What is efficiency? Thermal engine. Heat engine efficiency Determination of the heat engine efficiency

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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 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 goal 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. During isothermal expansion (1-2) at temperature T 1 , 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 ,

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

A 23 = -ΔU 23 ,

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

A 34 = Q 2,

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

Maximum efficiency value of ideal gas heat engines according to the Carnot cycle:

.

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

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.