A heat engine (machine) is a device that converts the internal energy of fuel into mechanical work, exchanging heat with surrounding bodies. Most modern automobile, aircraft, marine and rocket engines are designed on the principles of operation heat engine. The work is done by changing the volume of the working substance, and to characterize the efficiency of any type of engine, a value is used that is called the efficiency factor (COP).
How a heat engine works
From the point of view of thermodynamics (a branch of physics that studies the patterns of mutual transformations of internal and mechanical energies and the transfer of energy from one body to another), any heat engine consists of a heater, a refrigerator and a working fluid.
Rice. 1. Structural diagram of the heat engine:.
The first mention of a prototype heat engine refers to a steam turbine, which was invented in ancient Rome (2nd century BC). True, the invention did not then find wide application due to the lack of many auxiliary details at that time. For example, at that time such a key element for the operation of any mechanism as a bearing had not yet been invented.
The general scheme of operation of any heat engine looks like this:
- The heater has a temperature T 1 high enough to transfer a large amount of heat Q 1 . In most heat engines, heat is generated by combustion. fuel mixture(fuel-oxygen);
- The working fluid (steam or gas) of the engine performs useful work BUT, for example, moving a piston or rotating a turbine;
- The refrigerator absorbs part of the energy from the working fluid. Refrigerator temperature T 2< Т 1 . То есть, на совершение работы идет только часть теплоты Q 1 .
The heat engine (engine) must work continuously, so the working fluid must return to its original state so that its temperature becomes equal to T 1 . For the continuity of the process, the operation of the machine must occur cyclically, periodically repeating. In order to create a cyclic mechanism - to return the working fluid (gas) to its original state - a refrigerator is needed to cool the gas during the compression process. The atmosphere can serve as a refrigerator (for engines internal combustion) or cold water (for steam turbines).
What is the efficiency of a heat engine
To determine the efficiency of heat engines, the French mechanical engineer Sadi Carnot in 1824. introduced the concept thermal efficiency engine. The Greek letter η is used to denote efficiency. The value of η is calculated using the heat engine efficiency formula:
$$η=(A\over Q1)$$
Since $ A = Q1 - Q2 $, then
$η =(1 - Q2\over Q1)$
Since in all engines part of the heat is given off to the refrigerator, then always η< 1 (меньше 100 процентов).
The maximum possible efficiency of an ideal heat engine
As an ideal heat engine, Sadi Carnot proposed a machine with an ideal gas as a working fluid. The ideal Carnot model works on a cycle (Carnot cycle) consisting of two isotherms and two adiabats.
Rice. 2. Carnot cycle:.
Recall:
- adiabatic process is a thermodynamic process that occurs without heat exchange with the environment (Q=0);
- Isothermal process is a thermodynamic process that occurs when constant temperature. Since the internal energy of an ideal gas depends only on temperature, the amount of heat transferred to the gas Q goes entirely to work A (Q = A) .
Sadi Carnot proved that the maximum possible efficiency that can be achieved by an ideal heat engine is given by the following formula:
$$ηmax=1-(T2\over T1)$$
The Carnot formula allows you to calculate the maximum possible efficiency of a heat engine. The greater the difference between the temperatures of the heater and the refrigerator, the greater the efficiency.
What are the real efficiency of different types of engines
From the above examples, it can be seen that the highest efficiency values (40-50%) are internal combustion engines (in the diesel version) and liquid fuel jet engines.
Rice. 3. Efficiency of real heat engines:.
What have we learned?
So, we learned what engine efficiency is. The efficiency of any heat engine is always less than 100 percent. The greater the temperature difference between the heater T 1 and the refrigerator T 2 , the greater the efficiency.
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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 due to a change in the internal energy of the heater, i.e., due to the supply 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:
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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.
Since ancient times, people have tried to convert energy into mechanical work. They converted the kinetic energy of the wind, the potential energy of water, etc. Starting from the 18th century, machines began to appear that convert the internal energy of fuel into work. Such machines worked thanks to heat engines.
A heat engine is a device that converts thermal energy into mechanical work due to expansion (most often gases) from high temperature.
Any heat engines have components:
- Heating element. body with high temperature regarding the environment.
- working body. Since expansion provides the job, this element must expand well. As a rule, gas or steam is used.
- cooler. Body with low temperature.
The working fluid receives thermal energy from the heater. As a result, it begins to expand and do work. In order for the system to perform work again, it must be returned to its original state. Therefore, the working fluid is cooled, that is, excess thermal energy is, as it were, discharged into the cooling element. And the system comes to its original state, then the process repeats again.
Efficiency calculation
To calculate the efficiency, we introduce the following notation:
Q 1 - The amount of heat received from the heating element
A’– Work done by the working body
Q 2 - The amount of heat received by the working fluid from the cooler
In the process of cooling, the body transfers heat, so Q 2< 0.
The operation of such a device is a cyclic process. This means that after a complete cycle, the internal energy will return to its original state. Then, according to the first law of thermodynamics, the work done by the working fluid will be equal to the difference between the amount of heat received from the heater and the heat received from the cooler:
Q 2 is a negative value, so it is taken modulo
Efficiency is expressed as the ratio of useful work to the total work that the system has performed. In this case, the total work will be equal to the amount of heat that is spent on heating the working fluid. All expended energy is expressed through Q 1 .
Therefore, the efficiency factor is defined as.
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Mathematically, the definition of efficiency can be written as:
η = A Q , (\displaystyle \eta =(\frac (A)(Q)),)where BUT- useful work (energy), and Q- wasted energy.
If the efficiency is expressed as a percentage, then it is calculated by the formula:
η = A Q × 100 % (\displaystyle \eta =(\frac (A)(Q))\times 100\%) ε X = Q X / A (\displaystyle \varepsilon _(\mathrm (X) )=Q_(\mathrm (X) )/A),where Q X (\displaystyle Q_(\mathrm (X) ))- heat taken from the cold end (refrigeration capacity in refrigeration machines); A (\displaystyle A)
For heat pumps use the term transformation ratio
ε Γ = Q Γ / A (\displaystyle \varepsilon _(\Gamma )=Q_(\Gamma )/A),where Q Γ (\displaystyle Q_(\Gamma ))- condensation heat transferred to the coolant; A (\displaystyle A)- the work (or electricity) spent on this process.
In the perfect car Q Γ = Q X + A (\displaystyle Q_(\Gamma )=Q_(\mathrm (X) )+A), hence for the ideal machine ε Γ = ε X + 1 (\displaystyle \varepsilon _(\Gamma )=\varepsilon _(\mathrm (X) )+1)
The reverse Carnot cycle has the best performance indicators for refrigeration machines: in it the coefficient of performance
ε = T X T Γ − T X (\displaystyle \varepsilon =(T_(\mathrm (X) ) \over (T_(\Gamma )-T_(\mathrm (X) )))), since, in addition to the energy taken into account A(e.g. electrical), to heat Q there is also energy taken from a cold source.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 exceeding 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 rigorously.
Consider first heat engine operating on a reversible cycle with a real gas. The cycle can be any, 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 work with a common heater and a common cooler. Let the Carnot machine work in a reverse cycle (like a refrigeration machine), and the other machine in a direct cycle (Fig. 5.18). The heat engine performs work equal, according to formulas (5.12.3) and (5.12.5):
The 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 performed on it
(5.12.12)Since by condition η" > η , then A" > A. Therefore, the heat engine can drive the refrigeration engine, and there will still be an excess of work. This excess work is done at the expense of heat taken from one source. After all, heat is not transferred to the refrigerator under the action of two machines 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 Carnot's machine in a straight line. We again come to a contradiction with the second law of thermodynamics. Therefore, two machines operating on reversible cycles have the same efficiency: η " = η .
It is a different matter if the second machine operates in an irreversible cycle. If we allow η " > η , then we again come to a contradiction with the second law of thermodynamics. However, the assumption m|"< 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 of heat engines. It shows that a heat engine is more efficient the higher the temperature of the heater and the lower the temperature of the refrigerator. Only when the refrigerator temperature is equal to absolute zero, η = 1.
But the temperature of the refrigerator practically cannot be much lower than the ambient temperature. You can increase the temperature of the heater. However, any material (solid) has limited heat resistance, or heat resistance. When heated, it gradually loses its elastic properties, and melts at a sufficiently high temperature.
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 its incomplete combustion, etc. The real opportunities for increasing the efficiency here are still large. So, 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 value of the efficiency is:
The actual value of the efficiency due to various kinds of energy losses is approximately 40%. The maximum efficiency - about 44% - have internal combustion engines.
The efficiency of any heat engine cannot exceed the maximum possible value
,
where T 1
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absolute temperature of the heater, and T 2
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absolute temperature of the refrigerator.Increasing the efficiency of heat engines and bringing it closer to the maximum possible- the most important technical challenge.