huge the amount of precipitation that falls during this period in the region under consideration. This, in turn, is one of the main factors determining the prevailing type of vegetation in the area.
Moisture Index Calculation
The formula for calculating the moisture index looks like this: K \u003d R / E. In the indicated formula, the symbol K denotes the moisture index itself, and the symbol R denotes the number of precipitation that fell in a given area during the year, expressed in millimeters. Finally, the symbol E denotes the amount of precipitation that has evaporated from the earth's surface during the same period of time. The indicated 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 period, and other factors. Consequently, despite the apparent simplicity of the above formula, the calculation of the moisture index requires a large number of early measurements using accurate instruments and can only be carried out by a fairly large team of meteorologists. In turn, the value of the moisture index in a certain area, considering all these indicators, as usual , allows you to determine with a high degree of certainty which type of vegetation is predominant in this region. So, if the moisture index exceeds 1, this indicates a high level of humidity in the given territory, which entails the advantage of such types of vegetation as taiga, tundra or forest tundra. A contented moisture layer corresponds to a moisture index of 1 and, as usual, is characterized by the predominance of mixed or broad-leaved forests. Moisture index ranging from 0.6 to 1 is typical for forest-steppe massifs, from 0.3 to 0.6 - for steppes, from 0.1 to 0.3 - for semi-desert territories, and from 0 to 0.1 - for deserts .
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Efficiency
Suppose we are relaxing in the country, and we need to bring water from the well. We lower a bucket into it, scoop up water and begin to raise it. Have you forgotten what our goal is? That's right: get some water. But look: we are lifting not only 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 lifting water, we also perform other work - lifting a bucket and a chain. Of course, without a chain and a bucket, we would not be able to draw water, however, from the point of view of the final 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 the efficiency factor.
Task. Apples selected for processing, the loader pours out of 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 useful work of the loader 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 apples.
Let's introduce the notation: Fя is the force with which the hands lift only apples, and Fк is the force with which the hands lift only the basket. 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 \u003d + Fya lya \u003d mya g h and Auseless \u003d + Fk lk \u003d mk g h
The full work consists of two works, that is, it is equal to their sum:
Afull \u003d Auseful + Auseless \u003d mi g h + mk g h \u003d (mi + mk) g h
In the problem, we are asked to calculate the share of the loader's useful work from his total work. We do this by dividing the useful work by the total:
In physics, such shares are usually expressed as a percentage and denoted by the Greek letter "η" (read: "this"). As a result, we get:
η \u003d 0.9 or η \u003d 0.9 100% \u003d 90%, which is the same.
This number shows that out of 100% of the full work of the loader, the share of his useful work is 90%. Problem solved.
The physical quantity equal to the ratio of useful work to the complete work done has its own name in physics - efficiency - coefficient of efficiency:
After calculating the efficiency using this formula, it is customary to multiply it by 100%. And vice versa: to substitute the efficiency in this formula, its value must be converted from a percentage to a decimal fraction, dividing by 100%.
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heat engine efficiency. Heat engine efficiency
The operation of many types of machines is characterized by such an important indicator as the efficiency of a heat engine. Every year, engineers strive to create more advanced equipment that, at lower fuel costs, would give the maximum result from its use.
Heat engine device
Before understanding what efficiency is (coefficient of performance), 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 does work by using internal energy. Any heat engine that converts thermal energy into mechanical energy uses the thermal expansion of substances with increasing temperature. In solid-state engines, it is possible not only to change the volume of matter, but also the shape of the body. The operation 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 principle of operation of heat engines (the efficiency of heat engines) depends on their type. Often, the steam condenser acts as a refrigerator, and any type of fuel that burns in the furnace acts as a heater. The efficiency of an ideal heat engine is found by the following formula:
Efficiency = (Theating - Tcold.) / Theating. x 100%.
At the same time, the efficiency of a real engine can never exceed the value obtained according to this formula. Also, this indicator will never exceed the above value. To increase the efficiency, most often increase the temperature of the heater and reduce the temperature of the refrigerator. Both of these processes will be limited by the actual operating conditions of the equipment.
During the operation of a heat engine, work is done, as the gas begins to lose energy and cools to a certain temperature. The latter is usually a few degrees above the surrounding atmosphere. This is the refrigerator temperature. Such a special device is designed for cooling with subsequent condensation of the exhaust steam. Where condensers are present, the temperature of the refrigerator is sometimes lower than the ambient temperature.
In a heat engine, the body, when heated and expanded, is not able to give 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 the combustion of fuel, 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 expended energy, A is 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 as the following formula: η = (Q1-Q2)/ Q1, where Q1 is the heat received from the heater, and Q2 is given to the refrigerator. The work done by a heat engine is calculated by 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. The maximum efficiency of a heat engine is noted for the Carnot device. This is due to the fact that in this system it depends only on the absolute temperature of the heater (Тн) and cooler (Тх). The efficiency of a heat engine operating according to the Carnot cycle is determined by the following formula: (Tn - Tx) / Tn = - Tx - Tn. 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 the burning fuel is converted into mechanical energy. Such devices can be gas and liquid. There are 2-stroke and 4-stroke engines. They may have a continuous duty cycle. According to the method of preparing a mixture of fuel, such engines are carburetor (with external mixture formation) and diesel (with internal). According to the types of energy converter, they are divided into piston, jet, turbine, combined. The efficiency of such machines does not exceed 0.5. Stirling engine - a device in which the working fluid is in a closed space. It is a kind 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 a change 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 in thermal power plants. Turbine (rotary) internal combustion engines are used at thermal power plants in peak mode. Not as common as others. A turboprop engine generates some of the thrust due to the propeller. The rest comes from exhaust gases. Its design is a rotary engine (gas turbine), on the shaft of which a propeller is mounted. Rocket, turbojet and jet engines that obtain thrust from the return of exhaust gases. Solid state engines use a solid body as fuel. When working, it is not its volume that changes, but its shape. During operation of the equipment, an extremely small temperature difference is used. Is it possible to increase the efficiency of a heat engine? The answer must be sought in thermodynamics. It 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. At the same time, 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 the body heats up, the faster the molecules that make it up will move. Particle motion will become even more erratic. Along with this, everyone knows that order can be easily turned into chaos, which is very difficult to order. fb.ru Coefficient of performance (COP) - a term that can be applied, perhaps, to every system and device. Even a person has an efficiency, though, probably, there is no objective formula for finding it yet. In this article, we will explain in detail what efficiency is and how it can be calculated for various systems. Efficiency is an indicator that characterizes the efficiency of a particular system in relation to the return or conversion of energy. Efficiency is a measureless value and is represented either as a numerical value in the range from 0 to 1, or as a percentage. Efficiency is indicated by the symbol Ƞ. The general mathematical formula for finding the efficiency is written as follows: Ƞ=A/Q, where A is the useful energy/work done by the system, and Q is the energy consumed by this system to organize the process of obtaining a useful output. The efficiency factor, unfortunately, is always less than one or equal to it, since, according to the law of conservation of energy, we cannot get more work than the energy spent. In addition, the efficiency, in fact, is extremely rarely equal to one, since useful work is always accompanied by losses, for example, for heating the mechanism. A heat engine is a device that converts thermal energy into mechanical energy. In a heat engine, work is determined by the difference between the amount of heat received from the heater and the amount of heat given to the cooler, and therefore the efficiency is determined by the formula: It is believed that the highest efficiency is provided by engines operating on the Carnot cycle. In this case, the efficiency is determined by the formula: An electric motor is a device that converts electrical energy into mechanical energy, so the efficiency in this case is the efficiency ratio of the device in relation to the conversion of electrical energy into mechanical energy. The formula for finding the efficiency of an electric motor looks like this: Electrical power is found as the product of system current and voltage (P=UI), and mechanical power is found as the ratio of work to unit time (P=A/t) A transformer is a device that converts alternating current of one voltage into alternating current of another voltage while maintaining frequency. In addition, transformers can also convert AC to DC. The efficiency of the transformer is found by the formula: It is worth noting that in addition to efficiency, there are a number of indicators that characterize the efficiency of energy processes, and sometimes we can find descriptions of the type - efficiency of the order of 130%, however, in this case, you need to understand that the term is not used quite correctly, and, most likely, the author or the manufacturer understands a slightly different characteristic by this abbreviation. For example, heat pumps are distinguished by the fact that they can give off more heat than they consume. Thus, the refrigerating machine can remove more heat from the cooled object than is spent in energy equivalent for the organization of the removal. The efficiency indicator of a refrigerating machine is called the coefficient of performance, denoted by the letter Ɛ and is determined by the formula: Ɛ=Qx/A, where Qx is the heat removed from the cold end, A is the work expended on the removal process. However, sometimes the coefficient of performance is also called the efficiency of the refrigeration machine. It is also interesting that the efficiency of boilers running on fossil fuels is usually calculated on the basis of the lower calorific value, while it can turn out to be more than one. However, it is still traditionally referred to as efficiency. It is possible to determine the efficiency of the boiler by the gross calorific value, and then it will always be less than one, but in this case it will be inconvenient to compare the performance of the boilers with the data of other installations. slide 1 slide 2 slide 3 slide 4 slide 5 slide 6 Slide 7 Slide 8 Slide 9 « Physics - Grade 10 " To solve problems, it is necessary 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. Solution. The maximum work can be done by an ideal heat engine operating according to the Carnot cycle, the efficiency of which is η \u003d (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 \u003d A / Q 1, where A is the work done by the heat engine, Q 1 is the amount of heat received by the machine from the heater. Then whence A \u003d η 1 mq (1 - T 2 / T 1) \u003d 1.2 10 9 J. Task 2. A steam engine with a power of N = 14.7 kW consumes fuel with a mass of m = 8.1 kg for 1 hour of operation, with a specific heat of combustion q = 3.3 10 7 J/kg. Solution. The efficiency of a heat engine is equal to the ratio of the mechanical work A performed to the amount of heat Qlt released during the combustion of fuel. The work done during the same time A \u003d Nt. Thus, η = A/Q 1 = Nt/qm = 0.198, or η ≈ 20%. For an ideal heat engine Task 3. An ideal heat engine with efficiency η operates in the reverse cycle (Fig. 13.15). What is the maximum amount of heat that can be taken from the refrigerator by doing mechanical work A? Since the refrigeration machine operates on a reverse cycle, for the transfer of heat from a less heated body to a hotter one, it is necessary that external forces do positive work. Finally Q 2 = (A/η)(1 - η). Source: "Physics - Grade 10", 2014, textbook Myakishev, Bukhovtsev, Sotsky Fundamentals of thermodynamics. Thermal phenomena - Physics, textbook for grade 10 - Classroom physicsHeat engine operation
Carnot engine
The laws of thermodynamics made it possible to calculate the maximum efficiency that is possible. For the first time this indicator was calculated by the French scientist and engineer Sadi Carnot. He invented a heat engine that ran on ideal gas. It works on a cycle of 2 isotherms and 2 adiabats. The principle of its operation is quite simple: a heater contact is brought to the 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. After the vessel is thermally insulated. Despite this, the gas continues to expand, but already adiabatically (without heat exchange with the environment). At this time, its temperature drops to the refrigerator. At this moment, the gas is in contact with the refrigerator, as a result of which it gives it a certain amount of heat during isometric compression. Then the vessel is again thermally insulated. In this case, the gas is adiabatically compressed to its original volume and state.Varieties
Other types of heat engines
How can you increase efficiency
efficiency definition
General formula
Heat engine efficiency
Electric motor efficiency
transformer efficiency
Efficiency or not efficiency?
The task is to determine the efficiency factor according to the graph of pressure versus volume. Calculate the efficiency of a heat engine using a monatomic ideal gas as a working fluid and operating according to the cycle shown in the figure. The appearance of new drawings and records occurs only after a mouse click.
The task is to determine the efficiency factor according to the graph of pressure versus volume. Calculate the efficiency of a heat engine using a monatomic ideal gas as a working fluid and operating according to the cycle shown in the figure.
Hint No. 1 Therefore, it is necessary to determine in each process the amount of heat received or given out by changing the temperature. Calculation of the amount of heat produced on the basis of the first law of thermodynamics.
Hint #2 The work done in any process is numerically equal to the area of the figure enclosed under the graph in P(V) coordinates. The area of the shaded figure is equal to the work in the 2-3 process, and the area of the shaded figure is equal to the work in the 4-1 process, and it is this gas work that is negative, since from 4 to 1 the volume decreases. Work per cycle is equal to the sum of these works. Therefore, the work of the gas per cycle is numerically equal to the area of this cycle.
Algorithm for solving the problem. 1. Write down the efficiency formula. 2. Determine the work of the gas by the area of the process figure in the coordinates P,V. 3. Analyze in which of the processes the amount of heat is absorbed and not released. 4. Using the 1st law of thermodynamics, calculate the amount of heat received. 5. Calculate the efficiency.
1. Write down the efficiency formula. 2. Determine the work of the gas by the area of the process figure in the coordinates P,V. Solution
1. Process1 -2. V = const, P T Q is absorbed 2. Process 2 – 3. P = const, V , T Q is absorbed 3. Process 3 – 4. V = const, P , T Q is extracted 4. Process 4 – 1. P = const, V , T Q 3. Analyze in which of the processes the amount of heat is absorbed rather than released.
For process 1-2 4. Using the 1st law of thermodynamics, calculate the amount of heat received. hence For an isochoric process Subtract the upper equation from the lower equation
What maximum work can theoretically be performed by a machine 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%?
It is clear from the condition of the problem that Q 1 is a part of the amount of heat released during the combustion of fuel: Q 1 = η 1 mq.
Boiler temperature 200 °С, refrigerator 58 °С.
Determine the efficiency of this machine and compare it with the efficiency of an ideal heat engine.
The amount of heat Q 1 = mq.
η < η ид.
Schematic diagram of the refrigeration machine: the amount of heat Q 2 is taken from the refrigerator, work is done by external forces and the amount of heat Q 1 is transferred to the heater.
Hence, 
Q 2 \u003d Q 1 (1 - η), Q 1 \u003d A / η.