Determination of efficiency of a heat engine. Heat engine efficiency

The working fluid, receiving a certain amount of heat Q1 from the heater, gives part of this amount of heat, equal in modulus |Q2|, to the refrigerator. Therefore, the work done cannot be greater A = Q1 - |Q2|. The ratio of this work to the amount of heat received by the expanding gas from the heater is called efficiency heat engine:

The efficiency of a heat engine operating in a closed cycle is always less than one. The task of thermal power engineering is to make the efficiency as high as possible, that is, to use as much of the heat received from the heater as possible to produce work. For the first time, the most perfect cyclic process, consisting of isotherms and adiabats, was proposed by the French physicist and engineer S. Carnot in 1824.

3) By ideal we mean a heat engine that has maximum efficiency. at given values ​​of the heater T1 and refrigerator T2.
From the second law of thermodynamics it follows that even an ideal heat engine operating without losses has efficiency. fundamentally below 100% and is calculated using the formula:

The working fluid in an ideal heat engine is an ideal gas, and it operates according to the Carnot cycle:

4) Concept entropy was first introduced by Clausius in thermodynamics to determine the measure of irreversible energy dissipation, measures of deviation of a real process from an ideal one. Defined as the sum of reduced heats, it is a function of state and remains constant in closed reversible processes, while in irreversible processes its change is always positive.

Mathematically, entropy is defined as a function of the state of the system, equal in an equilibrium process to the amount of heat imparted to the system or removed from the system, related to the thermodynamic temperature of the system:

where is the entropy increment; - minimum heat supplied to the system; - absolute temperature of the process.

Entropy establishes a connection between macro- and micro-states. The peculiarity of this characteristic is that it is the only function in physics that shows the direction of processes. Since entropy is a function of state, it does not depend on how the transition from one state of the system to another is carried out, but is determined only by the initial and final states of the system.

For example, at a temperature of 0 °C, water can be in a liquid state and, with little external influence, begins to quickly turn into ice, releasing a certain amount of heat. In this case, the temperature of the substance remains 0 °C. The state of a substance changes, accompanied by the release of heat, due to a change in structure.

Rudolf Clausius gave the quantity the name "entropy", which comes from the Greek word τρoπή, "change" (change, transformation, transformation). This equality refers to the change in entropy, without completely defining the entropy itself.

« Physics - 10th grade"

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

Task 1.

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

Solution.

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

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

Task 2.

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

Solution.

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

Work done during the same time A = Nt.

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

For an ideal heat engine η < η ид.

Task 3.

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

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

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

Finally, Q 2 = (A/η)(1 - η).

Source: “Physics - 10th grade”, 2014, textbook Myakishev, Bukhovtsev, Sotsky

Fundamentals of thermodynamics. Thermal phenomena - Physics, textbook for grade 10 - Classroom physics

The working fluid, receiving a certain amount of heat Q 1 from the heater, gives part of this amount of heat, equal in modulus to |Q2|, to the refrigerator. Therefore, the work done cannot be greater A = Q 1- |Q 2 |. The ratio of this work to the amount of heat received by the expanding gas from the heater is called efficiency heat engine:

The efficiency of a heat engine operating in a closed cycle is always less than one. The task of thermal power engineering is to make the efficiency as high as possible, that is, to use as much of the heat received from the heater as possible to produce work. How can this be achieved?
For the first time, the most perfect cyclic process, consisting of isotherms and adiabats, was proposed by the French physicist and engineer S. Carnot in 1824.

Carnot cycle.

Let us assume that the gas is in a cylinder, the walls and piston of which are made of a heat-insulating material, and the bottom is made of a material with high thermal conductivity. The volume occupied by the gas is equal to V 1.

Figure 2

Let's bring the cylinder into contact with the heater (Figure 2) and give the gas the opportunity to expand isothermally and do work . The gas receives a certain amount of heat from the heater Q 1. This process is graphically represented by an isotherm (curve AB).

Figure 3

When the volume of gas becomes equal to a certain value V 1'< V 2 , the bottom of the cylinder is isolated from the heater , After this, the gas expands adiabatically to the volume V 2, corresponding to the maximum possible stroke of the piston in the cylinder (adiabatic Sun). In this case, the gas is cooled to a temperature T 2< T 1 .
The cooled gas can now be compressed isothermally at a temperature T2. To do this, it must be brought into contact with a body having the same temperature T 2, i.e. with a refrigerator , and compress the gas by an external force. However, in this process the gas will not return to its original state - its temperature will always be lower than T 1.
Therefore, isothermal compression is brought to a certain intermediate volume V 2 '>V 1(isotherm CD). In this case, the gas gives off some heat to the refrigerator Q2, equal to the work of compression performed on it. After this, the gas is compressed adiabatically to a volume V 1, at the same time its temperature rises to T 1(adiabatic D.A.). Now the gas has returned to its original state, in which its volume is equal to V 1, temperature - T1, pressure - p 1, and the cycle can be repeated again.

So, on the site ABC gas does work (A > 0), and on the site CDA work done on the gas (A< 0). At the sites Sun And AD work is done only by changing the internal energy of the gas. Since the change in internal energy UBC = – UDA, then the work during adiabatic processes is equal: ABC = –ADA. Consequently, the total work done per cycle is determined by the difference in work done during isothermal processes (sections AB And CD). Numerically, this work is equal to the area of ​​the figure bounded by the cycle curve ABCD.
Only part of the amount of heat is actually converted into useful work QT, received from the heater, equal to QT 1 – |QT 2 |. So, in the Carnot cycle, useful work A = QT 1– |QT 2 |.
The maximum efficiency of an ideal cycle, as shown by S. Carnot, can be expressed in terms of the heater temperature (T 1) and refrigerator (T 2):

In real engines it is not possible to implement a cycle consisting of ideal isothermal and adiabatic processes. Therefore, the efficiency of the cycle carried out in real engines is always less than the efficiency of the Carnot cycle (at the same temperatures of heaters and refrigerators):

The formula shows that the higher the heater temperature and the lower the refrigerator temperature, the greater the engine efficiency.

Carnot Nicolas Leonard Sadi (1796-1832) - a talented French engineer and physicist, one of the founders of thermodynamics. In his work “Reflections on the driving force of fire and on machines capable of developing this force” (1824), he first showed that heat engines can perform work only in the process of transferring heat from a hot body to a cold one. Carnot came up with an ideal heat engine, calculated the efficiency of the ideal machine and proved that this coefficient is the maximum possible for any real heat engine.
As an aid to his research, Carnot invented (on paper) in 1824 an ideal heat engine with an ideal gas as the working fluid. The important role of the Carnot engine lies not only in its possible practical application, but also in the fact that it allows us to explain the principles of operation of heat engines in general; It is equally important that Carnot, with the help of his engine, managed to make a significant contribution to the substantiation and understanding of the second law of thermodynamics. All processes in a Carnot machine are considered as equilibrium (reversible). A reversible process is a process that proceeds so slowly that it can be considered as a sequential transition from one equilibrium state to another, etc., and this entire process can be carried out in the opposite direction without changing the work done and the amount of heat transferred. (Note that all real processes are irreversible) A circular process or cycle is carried out in the machine, in which the system, after a series of transformations, returns to its original state. The Carnot cycle consists of two isotherms and two adiabats. Curves A - B and C - D are isotherms, and B - C and D - A are adiabats. First, the gas expands isothermally at temperature T 1 . At the same time, it receives the amount of heat Q 1 from the heater. Then it expands adiabatically and does not exchange heat with the surrounding bodies. This is followed by isothermal compression of the gas at temperature T 2 . In this process, the gas transfers the amount of heat Q 2 to the refrigerator. Finally, the gas is compressed adiabatically and returns to its original state. During isothermal expansion, the gas does work A" 1 >0, equal to the amount of heat Q 1. With adiabatic expansion B - C, positive work A" 3 is equal to the decrease in internal energy when the gas is cooled from temperature T 1 to temperature T 2: A" 3 =- dU 1.2 =U(T 1) -U(T 2). Isothermal compression at temperature T 2 requires work A 2 to be performed on the gas. The gas does correspondingly negative work A" 2 = -A 2 = Q 2. Finally, adiabatic compression requires work done on the gas A 4 = dU 2.1. The work of the gas itself A" 4 = -A 4 = -dU 2.1 = U(T 2) -U(T 1). Therefore, the total work of the gas during two adiabatic processes is zero. During the cycle, the gas does work A" = A" 1 + A" 2 =Q 1 +Q 2 =|Q 1 |-|Q 2 |. This work is numerically equal to the area of ​​the figure limited by the cycle curve. To calculate the efficiency, it is necessary to calculate the work for isothermal processes A - B and C - D. Calculations lead to the following result: (2) The efficiency of a Carnot heat engine is equal to the ratio of the difference between the absolute temperatures of the heater and refrigerator to the absolute temperature of the heater. The main significance of Carnot's formula (2) for the efficiency of an ideal machine is that it determines the maximum possible efficiency of any heat engine. Carnot proved the following theorem: any real heat engine operating with a heater at temperature T 1 and a refrigerator at temperature T 2 cannot have an efficiency that exceeds the efficiency of an ideal heat engine. Efficiency of real heat engines Formula (2) gives the theoretical limit for the maximum value of the efficiency 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 the efficiency equal 1. In real heat engines, processes proceed so quickly that the decrease and increase in the internal energy of the working substance when its volume changes does not have time to be compensated by the influx of energy from the heater and the release of energy to the refrigerator. Therefore, isothermal processes cannot be realized. The same applies to strictly adiabatic processes, since there are no ideal heat insulators in nature. The cycles carried out in real heat engines consist of two isochores and two adiabats (in the Otto cycle), of two adiabats, isobars and isochores (in the Diesel cycle), of two adiabats and two isobars (in a gas turbine), etc. In this case, one should have keeping in mind that these cycles can also be ideal, like the Carnot cycle. But for this it is necessary that the temperatures of the heater and refrigerator are not constant, as in the Carnot cycle, but change in the same way as the temperature of the working substance changes in the processes of isochoric heating and cooling. In other words, the working substance must be in contact with an infinitely large number of heaters and refrigerators - only in this case there will be equilibrium heat transfer at the isochores. Of course, in the cycles of real heat engines, the processes are nonequilibrium, as a result of which the efficiency of real heat engines at the same temperature range is significantly less than the efficiency of the Carnot cycle. At the same time, expression (2) plays a huge role in thermodynamics and is a kind of “beacon” indicating ways to increase the efficiency of real heat engines.
	In the Otto cycle, first the working mixture 1-2 is sucked into the cylinder, then adiabatic compression 2-3 and after its isochoric combustion 3-4, accompanied by an increase in the temperature and pressure of the combustion products, their adiabatic expansion 4-5 occurs, then an isochoric pressure drop 5 -2 and isobaric expulsion of exhaust gases by the piston 2-1. Since no work is done on isochores, and the work during suction of the working mixture and expulsion of exhaust gases is equal and opposite in sign, the useful work for one cycle is equal to the difference in work on the adiabats of expansion and compression and is graphically depicted by the area of ​​the cycle.
Comparing the efficiency of a real heat engine with the efficiency of the Carnot cycle, it should be noted that in expression (2) the temperature T 2 in exceptional cases may coincide with the ambient temperature, which we take for a refrigerator, but in the general case it exceeds the ambient temperature. So, for example, in internal combustion engines, T2 should be understood as the temperature of the exhaust gases, and not the temperature of the environment into which the exhaust is produced.
	The figure shows the cycle of a four-stroke internal combustion engine with isobaric combustion (Diesel cycle). Unlike the previous cycle, in section 1-2 it is absorbed. atmospheric air, which is subjected to adiabatic compression in section 2-3 to 3 10 6 -3 10 5 Pa. The injected liquid fuel ignites in an environment of highly compressed, and therefore heated, air and burns isobarically 3-4, and then an adiabatic expansion of the combustion products 4-5 occurs. The remaining processes 5-2 and 2-1 proceed in the same way as in the previous cycle. It should be remembered that in internal combustion engines the cycles are conditionally closed, since before each cycle the cylinder is filled with a certain mass of working substance, which is ejected from the cylinder at the end of the cycle.
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. So, for a steam turbine, the initial and final temperatures of the steam are approximately the following: T 1 = 800 K and T 2 = 300 K. At these temperatures, the maximum value of the efficiency coefficient 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 is the absolute temperature of the heater, and T 2 is the absolute temperature of the refrigerator. Increasing the efficiency of heat engines and bringing it closer to the maximum possible is the most important technical task.

Clausius inequality

(1854): The amount of heat obtained by a system in any circular process, divided by the absolute temperature at which it was received ( given amount of heat), non-positive.

The amount of heat supplied quasi-statically received by the system does not depend on the transition path (determined only by the initial and final states of the system) - for quasi-static processes The Clausius inequality turns into equality .

Entropy, state function S thermodynamic system, the change of which dS for an infinitesimal reversible change in the state of the system is equal to the ratio of the amount of heat received by the system in this process (or taken away from the system) to the absolute temperature T:

Magnitude dS is a total differential, i.e. its integration along any arbitrarily chosen path gives the difference between the values entropy in the initial (A) and final (B) states:

Heat is not a function of state, so the integral of δQ depends on the chosen transition path between states A and B. Entropy measured in J/(mol deg).

Concept entropy as a function of the state of the system is postulated second law of thermodynamics, which is expressed through entropy difference between irreversible and reversible processes. For the first dS>δQ/T for the second dS=δQ/T.

Entropy as a function internal energy U system, volume V and number of moles n i i th component is a characteristic function (see. Thermodynamic potentials). This is a consequence of the first and second laws of thermodynamics and is written by the equation:

Where R - pressure, μ i - chemical potential i th component. Derivatives entropy by natural variables U, V And n i are equal:

Simple formulas connect entropy with heat capacities at constant pressure S p and constant volume C v:

By using entropy conditions are formulated for achieving thermodynamic equilibrium of a system at constant internal energy, volume and number of moles i th component (isolated system) and the stability condition for such equilibrium:

It means that entropy of an isolated system reaches a maximum in a state of thermodynamic equilibrium. Spontaneous processes in the system can only occur in the direction of increasing entropy.

Entropy belongs to a group of thermodynamic functions called Massier-Planck functions. Other functions belonging to this group are the Massier function F 1 = S - (1/T)U and Planck function Ф 2 = S - (1/T)U - (p/T)V, can be obtained by applying the Legendre transform to the entropy.

According to the third law of thermodynamics (see. Thermal theorem), change entropy in a reversible chemical reaction between substances in a condensed state tends to zero at T→0:

Planck's postulate (an alternative formulation of the thermal theorem) states that entropy of any chemical compound in a condensed state at absolute zero temperature is conditionally zero and can be taken as the starting point when determining the absolute value entropy substances at any temperature. Equations (1) and (2) define entropy up to a constant term.

In chemical thermodynamics The following concepts are widely used: standard entropy S 0, i.e. entropy at pressure R=1.01·10 5 Pa (1 atm); standard entropy chemical reaction i.e. standard difference entropies products and reagents; partial molar entropy component of a multicomponent system.

To calculate chemical equilibria, use the formula:

Where TO - equilibrium constant, and - respectively standard Gibbs energy, enthalpy and entropy of reaction; R- gas constant.

Definition of the concept entropy for a nonequilibrium system is based on the idea of ​​local thermodynamic equilibrium. Local equilibrium implies the fulfillment of equation (3) for small volumes of a system that is nonequilibrium as a whole (see. Thermodynamics of irreversible processes). During irreversible processes in the system, production (occurrence) can occur entropy. Full differential entropy is determined in this case by the Carnot-Clausius inequality:

Where dS i > 0 - differential entropy, not related to heat flow but due to production entropy due to irreversible processes in the system ( diffusion. thermal conductivity, chemical reactions, etc.). Local production entropy (t- time) is represented as the sum of products of generalized thermodynamic forces X i to generalized thermodynamic flows J i:

Production entropy due, for example, to the diffusion of a component i due to the force and flow of matter J; production entropy due to a chemical reaction - by force X=A/T, Where A-chemical affinity, and flow J, equal to the reaction rate. In statistical thermodynamics entropy isolated system is determined by the relation: where k - Boltzmann constant. - thermodynamic weight of the state, equal to the number of possible quantum states of the system with given values ​​of energy, volume, number of particles. The equilibrium state of the system corresponds to the equality of populations of single (non-degenerate) quantum states. Increasing entropy in irreversible processes is associated with the establishment of a more probable distribution of the given energy of the system among individual subsystems. Generalized statistical definition entropy, which also applies to non-isolated systems, connects entropy with the probabilities of various microstates as follows:

Where w i- probability i-th state.

Absolute entropy a chemical compound is determined experimentally, mainly by the calorimetric method, based on the ratio:

The use of the second principle allows us to determine entropy chemical reactions based on experimental data (electromotive force method, vapor pressure method, etc.). Calculation possible entropy chemical compounds using statistical thermodynamics methods, based on molecular constants, molecular weight, molecular geometry, and normal vibration frequencies. This approach is successfully carried out for ideal gases. For condensed phases, statistical calculations provide significantly less accuracy and are carried out in a limited number of cases; In recent years, significant progress has been made in this area.

Related information.

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.

« Physics - 10th grade"

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 not enough. It is also necessary to be able to use energy to set in motion machine tools in factories and factories, vehicles, tractors and other machines, to rotate the rotors of electric current generators, etc. Humanity 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 fuel into mechanical work.

Operating principle of heat engines.

In order for an engine to do work, there needs to be a pressure difference on both sides of the engine piston or turbine blades. In all heat engines, this pressure difference is achieved by increasing the temperature working fluid(gas) by hundreds or thousands of degrees compared to the ambient temperature. This temperature increase occurs when fuel burns.

One of the main parts of the engine is a gas-filled vessel with a movable piston. The working fluid of all heat engines is gas, which does work during expansion. Let us denote the initial temperature of the working fluid (gas) by T 1 . This temperature in steam turbines or machines is achieved by the steam in the steam boiler. In internal combustion engines and gas turbines, the temperature rise occurs as fuel burns inside the engine itself. Temperature T 1 is called heater temperature.

The role of the refrigerator.

As work is performed, the gas loses energy and inevitably cools to a certain temperature T2, which is usually slightly higher than the ambient temperature. They call her refrigerator temperature. The refrigerator is the atmosphere or special devices for cooling and condensing waste steam - capacitors. In the latter case, the temperature of the refrigerator may be slightly lower than the ambient temperature.

Thus, in an engine, the working fluid during expansion cannot give up all its internal energy to do work. Some of the heat is inevitably transferred to the refrigerator (atmosphere) along with waste 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). The schematic diagram of a heat engine is shown in Figure 13.13.

The working fluid of the engine receives from the heater during fuel combustion the amount of heat Q 1, does work A" and transfers the amount of heat to the refrigerator Q 2< Q 1 .

In order for the engine to operate 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 that the engine operates according to periodically repeating closed processes, or, as they say, in a cycle.

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

Coefficient of performance (efficiency) of a heat engine.

The impossibility of completely converting the internal energy of gas into the work of heat engines is due to the irreversibility of processes in nature. If heat could return spontaneously from the refrigerator to the heater, then the internal energy could be completely converted into useful work by any heat engine. The second law of thermodynamics can be stated 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 equal to:

A" = Q 1 - |Q 2 |, (13.15)

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

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

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

Maximum efficiency value of heat engines.

The laws of thermodynamics make it possible to calculate the maximum possible efficiency of a heat engine operating with a heater at temperature T1 and a refrigerator at temperature T2, as well as 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 a working fluid. An ideal Carnot heat engine operates on 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 the heater, the gas expands isothermally, doing positive work, at temperature T 1, and it receives an amount of heat Q 1.

Then the vessel is thermally insulated, the gas continues to expand adiabatically, while its temperature drops to the temperature of the refrigerator T 2. After this, the gas is brought into contact with the refrigerator; during isothermal compression, it gives 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 a Carnot machine is directly proportional to the difference in the absolute temperatures of the heater and refrigerator.

The main significance of this formula is that it indicates the way to increase 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 at temperature T1 and a refrigerator at temperature T2 cannot have an efficiency exceeding that of an ideal heat engine: The processes that make up the cycle of a real heat engine are not reversible.

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

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

But the temperature of the refrigerator, whose role is usually played by the atmosphere, practically cannot be lower than the ambient air temperature. You can increase the heater temperature. However, any material (solid) 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.

For a steam turbine, the initial and final steam temperatures are approximately the following: T 1 - 800 K and T 2 - 300 K. At these temperatures, the maximum efficiency value is 62% (note that efficiency is usually measured as a percentage). The actual efficiency value due to various types of energy losses is approximately 40%. The maximum efficiency - about 44% - is achieved by Diesel engines.

Environmental protection.

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

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

When fuel burns, 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 airplane flight is accompanied by emissions of harmful impurities into the atmosphere.

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

Let us 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. An 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 release of harmful substances into the atmosphere, and engine designs are being improved. There is a continuous improvement of fuel that produces less harmful substances during combustion, as well as the technology of its combustion. Alternative energy sources using wind, solar radiation, and nuclear energy are being actively developed. Electric cars and cars powered by solar energy are already being produced.