The work done by the engine per cycle formula. heat engine

Example. The average traction force of the engine is 882 N. It consumes 7 kg of gasoline per 100 km. Determine the efficiency of its engine. Find a useful 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 expended work Аз=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. Engine efficiency will be equal to efficiency=(F∙S)/(q∙m)∙100%= (882∙100000)/(42∙10^6∙7)∙100%=30%.

In general, to find the efficiency of any heat engine (internal combustion engine, steam engine, turbine, etc.), where the work is done by gas, has a coefficient of efficiency equal to the difference in the 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, the efficiency is measured in submultiples from 0 to 1, to convert the result into a percentage, multiply it by 100.

To obtain the efficiency of an ideal heat engine (Carnot engine), find the ratio of the temperature difference between the heater T1 and cooler T2 to the temperature of the heater COP=(T1-T2)/T1. This is the maximum possible efficiency for a specific type of heat engine with given temperatures of the heater and refrigerator.

For an electric motor, find the work expended as the product of power and the time it is performed. For example, 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 useful work Ap=m∙g∙h, where m is the mass of the load, g≈10 m /s² acceleration free fall, h is the height to which the load was lifted, and the expended work Az=P∙t, where P is the engine power, t is the time of its operation. Get the formula for determining efficiency = Ap / Az ∙ 100% = (m ∙ g ∙ h) / (Р ∙ t) ∙ 100% =% = (800 ∙ 10 ∙ 3.6) / (3200 ∙ 10) ∙ 100% =90%.

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• how to determine efficiency

Efficiency (efficiency factor) is a dimensionless value that characterizes the efficiency of work. Work is a force that affects a process over time. Energy is expended in the action of force. Energy is invested in strength, strength is invested in work, work is characterized by effectiveness.

Instruction

Calculation of efficiency from the determination of the energy spent directly to achieve the result. It can be expressed in units necessary to achieve the result of energy, strength, power.
In order not to be mistaken, it is useful to keep the following diagram in mind. The simplest one includes the element: “worker”, energy source, controls, ways and elements of conducting and converting energy. The energy spent on achieving the result is the energy spent only by the “working tool”.

Next, you determine the energy actually expended by the entire system in the process of achieving the result. That is, not only a "working tool", but also controls, energy converters, as well as the costs should include the energy dissipated in the energy pathways.

And then you calculate the efficiency using the formula:
K.P.D. = (A / B) * 100%, where
A - the energy required to achieve the result
B is the energy actually expended by the system to achieve results. For example: 100 kW were spent on power tool work, while the entire power system of the workshop consumed 120 kW during this time. The efficiency of the system (shop energy system) in this case will be equal to 100 kW / 120 kW = 0.83 * 100% = 83%.

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note

Often the concept of efficiency is used, evaluating the ratio of planned energy costs and actually spent. For example, the ratio of the planned amount of work (or the time required to complete the work) to the actual work performed and the time spent. Here you should be extremely careful. For example, they planned to spend 200 kW on work, but spent 100 kW. Or they planned to complete the work in 1 hour, but spent 0.5 hours; in both cases, the efficiency is 200%, which is impossible. In fact, in such cases, as economists say, there is a "Stakhanov syndrome", that is, a conscious underestimation of the plan in relation to the really necessary costs.

Useful advice

1. You must evaluate energy costs in the same units.

2. The energy spent by the entire system cannot be less than the energy spent directly on achieving the result, that is, the efficiency cannot be more than 100%.

Sources:

• how to calculate energy

Tip 3: How to calculate tank efficiency in World of Tanks

The rating of a tank's efficiency or its efficiency is one of the complex indicators of in-game skill. It is taken into account when joining top clans, esports teams, and companies. The calculation formula is quite complicated, so players use various online calculators.

Calculation formula

The formula itself is shown in the picture. This formula contains the following variables:
- R - combat effectiveness of the player;
- K - the average number of destroyed tanks (total number of frags divided by the total number of battles):
- L - the average level of the tank;
- S - the average number of detected tanks;
- Ddmg - the average amount of damage dealt per battle;
- Ddef - the average number of base defense points;
- C - the average number of base capture points.

The meaning of the received numbers:
- less than 600 - a bad player; about 6% of all players have such efficiency;
- from 600 to 900 - the player is below average; 25% of all players have such efficiency;
- from 900 to 1200 - an average player; 43% of players have such efficiency;
- from 1200 and above - a strong player; such players are about 25%;
- over 1800 - a unique player; these are no more than 1%.

American players use their WN6 formula, which looks like this:
wn6=(1240 – 1040 / (MIN (TIER,6)) ^ 0.164) x FRAGS + DAMAGE x 530 / (184 x e ^ (0.24 x TIER) + 130) + SPOT x 125 + MIN(DEF,2.2) x 100 + ((185 / (0.17+ e ^ ((WINRATE - 35) x 0.134))) - 500) x 0.45 + (6-MIN(TIER,6)) x 60

In this formula:
MIN (TIER,6) - the average level of the player's tank, if it is more than 6, the value 6 is used
FRAGS - average number of tanks destroyed
TIER - the average level of the player's tanks
DAMAGE - average damage in battle
MIN (DEF,2,2) - the average number of captured base capture points, if the value is greater than 2.2, 2.2 is used
WINRATE - overall percentage of wins

As you can see, this formula does not take into account base capture points, the number of frags on low-level vehicles, the percentage of wins and the influence of the initial light on the rating do not affect the rating very much.

In an update, Wargeiming introduced a player's Personal Performance Rating indicator, which is calculated using a more complex formula that takes into account all possible statistical indicators.

How to improve efficiency

From the Kx(350-20xL) formula, it can be seen that the higher the level of the tank, the lower the number of efficiency points obtained for destroying tanks, but more for causing damage. Therefore, when playing on low-level vehicles, try to take more frags. At a high level - deal more damage (damage). The number of base capture points received or knocked down does not affect the rating much, moreover, more efficiency points are awarded for the knocked down capture points than for the base capture points received.

Therefore, most players improve their statistics by playing at lower levels, in the so-called sandbox. First, most of the players lower levels- beginners who do not have skills, do not use a pumped crew with skills and abilities, do not use additional equipment, do not know the advantages and disadvantages of a particular tank.

No matter what vehicle you use, try to shoot down as many base capture points as possible. Platoon battles greatly increase the efficiency rating, as the players in the platoon act in a coordinated manner and achieve victory more often.

The term "efficiency" is an abbreviation derived from the phrase "efficiency". In the very general view it represents the ratio of the resources spent and the result of the work performed with their use.

efficiency

In general terms, the efficiency formula can be written as follows: n = A*100%/Q. In this formula, the symbol n is used as a designation for efficiency, symbol A represents the amount of work done, and Q is the amount of energy expended. At the same time, it should be emphasized that the unit of measurement of efficiency is percent. Theoretically, the maximum value of this coefficient is 100%, but in practice it is almost impossible to achieve such an indicator, since certain energy losses are present in the operation of each mechanism.

Engine efficiency

The internal combustion engine (ICE), which is one of the key components of the mechanism of a modern car, is also a variant of a system based on the use of a resource - gasoline or diesel fuel. Therefore, it is possible to calculate the efficiency value for it.

Despite all the technical achievements of the automotive industry, the standard efficiency of internal combustion engines remains quite low: depending on the technologies used in the design of the engine, it can be from 25% to 60%. This is due to the fact that the operation of such an engine is associated with significant energy losses.

Thus, the greatest losses in the efficiency of the internal combustion engine occur in the operation of the cooling system, which takes up to 40% of the energy generated by the engine. A significant part of the energy - up to 25% - is lost in the process of removing exhaust gases, that is, it is simply carried away into the atmosphere. Finally, about 10% of the energy generated by the engine goes to overcome the friction between the various parts of the internal combustion engine.

Therefore, technologists and engineers employed in the automotive industry are making significant efforts to improve the efficiency of engines by reducing losses in all of the above items. Thus, the main direction of design developments aimed at reducing losses related to the operation of the cooling system is associated with attempts to reduce the size of the surfaces through which heat transfer occurs. Reducing losses in the process of gas exchange is carried out mainly using a turbocharging system, and reducing losses associated with friction - through the use of more technologically advanced and modern materials in the design of the engine. According to experts, the use of these and other technologies can raise the efficiency of internal combustion engines to the level of 80% and above.

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• About the internal combustion engine, its reserves and development prospects through the eyes of a specialist

The work done by the engine is:

This process was first considered by the French engineer and scientist N. L. S. Carnot in 1824 in the book Reflections on the driving force of fire and on machines capable of developing this force.

The purpose of Carnot's research was to find out the reasons for the imperfection of heat engines of that time (they had an efficiency of ≤ 5%) and to find ways to improve them.

The Carnot cycle is the most efficient of all. Its efficiency is maximum.

The figure shows the thermodynamic processes of the cycle. In the process of isothermal expansion (1-2) at a temperature T 1 , the work is done by changing the internal energy of the heater, i.e., by supplying the amount of heat to the gas Q:

A 12 = Q 1 ,

Cooling of the gas before compression (3-4) occurs during adiabatic expansion (2-3). Change in internal energy ΔU 23 in an adiabatic process ( Q=0) is completely converted into mechanical work:

A 23 = -ΔU 23 ,

The temperature of the gas as a result of adiabatic expansion (2-3) decreases to the temperature of the refrigerator T 2 < T 1 . In the process (3-4), the gas is isothermally compressed, transferring the amount of heat to the refrigerator Q2:

A 34 = Q 2,

The cycle is completed by the process of adiabatic compression (4-1), in which the gas is heated to a temperature T 1.

The maximum value of the efficiency of heat engines operating on ideal gas, according to the Carnot cycle:

.

The essence of the formula is expressed in the proven FROM. Carnot's theorem that the efficiency of any heat engine cannot exceed the efficiency of the Carnot cycle carried out at the same temperature of the heater and refrigerator.

A thermal engine is an engine that performs work at the expense of a source of thermal energy.

Thermal energy ( Q heater) from the source is transferred to the engine, while part of the received energy the engine spends on doing work W, unspent energy ( Q refrigerator) is sent to a refrigerator, the role of which can be performed, for example, by ambient air. The heat engine can only work if the temperature of the refrigerator is less than the temperature of the heater.

The coefficient of performance (COP) of a heat engine can be calculated by the formula: Efficiency = W/Q ng.

Efficiency = 1 (100%) if all thermal energy is converted into work. Efficiency=0 (0%) if no thermal energy is converted into work.

The efficiency of a real heat engine lies in the range from 0 to 1, the higher the efficiency, the more efficient the engine.

Q x / Q ng \u003d T x / T ng Efficiency \u003d 1- (Q x / Q ng) Efficiency \u003d 1- (T x / T ng)

Taking into account the third law of thermodynamics, which states that the temperature of absolute zero (T=0K) cannot be reached, we can say that it is impossible to develop a heat engine with efficiency=1, since always T x > 0.

The efficiency of the heat engine will be the greater, the higher the temperature of the heater, and the lower the temperature of the refrigerator.

« Physics - Grade 10 "

What is a thermodynamic system and what parameters characterize its state.
State the first and second laws of thermodynamics.

It was the creation of the theory of heat engines that led to the formulation of the second law of thermodynamics.

The reserves of internal energy in the earth's crust and oceans can be considered practically unlimited. But to solve practical problems, having energy reserves is still not enough. It is also necessary to be able to use energy to set in motion machine tools in factories and plants, means of transport, tractors and other machines, rotate the rotors of electric current generators, etc. Mankind needs engines - devices capable of doing work. Most of the engines on Earth are heat engines.

Heat engines- These are devices that convert the internal energy of the fuel into mechanical work.

The principle of operation of heat engines.

In order for the engine to do work, a pressure difference is needed on both sides of the engine piston or turbine blades. In all heat engines, this pressure difference is achieved by increasing the temperature working body(gas) hundreds or thousands of degrees above the temperature environment. This increase in temperature occurs during the combustion of fuel.

One of the main parts of the engine is a gas-filled vessel with a movable piston. The working fluid in all heat engines is a gas that does work during expansion. Let's denote the initial temperature of the working fluid (gas) through T 1 . This temperature in steam turbines or machines is acquired by steam in a steam boiler. In internal combustion engines and gas turbines, the temperature increase occurs when fuel is burned inside the engine itself. The temperature T 1 is called heater temperature.

The role of the refrigerator

As work is done, the gas loses energy and inevitably cools to a certain temperature T 2 , which is usually somewhat higher than the ambient temperature. They call her refrigerator temperature. The refrigerator is the atmosphere or special devices for cooling and condensing exhaust steam - capacitors. In the latter case, the temperature of the refrigerator may be slightly lower than the ambient temperature.

Thus, in the engine, the working fluid during expansion cannot give all its internal energy to do work. Part of the heat is inevitably transferred to the cooler (atmosphere) along with exhaust steam or exhaust gases from internal combustion engines and gas turbines.

This part of the internal energy of the fuel is lost. A heat engine performs work due to the internal energy of the working fluid. Moreover, in this process, heat is transferred from hotter bodies (heater) to colder ones (refrigerator). A schematic diagram of a heat engine is shown in Figure 13.13.

The working fluid of the engine receives from the heater during the combustion of fuel the amount of heat Q 1, does work A "and transfers the amount of heat to the refrigerator Q2< Q 1 .

In order for the engine to work continuously, it is necessary to return the working fluid to its initial state, at which the temperature of the working fluid is equal to T 1 . It follows from this that the operation of the engine occurs according to periodically repeating closed processes, or, as they say, according to a cycle.

Cycle is a series of processes, as a result of which the system returns to its initial state.

Coefficient of performance (COP) of a heat engine.

The impossibility of complete conversion of the internal energy of the gas into the work of heat engines is due to the irreversibility of processes in nature. If heat could spontaneously return from the refrigerator to the heater, then the internal energy could be completely converted into useful work using any heat engine. The second law of thermodynamics can be formulated as follows:

Second law of thermodynamics:
it is impossible to create a perpetual motion machine of the second kind, which would completely convert heat into mechanical work.

According to the law of conservation of energy, the work done by the engine is:

A" \u003d Q 1 - | Q 2 |, (13.15)

where Q 1 - the amount of heat received from the heater, and Q2 - the amount of heat given to the refrigerator.

The coefficient of performance (COP) of a heat engine is the ratio of work A "performed by the engine to the amount of heat received from the heater:

Since in all engines some amount of heat is transferred to the refrigerator, then η< 1.

The maximum value of the efficiency of heat engines.

The laws of thermodynamics make it possible to calculate the maximum possible efficiency of a heat engine operating with a heater having a temperature of T 1 and a refrigerator with a temperature of T 2, and also to determine ways to increase it.

For the first time, the maximum possible efficiency of a heat engine was calculated by the French engineer and scientist Sadi Carnot (1796-1832) in his work “Reflections on the driving force of fire and on machines capable of developing this force” (1824).

Carnot came up with an ideal heat engine with an ideal gas as the working fluid. An ideal Carnot heat engine operates in a cycle consisting of two isotherms and two adiabats, and these processes are considered reversible (Fig. 13.14). First, a vessel with gas is brought into contact with a heater, the gas expands isothermally, doing positive work, at a temperature T 1 , while it receives an amount of heat Q 1 .

Then the vessel is thermally insulated, the gas continues to expand already adiabatically, while its temperature decreases to the temperature of the refrigerator T 2 . After that, the gas is brought into contact with the refrigerator, under isothermal compression, it gives off the amount of heat Q 2 to the refrigerator, compressing to a volume V 4< V 1 . Затем сосуд снова теплоизолируют, газ сжимается адиабатно до объёма V 1 и возвращается в первоначальное состояние. Для КПД этой машины было получено следующее выражение:

As follows from formula (13.17), the efficiency of the Carnot machine is directly proportional to the difference in the absolute temperatures of the heater and refrigerator.

The main meaning of this formula is that it indicates the way to increase the efficiency, for this it is necessary to increase the temperature of the heater or lower the temperature of the refrigerator.

Any real heat engine operating with a heater having a temperature T 1 and a refrigerator with a temperature T 2 cannot have an efficiency exceeding the efficiency of an ideal heat engine: The processes that make up the cycle of a real heat engine are not reversible.

Formula (13.17) gives the theoretical limit for the maximum value of the efficiency of heat engines. It shows that a heat engine is more efficient, the greater the temperature difference between the heater and the refrigerator.

Only at the temperature of the refrigerator, equal to absolute zero, η = 1. In addition, it has been proved that the efficiency calculated by formula (13.17) does not depend on the working substance.

But the temperature of the refrigerator, the role of which is usually played by the atmosphere, practically cannot be lower than the ambient temperature. You can increase the temperature of the heater. However, any material (solid body) has limited heat resistance or heat resistance. When heated, it gradually loses its elastic properties, and when sufficiently high temperature 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.

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 is 62% (note that efficiency is usually measured as a percentage). The actual value of the efficiency due to various kinds of energy losses is approximately 40%. Diesel engines have the maximum efficiency - about 44%.

Environmental protection.

It is hard to imagine modern world without heat engines. They provide us with a comfortable life. Heat engines drive vehicles. About 80% of electricity, despite the presence of nuclear power plants, is generated using heat engines.

However, during the operation of heat engines, inevitable environmental pollution occurs. This is a contradiction: on the one hand, every year humanity needs more and more energy, the main part of which is obtained by burning fuel, on the other hand, combustion processes are inevitably accompanied by environmental pollution.

When fuel is burned, the oxygen content in the atmosphere decreases. In addition, the combustion products themselves form chemical compounds that are harmful to living organisms. Pollution occurs not only on the ground, but also in the air, since any aircraft flight is accompanied by emissions of harmful impurities into the atmosphere.

One of the consequences of the operation of the engines is the formation of carbon dioxide, which absorbs infrared radiation from the Earth's surface, which leads to an increase in the temperature of the atmosphere. This is the so-called greenhouse effect. Measurements show that the temperature of the atmosphere rises by 0.05 °C per year. Such a continuous increase in temperature can cause the ice to melt, which in turn will lead to a change in the water level in the oceans, i.e., to the flooding of the continents.

We note one more negative point when using heat engines. So, sometimes water from rivers and lakes is used to cool engines. The heated water is then returned back. The increase in temperature in water bodies disrupts the natural balance, this phenomenon is called thermal pollution.

To protect the environment, various cleaning filters are widely used to prevent the emission of harmful substances into the atmosphere, and engine designs are being improved. There is a continuous improvement of fuel, which gives less harmful substances during combustion, as well as the technology of its combustion. Alternative energy sources using wind, solar radiation, and core energy are being actively developed. Electric vehicles and vehicles powered by solar energy are already being produced.

The topic of the current lesson will be the consideration of the processes occurring in quite specific, and not abstract, as in previous lessons, devices - heat engines. We will define such machines, describe their main components and the principle of operation. Also during this lesson, the question of finding efficiency - the efficiency of thermal engines, both real and maximum possible, will be considered.

Topic: Fundamentals of thermodynamics
Lesson: The principle of operation of a heat engine

The topic of the last lesson was the first law of thermodynamics, which set the relationship between a certain amount of heat that was transferred to a portion of a gas and the work done by this gas during expansion. And now it's time to say that this formula is of interest not only for some theoretical calculations, but also in full practical application, because the work of a gas is nothing more than the useful work that we extract when using heat engines.

Definition. heat engine- a device in which the internal energy of the fuel is converted into mechanical work (Fig. 1).

Rice. 1. Various examples of heat engines (), ()

As can be seen from the figure, heat engines are any devices that work according to the above principle, and they range from incredibly simple to very complex in design.

Without exception, all heat engines are functionally divided into three components (see Fig. 2):

• Heater
• working body
• Fridge

Rice. 2. Functional diagram of a heat engine ()

The heater is the process of combustion of fuel, which, when burned, transfers a large number of heat to the gas, heating it to high temperatures. Hot gas, which is a working fluid, due to an increase in temperature and, consequently, pressure, expands, doing work. Of course, since there is always heat transfer with the engine case, ambient air, etc., the work will not be numerically equal to the transferred heat - part of the energy goes to the refrigerator, which, as a rule, is the environment.

The easiest way is to imagine the process taking place in a simple cylinder under a movable piston (for example, the cylinder of an internal combustion engine). Naturally, for the engine to work and make sense, the process must occur cyclically, and not one-time. That is, after each expansion, the gas must return to its original position (Fig. 3).

Rice. 3. An example of the cyclic operation of a heat engine ()

In order for the gas to return to its initial position, it is necessary to perform some work on it (the work of external forces). And since the work of the gas is equal to the work on the gas with the opposite sign, in order for the gas to perform a total positive work for the entire cycle (otherwise there would be no point in the engine), it is necessary that the work of external forces be less than the work of the gas. That is, the graph of the cyclic process in P-V coordinates should look like: a closed loop with a clockwise bypass. At this condition the work of the gas (in the section of the graph where the volume increases) is greater than the work on the gas (in the section where the volume decreases) (Fig. 4).

Rice. 4. An example of a graph of a process occurring in a heat engine

Since we are talking about a certain mechanism, it is imperative to say what its efficiency is.

Definition. Efficiency (coefficient of performance) of a heat engine- the ratio of useful work performed by the working fluid to the amount of heat transferred to the body from the heater.

If we take into account the conservation of energy: the energy that has departed from the heater does not disappear anywhere - part of it is removed in the form of work, the rest goes to the refrigerator:

We get:

This is an expression for efficiency in parts, if you need to get the efficiency value as a percentage, you must multiply the resulting number by 100. The efficiency in the SI measurement system is a dimensionless value and, as can be seen from the formula, cannot be more than one (or 100).

It should also be said that this expression is called the real efficiency or the efficiency of a real heat engine (heat engine). If we assume that we somehow manage to completely get rid of the design flaws of the engine, then we will get an ideal engine, and its efficiency will be calculated according to the formula for the efficiency of an ideal heat engine. This formula was obtained by the French engineer Sadi Carnot (Fig. 5):