Thermodynamics is a branch of physics that studies the thermal properties of macroscopic bodies and systems of bodies in a state of thermal equilibrium, based on the law of conservation of energy, without taking into account internal structure bodies that make up the system.

Thermodynamics does not consider microscopic quantities - the size of atoms and molecules, their mass and number.

The laws of thermodynamics establish relationships between directly observable physical quantities characterizing the state of a system, such as pressure ​\(p \) ​, volume ​\(V \) ​, temperature ​\(T \) ​.

Internal energy- this is physical quantity, equal to the sum kinetic energy thermal motion particles of the body and the potential energy of their interaction with each other.

Designation - \\ (U \) , in SI unit of measurement - Joule (J).

In thermodynamics, internal energy depends on the temperature and volume of the body.

The internal energy of bodies depends on their temperature, mass and state of aggregation. As the temperature rises, the internal energy increases. The greatest internal energy of a substance in gaseous state, the smallest - in the solid.

Internal energy ideal gas represents only the kinetic energy of the thermal motion of its particles; potential energy particle interaction is zero.

The internal energy of an ideal gas is directly proportional to its temperature, and does not depend on volume (ideal gas molecules do not interact with each other):

where ​\(i \) ​ is the coefficient, equal to the number degrees of freedom of the molecule, ​\(\nu \) ​ is the amount of matter, ​\(R \) ​ is the universal gas constant, ​\(T \) ​ is the absolute temperature.

The number of degrees of freedom is equal to the number of possible motions of the particle.

Important!
For monatomic gases, the coefficient ​\(i \) ​ = 3, for diatomic gases ​\(i \) ​ = 5.

In practice, it is often important to be able to find the change in internal energy:

When solving problems, you can write a formula for calculating the internal energy using the Mendeleev–Clapeyron equation:

where ​\(p \) ​ is the pressure, ​\(V \) ​ is the gas volume.

The internal energy of real gases depends on both temperature and volume.

Change internal energy It is possible due to changes in temperature (during heat transfer) and due to changes in pressure and volume (during work).

Thermal equilibrium

Thermal equilibrium is the state of the system in which all its macroscopic parameters remain unchanged for an arbitrarily long time.

Quantities characterizing the state of macroscopic bodies without taking into account their molecular structure, are called macroscopic parameters. These include pressure and temperature, volume, mass, concentration of individual components of a gas mixture, etc. In a state of thermal equilibrium, there is no heat exchange with surrounding bodies, there are no transitions of matter from one state of aggregation to another, temperature, pressure, volume do not change.

Any thermodynamic system goes spontaneously into a state of thermal equilibrium. Each state of thermal equilibrium, in which a thermodynamic system can be, corresponds to a certain temperature.

Important!
In a state of thermal equilibrium, volume, pressure can be different in different parts thermodynamic system, but only the temperature in all parts of a thermodynamic system in thermal equilibrium is the same. Microscopic processes inside the body do not stop even at thermal equilibrium: the positions of molecules change, their speeds during collisions.

Heat transfer

Heat transfer- the process of changing the internal energy of the body without doing work.

There are three types heat transfers: conduction, convection and radiation (radiant heat transfer). Heat transfer occurs between bodies at different temperatures. Heat is transferred from a body with a higher temperature to a body with a lower temperature.

Thermal conductivity- this is the process of energy transfer from more heated bodies (parts of the body) to less heated ones as a result of the movement and interaction of body particles. Metals have high thermal conductivity - for example, the best conductors of heat are copper, gold, silver. The thermal conductivity of liquids is less, and gases are poor conductors of heat. Porous bodies do not conduct heat well, since air is contained in the pores. Substances with low thermal conductivity are used as heat insulators. Heat conduction is impossible in a vacuum. With heat conduction, there is no transfer of matter.

The phenomenon of thermal conductivity of gases is similar to the phenomenon of diffusion. Fast molecules move from a layer with a higher temperature to a colder layer, and molecules from a cold layer move to a hotter one. Due to this, the average kinetic energy molecules of the warmer layer decreases, and its temperature becomes lower.

In liquids and solids with an increase in the temperature of any area solid body or liquid its particles begin to oscillate more strongly. Colliding with neighboring particles, where the temperature is lower, these particles transfer part of their energy to them, and the temperature of this area increases.

Convection- energy transfer by liquid or gas flows.

The mechanism of convection can be explained on the basis of thermal expansion bodies and the law of Archimedes. When heated, the volume of a liquid increases and the density decreases. The heated layer under the action of the Archimedes force rises, and the cold one falls down. it natural convection. It occurs when a liquid or gas is heated unevenly from below in the gravitational field.

At forced convection the movement of the substance occurs under the action of pumps, fan blades. Such convection is used in a state of weightlessness. The intensity of convection depends on the temperature difference between the layers of the medium and the state of aggregation of the substance. Convection currents rise up. Convection is the transfer of matter.

In solids, convection is impossible, since particles cannot leave their places due to strong interaction. Convection is also impossible in a vacuum.

An example of convective currents in nature are winds (day and night breezes, monsoons).

Radiation(radiant heat transfer) - energy transfer electromagnetic waves. Heat transfer by radiation is possible in a vacuum. Radiation source is any body whose temperature is different from zero To. When absorbed energy thermal radiation goes into internal energy. Dark bodies are heated faster by radiation than bodies with a shiny surface, but they also cool faster. Radiation power depends on body temperature. As the temperature of the body increases, the radiation energy increases. The larger the surface area of ​​the body, the more intense the radiation.

Quantity of heat. Specific heat capacity of a substance

Quantity of heat is a scalar physical quantity equal to the energy that the body received or gave away during heat transfer.

Designation - \\ (Q \) , in SI unit of measurement - J.

Specific heat is a scalar physical quantity, numerically equal to the number heat that a body of mass 1 kg receives or gives off when its temperature changes by 1 K.

Designation - \\ (c \) , in SI unit of measurement - J / (kg K).

The specific heat capacity is determined not only by the properties of the substance, but also by the process in which heat transfer takes place. Therefore, the specific heat capacity of the gas is isolated at constant pressure- ​\(c_P \) ​ and the specific heat capacity of the gas at constant volume - ​\(c_V \) . Heating a gas by 1 K at constant pressure requires large quantity heat than at constant volume – ​\(c_P > c_V \) .

The formula for calculating the amount of heat that a body receives when heated or gives off when cooled:

where ​\(m \) ​ is the mass of the body, ​\(c \) ​ is specific heat, ​\(T_2 \) ​ - final body temperature, ​\(T_1 \) ​ - initial body temperature.

Important!
When solving problems for calculating the amount of heat during heating or cooling, you can not convert the temperature to kelvins. Since 1K \u003d 1 ° C, then\ ( \ Delta T \u003d \ Delta t \) .

Work in thermodynamics

Work in thermodynamics is equal to the change in the internal energy of the body.

The designation for the work of a gas is ​\(A' \) ​, the unit of measure in SI is the joule (J). Job designation external forces over gas - ​\(A \) .

Gas work ​\(A' =-A \) .

The work of expansion of an ideal gas is the work that the gas does against external pressure.

The work done by a gas is positive when it expands and negative when it is compressed. If the volume of the gas does not change (isochoric process), then the gas does not perform work.

Graphically, the work done by a gas can be calculated as the area of ​​the figure under the pressure-volume graph in coordinate axes​\((p,V) \) ​limited by the graph, the ​\(V \) axis and perpendiculars drawn from the points of the initial and final values volume.

The formula for calculating the work of a gas is:

in an isobaric process ​\(A’=p\cdot\Delta V. \) ​

in isothermal process \(A'=\frac(m)(M)RT\ln\frac(V_2)(V_1). \)​

Heat balance equation

If a system of bodies is thermally insulated, then its internal energy will not change despite the changes occurring within the system. If ​\(A \) ​ = 0, ​\(Q \) ​ = 0, then ​\(\Delta U \) ​ = 0 .

For any processes occurring in a thermally insulated system, its internal energy does not change (the law of conservation of internal energy).

Consider a thermally insulated two-body system with different temperatures. Upon contact, heat exchange will take place between them. A body with a higher temperature will give off a certain amount of heat, and a body with a lower temperature will receive it until the temperatures of the bodies become equal. Since the total internal energy should not change, then by how much the internal energy of a more heated body decreases, the internal energy of the second body must increase by that much. Since no work is done, the change in internal energy is equal to the amount of heat.

The amount of heat given off during heat exchange by a body with a higher temperature is equal in modulus to the amount of heat received by a body with a lower temperature:

Another wording: if the bodies form closed system and only heat exchange takes place between them, then algebraic sum given \\ (Q_ (otd) \) and received \ (Q_ (floor) \) amounts of heat is zero:

First law of thermodynamics

The law of conservation and transformation of energy, extended to thermal phenomena, is called the first law (beginning) of thermodynamics.

It is possible to formulate this law proceeding from the ways of changing the internal energy.

The change in the internal energy of the system during its transition from one state to another is equal to the sum of the work of external forces and the amount of heat transferred to the system:

If we consider the work of the system itself on external bodies, then the law can be formulated as follows:

the amount of heat transferred to the system goes to change its internal energy and the system performs work on external bodies:

If the system is isolated and no work is done on it and there is no heat exchange with external bodies, then in this case the internal energy does not change. If heat is not supplied to the system, then the work of the system can be performed only by reducing the internal energy. This means that it is impossible to create perpetual motion machine- a device capable of doing work without any fuel consumption.

First law of thermodynamics for isoprocesses

Isothermal process:​\(Q=A'\,(T=const, \Delta U=0) \)​
Physical meaning: All the heat transferred to the gas is used to do work.

Isobaric process:\(Q=\Delta U+A' \) ​
Physical meaning: The heat supplied to the gas is used to increase its internal energy and to perform work on the gas.

Isochoric process: \(Q=\Delta U\,(V=const, A'=0) \)​
Physical meaning: the internal energy of the gas increases due to the heat input.

adiabatic process:\(\Delta U=-A' \) ​ or ​ \(A=\Delta U\,\mathbf((Q=0)) \)​
Physical meaning: The internal energy of the gas is reduced by the work done by the gas. As a result, the temperature of the gas decreases.

Problems of changing the internal energy of bodies

These tasks can be divided into groups:

• When bodies interact, their internal energy changes without doing work on external environment.
• Phenomena associated with the transformation of one type of energy into another during the interaction of two bodies are considered. As a result, there is a change in the internal energy of one body due to the work done by it or on it.

When solving problems of the first group:

• to establish in which bodies the internal energy decreases, and in which it increases;
• write an equation heat balance​\((\Delta U=0) \) , when written in the expression ​\(Q = cm(t_2 - t_1) \) , to change the internal energy, you need to subtract the initial temperature from the final temperature of the body and sum the terms, taking into account the resulting sign ;
• check the solution.

When solving problems of the second group:

• make sure that in the process of interaction of bodies, heat from the outside is not supplied to them, i.e. is ​\(Q = 0 \) ​;
• establish which of the two interacting bodies has a change in internal energy and what is the cause of this change - the work done by the body itself, or the work done on the body;
• write down the equation ​\(Q = \Delta U + A \) for a body whose internal energy changes, taking into account the sign before work and the efficiency of the process under consideration;
• if the work is done due to a decrease in the internal energy of one of the bodies, then ​ \ (A \u003d - \ Delta U \) , and if the internal energy of the body increases due to the work done on the body, then ​ \ (A \u003d \ Delta U \ ) ​;
• find expressions for ​\(\Delta U \) ​ and ​\(A \) ​;
• substitute in the original equation instead of \(\Delta U \) and \(A \) expressions for them, get the final ratio to determine the desired value;
• solve the resulting equation with respect to the desired value;
• check the solution.

Second law of thermodynamics

All processes in nature proceed in only one direction. AT reverse direction they cannot proceed spontaneously. irreversible a process is called, the reverse of which can proceed only as a component of a more complex process.

Examples of irreversible processes:

• the transfer of heat from a hotter body to a less heated body;
• conversion of mechanical energy into internal energy.

The first law of thermodynamics says nothing about the direction of processes in nature.

The second law of thermodynamics expresses the irreversibility of processes occurring in nature. There are several formulations.

The second law of thermodynamics (Clausius' formulation):
it is impossible to transfer heat from more cold system to a hotter one in the absence of simultaneous changes in both systems or surrounding bodies.

The second law of thermodynamics (Kelvin's formulation):
it is impossible to carry out such a periodic process, the only result of which would be the production of work due to the heat taken from one source.

This formulation also says that it is impossible to build a perpetual motion machine of the second kind, that is, an engine that does work by cooling any one body.

Important!
In the formulation of the second law of thermodynamics great importance have the words "single result". If the processes in question are not the only ones, then the prohibitions are lifted. For example, in a refrigerator, heat is transferred from a colder body to a heated one, and at the same time, a compensating process of converting the mechanical energy of the surrounding bodies into internal energy is carried out.

The second law of thermodynamics is valid for systems with a huge number of particles. In systems with a small number of particles, fluctuations are possible - deviations from equilibrium.

heat engine efficiency

Coefficient useful action(efficiency) of a heat engine (engine) is the ratio of work ​\(A \) ​performed by the engine per cycle to the amount of heat ​\(Q_1 \) ​received per cycle from the heater:

The heat engine with maximum efficiency was created by Carnot. The machine carries out a circular process ( carnot cycle), at which, after a series of transformations, the system returns to its initial state.

Carnot cycle consists of four stages:

1. Isothermal expansion (in the figure - process 1–2). At the beginning of the process working body has a temperature ​\(T_1 \) , that is, the temperature of the heater. Then the body is brought into contact with the heater, which isothermally (at a constant temperature) transfers to it the amount of heat ​\(Q_1 \) . At the same time, the volume of the working fluid increases.
2. Adiabatic expansion (in the figure - process 2–3). The working fluid is detached from the heater and continues to expand without heat exchange with environment. At the same time, its temperature decreases to the temperature of the refrigerator ​ \ (T_2 \) .
3. Isothermal compression (in the figure - process 3-4). The working fluid, which by that time has a temperature \\ (T_2 \) , is brought into contact with the refrigerator and begins to contract isothermally, giving the refrigerator an amount of heat \\ (Q_2 \) .
4. Adiabatic compression (in the figure - process 4–1). The working fluid is separated from the refrigerator. At the same time, its temperature increases to the temperature of the heater ​ \ (T_1 \) .

Carnot cycle efficiency:

This shows that the efficiency of the Carnot cycle with an ideal gas depends only on the temperature of the heater ​\((T_1) \) ​ and the cooler \((T_2) \) .

The following conclusions follow from the equation:

• to increase the efficiency of a heat engine, it is necessary to increase the temperature of the heater and reduce the temperature of the refrigerator;
• The efficiency of a heat engine is always less than 1.

The Carnot cycle is reversible, since all its constituent parts are equilibrium processes.

Efficiency of heat engines: engine internal combustion- 30%, diesel engine - 40%, steam turbine - 40%, gas turbine - 25–30%.

Principles of operation of heat engines

heat engine called a device that converts the internal energy of the fuel into mechanical energy.

The main parts of a heat engine:

• Heater- a body with a constant temperature that converts the internal energy of the fuel into the energy of the gas. In each cycle of engine operation, the heater transfers a certain amount of heat to the working fluid.
• working body is a gas that does work when it expands.
• Fridge- a body with a constant temperature, to which the working fluid transfers part of the heat.

Any heat engine receives some heat from the heater ​\(Q_1 \)​ and transfers the amount of heat ​\(Q_2 \) to the refrigerator. Since ​\(Q_1 > Q_2 \) , then the work is done ​\(A’ = Q_1 – Q_2 \) .

The heat engine must operate cyclically, so the expansion of the working fluid must be replaced by its compression. The work of expanding the gas must be more work compression performed by external forces (the condition for useful work). The temperature of the gas during expansion must be higher than the temperature during compression. Then the gas pressure in all intermediate states during compression will be less than during expansion.

In real heat engines, the heater is the combustion chamber. In them, the working fluid is heated by the heat released during the combustion of fuel. The amount of heat released during the combustion of fuel is calculated by the formula:

where ​\(q \) ​ – specific heat fuel combustion, ​ \ (m \) ​ - mass of fuel.

The refrigerator most often in real engines is the atmosphere.

Types of heat engines:

• steam engine;
• turbine (steam, gas);
• internal combustion engine (carburetor, diesel);
• jet engine.

Thermal engines are widely used in all types of transport: in cars - internal combustion engines; on the railway transport– diesel engines (on diesel locomotives); on the water transport– turbines; in aviation - turbojet and jet engines. At thermal and nuclear power plants heat engines drive the rotors of alternators.

Energy and environmental issues

Thermal engines are widely used in transport and energy (thermal and nuclear power plants). The use of heat engines greatly affects the state of the Earth's biosphere. The following harmful factors can be distinguished:

• when fuel is burned, oxygen from the atmosphere is used, which leads to a decrease in the oxygen content in the air;
• When fuel is burned, carbon dioxide is released into the atmosphere. Concentration carbon dioxide rises in the atmosphere. This changes the transparency of the atmosphere as carbon dioxide molecules absorb infrared radiation, which leads to an increase in temperature (greenhouse effect);
• When coal is burned, nitrogen gases are released into the atmosphere sulfur compounds and lead compounds harmful to human health.

Solving the problem of environmental protection from harmful effects thermal energy enterprises requires an integrated approach. Mass pollutants during the operation of thermal power plants are fly ash, sulfur dioxide and nitrogen oxides. Methods for reducing emissions depend on the properties of the fuel and the conditions for its liquefaction. Prevention of fly ash pollution is achieved by cleaning the entire volume of solid fuel combustion products in high-performance ash collectors. The reduction of nitrogen oxide emissions from fuel combustion products at thermal power plants, as well as in combined-cycle and gas turbine installations, is mainly ensured by fuel combustion technology. A reduction in sulfur dioxide emissions can be achieved various methods upgrading and processing of fuel outside thermal power plants or directly at thermal power plants, as well as flue gas cleaning.

Emission control harmful substances power plants is carried out by special devices.

In some cases it is enough effective solution The construction of filters-traps and chimneys remains the issue of purification of emissions into the atmosphere. The chimney has two purposes: the first is to create draft and thereby force air - an obligatory participant in the combustion process - to enter the furnace in the right amount and at the right speed; the second is to remove combustion products (harmful gases and those present in the smoke particulate matter) to the upper atmosphere. Due to the continuous turbulent movement, harmful gases and solid particles are carried away from their source and dispersed.

To dissipate sulfur dioxide contained in the chimneys of thermal power plants, chimneys are constructed with a height of 180, 250 and 320 m. Thermal power plants In Russia, working on solid fuels, about 100 million tons of ash and slag are thrown into dumps per year. Ashes and slags take large areas land adversely affect the environment.

More than half of all pollution is created by transport. One of the ways to solve the problem of environmental protection is to switch to diesel engines, electric motors, and increase efficiency.

Algorithm for solving problems of the section "Thermodynamics":

• select a system of bodies and determine its type (closed, adiabatically closed, mechanically closed, open);
• find out how the state parameters ​\((p,V,T) \) and the internal energy of each body of the system change during the transition from one state to another;
• write equations that relate the parameters of two states of the system, formulas for calculating the change in the internal energy of each body of the system during the transition from one state to another;
• determine the change in the mechanical energy of the system and the work of external forces to change its volume;
• write down the formula of the first law of thermodynamics or the law of conservation and transformation of energy;
• solve the system of equations for the desired value;
• check the solution.

Basic formulas of the section "Thermodynamics"

LECTURE #1

DEFINITION OF ENERGY AND ITS TYPES.

THERMODYNAMICS AND ITS METHODS.

THERMODYNAMIC SYSTEMS.

Heat engineering - general technical discipline that studies the methods of obtaining, converting, transferring and using heat, as well as the principles of operation and design features heat and steam generators, heat engines, apparatuses and devices.

Thermodynamics ( component heat engineering) studies the laws of energy conversion in various physical and chemical processes occurring in macroscopic systems and accompanied by thermal effects.

known different kinds energy: thermal, electrical, chemical, magnetic, etc. The tasks of research can be different - this is the thermodynamics of biosystems, technical thermodynamics, etc. We are interested in technical thermodynamics, which studies the patterns of mutual transformation of heat and mechanical energy(together with the theory of heat transfer) and therefore is the theoretical foundation of heat engineering. Without this theoretical foundation, it is impossible to calculate and design a heat engine.

The thermodynamic method is phenomenological. The phenomenon is considered as a whole. The relationship between the macroscopic parameters that determine the behavior of the system is established by the two principles of thermodynamics. Thermodynamic system is a set of material bodies that are in mechanical and thermal interaction with each other and with external bodies surrounding the system.

Thermodynamic state body (for example, gas) is characterized by its mass, molar mass μ, pressure, volume, temperature (and possibly other quantities, for example, defining it chemical composition). All these quantities are called thermodynamic parameters of the body. However, as will be seen from what follows, such parameters as , have meaning only when the body is, at least approximately, in the so-called state of thermodynamic equilibrium (t.d.r.). This is the name of the state in which all thermodynamic parameters remain constant over time (to this we should add the condition of the absence of stationary flows). If, for example, the gas is rapidly heated, as shown in Fig. 9.1, the temperature of the directly heated part of the vessel A will be higher than the temperature of part B. The pressures in parts A and B will not be equal either. In this case, the concept of temperature or pressure of the entire gas does not make sense. Another example is to let a beam of fast molecules into a gas. It is clear that it makes no sense to talk about the temperature of the gas until fast molecules, due to a series of collisions with others, acquire velocities of the order average speed other molecules, in other words, until the system reaches the state of s.f.r.

In a state of etc. for each substance, the thermodynamic parameters are interconnected by the so-called equation of state:

Here R=8.31 ​​J/(molK) is the universal gas constant, μ - molar mass. For carbon (C), the value of μ is 12g, for hydrogen (H 2) - 2g, for oxygen (O 2) - 32g, for water (H 2 O) - 18g, etc.

A mole of any substance contains the same number of molecules N 0, called the Avogadro number:

The ratio of the universal gas constant R to the Avogadro number (i.e. the universal gas constant per molecule) is called Boltzmann constant:

An ideal gas is a gas so rarefied that it obeys equation (1.2) or (1.6). The meaning of this definition is, obviously, that in order to obey equation (1.6), the gas must be sufficiently rarefied. If the gas, on the other hand, is compressed to a sufficient high densities(so-called real gas), then instead of (1.6) we have

The choice of the thermodynamic system is arbitrary. The choice is dictated by the conditions of the problem being solved. The bodies that are not included in the system are the environment. The separation of the thermodynamic system and the environment is carried out by the control surface. So, for example, for the simplest thermodynamic system cylinder-gas-piston, the environment ambient air, and the control surface is the shell of the cylinder and the piston. The mechanical and thermal interaction of the thermodynamic system is carried out through the control surfaces.

During the mechanical interaction of the system itself or on it, work is done. It should be noted that work can be done under the influence of other power- electric, magnetic.

Considering the example with the cylinder-piston system, we can note the following: mechanical work is produced when the piston moves and is accompanied by a change in volume. Thermal interaction consists in the transfer of heat between the individual bodies of the system and between the system and the environment. In the example under consideration, heat can be supplied to the gas through the walls of the cylinder. For an open thermodynamic system, the exchange takes place with the environment and matter (mass transfer processes). In what follows, we will consider closed thermodynamic systems. If the system is thermally insulated, then we call it adiabatic, for example, a gas in a vessel with ideal thermal insulation. Such a system does not exchange either heat or matter with the environment and is called closed (isolated).

The transformation of heat into work and vice versa work into heat is carried out by systems representing gases and vapors, they are called working bodies.

In the development of thermodynamics as a science huge contribution made by Russian scientists: M.V. Lomonosov - defined the essence of heat as internal movement matter, in addition, he determined the essence of the subsequently developed laws of thermodynamics, a hundred years before Clausius (1850), gave the content of the second law of thermodynamics, quantification was given by Lomonosov in two of his works of 1750 and 1760. We can mention G.G. Hess (1840), who established a law on thermal effect chemical reaction, prof. Schiller N.N. (Kyiv University) - gave more than rigorous justification second law of thermodynamics, prof. Afanas'eva-Ehrenfest T.A. for the first time showed the expediency of a separate interpretation of the second law of thermodynamics for equilibrium and non-equilibrium processes. Research in applied and theoretical terms was carried out by the scientists of Moscow Higher Technical School Grinevetsky V.I., Kirsh K.V., Mertsalov N.I., Ramzin L.K., Oshurkov B.M. The first Soviet textbook on thermodynamics was written by Oshurkov B.M. Scientists VTI, MPEI Vukalovich M.P., Kirillin V.A., Novikov I.I., Timrot D.A., Vargaftik N.B. conducted extensive research to obtain new data on thermophysical properties a number of new working bodies. From foreign scientists huge contribution Sadi Carnot, R. Stirling, R. Mayer, Clausius, Helmholtz, Joule, Thomson, Reynolds and others contributed to the development of thermodynamics. By the way, R. Stirling 8 years before S. Carnot in 1816 patented a machine that does work due to heated air.

1 DK 536.7(07) + 536.24 Reviewers: Department of Heat Engineering and Thermal Power Plants of St. Petersburg state university means of communication (Doctor of Technical Sciences, Prof. I.G. Kiselev), Professor B.S. Fokin (JSC NPO "TsKTI named after I.I. Polzunov") Sapozhnikov S.Z., Kitanin E.L. Technical thermodynamics and heat transfer: Textbook for universities. St. Petersburg: Publishing house of St. Petersburg State Technical University, 1999. 319 p. ISBN 5-7422-0098-6 The fundamentals of technical thermodynamics and heat transfer are outlined. The principles of thermodynamics, methods for calculating thermodynamic processes with an ideal gas and with real working fluids, cycles of power plants, refrigeration machines and heat pumps are presented. The processes of stationary and non-stationary heat conduction, convective heat transfer, and heat transfer by radiation are described. The basics of thermal calculation of heat exchangers are given. Designed for bachelors in the direction 551400 “Terrestrial transport systems ". I8BN 5-7422-0098-6 St. Petersburg State Technical University, 1999 Sapozhnikov S.Z., Kitanin E.L., 1999 2 CONTENTS Foreword................................. ................................................. .... 1. TECHNICAL THERMODYNAMICS ............... 1.1. The subject and method of technical thermodynamics ....... 1.2. Basic concepts of thermodynamics ........................ 1.2.1. Thermodynamic system and thermodynamic parameters .............................................................. .............. 1.2.2. Thermodynamic equilibrium and equilibrium thermodynamic process .................................................. 1.2.3. Thermal equation of state. Thermodynamic surface and state diagrams…………………………………………………. 1.2.4. Mixtures of ideal gases............................................... 1.2.5. Energy, work, heat ....................................... 1.2.6. Heat capacity................................................. ........ 1.3. The first law of thermodynamics .............................................. 1.3.1. Equation of the first beginning .............................. 1.3.2. Internal energy as a function of state .............................................................. ............................... 1.3.3. Enthalpy and its properties .............................................. 1.3.4. Equation of the first law for an ideal gas .............................................................. ............................................... 1.4. Analysis of processes with an ideal gas ....................... 1.4.1. Isobaric process.............................................. 1.4. 2. Isochoric process.................................................... 1.4 .3. Isothermal process.............................................. 1.4.4. Adiabatic process.................................................... 1.4.5 . Polytropic processes ........................................ 1.4.6. Compression of gas in a reciprocating compressor ............... 1.5. The second law of thermodynamics .............................................. 1.5.1. Reversible and irreversible processes ................. 1.5.2. Cycles and their efficiency ....................................................... ...... 1.5.3. Statements of the second law .............................. 1.5.4. Carnot cycle. Carnot's theorem.............................. 3 1.5.5. Entropy, its change in reversible and irreversible processes .............................................................. ......................... 1.5.6. T–s state diagram. Entropy change in ideal gas processes....................... ................................................. ................... 1.5.7. Thermodynamic temperature scale ............... 1.6. Cycles of reciprocating internal combustion engines .............................................................. .................................... 1.6.1. Cycle with isochoric heat supply (Otto cycle) 1.6.2. Cycle with isobaric heat supply (Diesel cycle) .............................................................. ................................................. ................ 1.6.3. Comparison of the efficiency of internal combustion engine cycles .............. 1.7. Cycles of gas turbine plants.............................................. 1.7.1. Scheme and cycle with isobaric heat supply. 1.7.2. Thermal efficiency of the Brayton cycle.............................. 1.7.3. GTU regenerative cycle .............................................. 1.7.4. Efficiency of real cycles................... 1.8. Thermodynamics of real working bodies.............................. 1.8.1. Equations of state of real gases ............... 1.8.2. Change of aggregate state of matter.... 1.8.3. State Diagrams and Tables .................................. 1.9. Cycles of steam power plants .................................. 1.9.1. Steam Carnot cycle .................................................. 1.9.2. Rankine Cycle .................................................. ..... 1.10. Cycles of refrigeration machines and heat pumps 1.10.1. Reverse Carnot cycle .................................................. 1.10 .2. Vapour-compression refrigeration cycle with steam superheat and throttling .............................. 1.10.3. Heat pump cycle.............................................. 1.11. Wet air................................................ .......... 1.11.1 Basic concepts and definitions .................. 1.11.2. h–d-diagram of humid air............... 2. HEAT TRANSFER....................... ................................... 4 2.1. General representations about heat transfer ........................ 2.2. Thermal conductivity................................................. ....... 2.2.1. Basic concepts and definitions ............... 2.2.2. Hypothesis Bio-Fourier .................................. 2.2.3. Differential equation of heat conduction. …………………………………………………………… 2.2.4. Conditions for uniqueness .............................. 2.2.5. Models of bodies in problems of heat conduction .............. 2.3. Stationary thermal conductivity ........................................ 2.3.1. Thermal conductivity of plates and shells ......... 2.3.2. Thermal conductivity of ribbed surfaces. 2.4. Non-stationary thermal conductivity .............................. 2.4.1. Thermal conductivity of thermally thin bodies....... 2.4.2. Thermal conductivity of a semi-infinite body and rod .............................................................. .......... 2.4.3. Heating and cooling of plate, cylinder and ball. 2.4.4. Heating and cooling of bodies of finite dimensions…….. 2.4.5. Regular thermal regime ............................... 2.5. Approximate methods of the theory of heat conduction. 2.5.1. Electrothermal analogy .............................. 2.5.2. Graphical method ........................................ 2.5.3. Finite difference method ........................................ 2.6. Physical foundations convective heat transfer.. 2.6.1. Basic concepts and definitions .................. 2.6.2. Differential equations of convective heat transfer .................. ......................................... 2.7. Fundamentals of the theory of similarity .............................................. 2.7.1. Similarity of physical phenomena ............................... 2.7.2. Similarity theorems.................................................... 2.7.3 . Similarity equations .................................................. 2.7.4. Modeling Rules .................................. 2.8. Convective heat transfer in a single-phase medium..... 2.8.1. Flow regimes of liquids and gases ............... 5 2.8.2. Boundary layer.............................................. 2.8.3. Heat transfer in a laminar boundary layer on a flat surface .............................................................. ....... 2.8.4. Heat transfer in a turbulent boundary layer on a flat surface .............................................................. ... 2.8.5. Heat transfer during forced convection in pipes and channels .................................................. 2.8.6. Heat transfer in a stabilized flow section. Integral Lyon................................... 2.8.7. Heat transfer in laminar flow in pipes ……………………………………………………….. 2.8.8. Heat transfer at turbulent flow in pipes... 2.8.9. Heat transfer in the flow around pipes and tube bundles .............................................................. ............................... 2.8.10. Heat transfer with free convection ........ 2.8.11. Heat transfer in fluidized media ....... 2.9. Convective heat transfer during boiling and condensation .............................................................. ............................... 2.9.1. Boiling heat exchange ......................................... 2.9.2. Condensing Heat Transfer .......................................... 2.9.3. Heat pipes ................................................................ 2.10. Heat exchange by radiation .............................................. 2.10.1. Physical bases of radiation.............................. 2.10.2. Calculation of heat transfer by radiation ............... 2.10.3. Solar radiation .................................................. 2.10.4. Complex heat transfer ........................................ 2.11. Heat exchangers ................................................................ ......... 2.11.1 Classification and purpose .......... 2.11.2. Fundamentals of thermal calculation .............................. 2.11.3. Efficiency of heat exchangers. Actual heat transfer coefficients .............................................. 2.11.4. Hydraulic calculation of heat exchangers ... References .................................................. ................... 6 FOREWORD “Technical thermodynamics and heat transfer” is one of the main courses given to bachelors in the direction “Land transport systems”. It is saturated with information and compressed in terms of study time to 1–2 semesters, so most fundamental textbooks will not help students much: they are too detailed, not focused on the range of tasks associated with transport systems, and, finally, are simply designed for much larger courses. For transport engineers, the main thing is to understand the subject and basic ideas of thermodynamics and heat transfer, to master the established terminology of these sciences. It is absolutely necessary to remember 10-15 basic formulas(such as, for example, the ideal gas equation of state, the formula for calculating heat transfer through a multilayer plate, the Stefan-Boltzmann law, etc.). The rest of the information, for all its importance, you just need to understand, present physically, connect with examples from various fields of life and technology. Therefore, the authors tried to pay the main attention to the physical side of the phenomena under consideration, and left a worthy, but modest place to the mathematical apparatus. The authors express their deep gratitude to the reviewers - the department "Heat engineering and thermal power plants" of the St. Petersburg State University of Railways represented by Dr. Sciences prof. I. G. Kiseleva and Ph.D. tech. Sciences Assoc. V. I. Krylov, as well as Dr. tech. Sciences prof. B. S. Fokin for valuable remarks, which made it possible to improve the original text. Special thanks - Cand. tech. Sciences G. G. Gavre for great help in preparing the manuscript; she came up with the idea to compare N, ε - a method for calculating heat exchangers with a traditional calculation scheme. And, of course, the help in the design of the book of the employees of the department was very valuable. Theoretical basis Heat Engineering” of St. Petersburg State Technical University 7 E. O. Vvedenskaya, R. M. Groznoy, graduate students Yu. V. Burtseva and E. M. Rotinyan. S. Sapozhnikov E. Kitanin 8 1. TECHNICAL THERMODYNAMICS 1.1. SUBJECT AND METHOD OF TECHNICAL THERMODYNAMICS Thermodynamics - the science of energy transformations - is fundamental for a power engineering engineer. The birth of thermodynamics coincides in time with the appearance of the first steam engines. In 1824, the French engineer S. Carnot considered energy interaction water and steam with various parts of the engine and with the environment, he owns the first efficiency rating steam engine. Since then, processes in power machines, aggregate transformations of substances, physicochemical, plasma and other processes have become the subject of study of thermodynamics. These studies are based on thermodynamic method: the object of study can be any bodies included in the so-called thermodynamic system. This system should be: sufficiently extensive and complex so that statistical regularities are observed in it (the movement of molecules of a substance in a certain volume, heating and cooling of particles of a solid material in a backfill, etc.); closed, i.e., have limits in all spatial directions and consist of a finite number of particles. There are no other restrictions for the thermodynamic system. Objects material world, not included in the thermodynamic system, is called the environment. Returning to the works of S. Carnot, we note that water and the steam obtained from it are a thermodynamic system. By tracing the energy interaction of water and steam with the surrounding bodies, it is possible to evaluate the efficiency of converting the heat supplied to the machine into work. But modern power machines do not always use water to convert energy. We agree to call any medium that is used to convert energy a working body. 9 Thus, the subject of technical thermodynamics is the laws of energy conversion in the processes of interaction of working bodies with elements of power machines and with the environment, analysis of the perfection of power machines, as well as the study of the properties of working bodies and their changes in the processes of interaction. Unlike statistical physics, which studies the physical model of a system with clear patterns of interaction between microparticles, thermodynamics is not connected in its conclusions with any structure of the body and with certain forms of connection between the elements of this structure. Thermodynamics uses the laws universal character, i.e., valid for all bodies, regardless of their structure. These laws form the basis of all thermodynamic reasoning and are called the principles of thermodynamics. The first principle expresses the law of conservation of energy - the universal law of nature. It determines the balance of energy in interactions within the thermodynamic system, as well as between the thermodynamic system and the environment. The second law determines the direction of energy transformations and significantly expands the possibilities of the thermodynamic method. Both principles are of an experimental nature and are applicable to all thermodynamic systems. Based on these two principles, presented in mathematical form, it is possible to express the parameters of energy exchange at various interactions, establish connections between the properties of substances, etc. However, in order to bring the results to specific numbers, the "internal resources" of thermodynamics alone are not enough. It is necessary to use experimental or theoretical results that take into account the nature of the working fluid in a real thermodynamic system. If, for example, one uses experimental data on the density of a substance, then with the help of thermodynamic analysis one can calculate its heat capacity, etc. 10 Thus, thermodynamic studies are based on the fundamental laws of nature. At the same time, engineering calculations in thermodynamics are impossible without the use of experimental data or the results of theoretical studies. physical properties working bodies. 1.2. BASIC CONCEPTS OF THERMODYNAMICS 1.2.1. Thermodynamic system and thermodynamic parameters We have called a thermodynamic system any body or system of bodies interacting with each other and (or) with the environment (such a system may, in particular, include the working bodies of power machines). The definition does not specify what exactly is considered a thermodynamic system, and what is considered an environment. It is possible, for example, to consider the working fluid itself as a thermodynamic system, and to consider “everything else” as the environment; it is possible to single out only a part of the body, and consider the rest of the body and all other bodies as the environment. It is possible, on the contrary, to expand the thermodynamic system - to include in it, besides the first body, several others, and consider all other bodies as the environment. Such an expansion or narrowing of the circle of objects that make up a thermodynamic system allows us to find out important features working bodies and energy interactions between them. It is known that the same substance can be in a liquid, gaseous or solid state. In this case, naturally, the properties of this substance, this thermodynamic system, will also be different, for example, density, coefficient of volumetric expansion, magnetic permeability, sound speed, etc. All these, as well as other quantities characterizing the state of a thermodynamic system, are called thermodynamic parameters states. There are a lot of them; traditionally allocate

Definition 1

Thermodynamics is considered a branch of physics that studies the mutual transformations of various types of energy, interconnected with its transition to the format of heat and work.

The main thing practical value thermodynamics lies in the possibility of calculating the thermal effects of the reaction, the preliminary indication of the probability or improbability of the reaction, and also the conditions for its passage.

Definition 2

Heat transfer is a physical process whose essence will be the transfer of thermal energy. The exchange is made between two bodies or their system. A prerequisite in this case, the transfer of heat from strongly heated bodies will become less heated.

The essence of thermodynamics in physics

Thermodynamics, being integral part heat engineering, is engaged in the study of the laws of energy transformations in various chemical and physical processes, which are produced in macroscopic systems and are accompanied by thermal effects.

The following types of energy are known:

• thermal;
• electric;
• chemical;
• magnetic, etc.

The main tasks of research in physics are the thermodynamics of biosystems and technical thermodynamics.

Technical thermodynamics, in turn, deals with the study of the patterns of mutual transformations of mechanical and thermal energies (in combination with the theory of heat transfer) and therefore acts as a theoretical foundation for heat engineering, the absence of which would make it impossible to calculate and design a heat engine.

The method involved in thermodynamics is phenomenological. The phenomenon is considered here as a whole. The relationship between the macroscopic parameters that determine the behavior of the system is established by the two principles of thermodynamics.

Also in thermodynamics there is such important concept, as a thermodynamic system, which should be considered in more detail, for a better understanding of the processes of thermodynamics.

Thermodynamic system

Figure 1. Thermodynamic system. Author24 - online exchange of student papers

Remark 1

A thermodynamic system is a complex of material bodies that are in a state of mechanical and thermal interactions between themselves and also with external bodies that surround the system ( we are talking about the external environment).

The choice of the system in this case will be arbitrary and dictated by the conditions of the problem proposed for solving. The bodies outside the system are called the environment. The system itself, at the same time, is separated from the environment by means of a control surface (special shell).

Yes, for the simplest system(for example, gas), which is enclosed under the piston in the cylinder, the surrounding air will act as an external environment, and the control surfaces will be the walls of the cylinder and the piston itself.

The interaction of mechanical and thermal types of a thermodynamic system is carried out at the expense of control surfaces. In the process of mechanical interaction, work will be performed either by the system itself or on it.

AT general case the system can be affected by magnetic, electrical and other forces, under whose influence it will perform work. These types of work can also be taken into account in the framework of thermodynamics.

Thermal interaction will be within the framework of the transfer of heat between the individual bodies of the system, as well as between the system and the environment. In the most common examples, heat can be supplied to the gas by the walls of the cylinder.

In the most general case, the system can exchange with the environment and matter (a type of mass transfer interaction). Such a system is called an open system. Steam or gas flows in turbines and pipelines are examples open systems. If the substance does not pass through the boundaries of the system, it will be called closed.

A thermodynamic system that is not able to exchange heat with the environment is considered to be thermally isolated (or adiabatic). An example of such a system can be a gas inside a vessel, whose walls are covered with ideal thermal insulation, which excludes the possibility of heat exchange between the gas contained in the vessel and the surrounding bodies (adiabatic insulating shell).

A closed (isolated) system is a system that does not exchange with the environment either through energy or through matter.

The simplest thermodynamic system can be a working fluid capable of carrying out the mutual transformation of work and heat. In an internal combustion engine, for example, the working fluid will be a combustible mixture that is prepared in a carburetor (consisting of gasoline vapors and air).

Features of the heat transfer process

Heat transfer is considered to be the very kind of phenomenon whose implementation is possible under conditions direct contact, and in the presence of separating partitions (where used bodies, as well as environmental materials, can become barriers).

The origin of the heat transfer process becomes probable in those cases when a state of thermal equilibrium is not observed. In other words, when one of the objects has a higher or lower temperature than the other. Only in such cases is the transfer of thermal energy carried out.

Its completion will occur when the system itself comes to a state of thermal (or thermodynamic) equilibrium. The process will be carried out spontaneously (as evidenced by the second law of thermodynamics).

Heat transfer methods and thermal conductivity

The heat transfer process can be divided into the following three ways, which are inherent in the main nature (and within them certain subcategories are distinguished with their own characteristic features):

• thermal conductivity (the property of a certain material body to carry out the transfer of energy from a hotter one to a colder one);
• convection (a kind of heat transfer process, during which particles of substances will mix with each other, a similar effect is observed in liquids and gases);
• radiation ( electromagnetic radiation, whose occurrence becomes possible due to the internal energy of the body. It has a continuous spectrum, the intensity and location of the maximum of which are dependent on body temperature).

The basis of such a phenomenon as thermal conductivity is the principle of the chaotic movement of the movement of molecules (which is the so-called Brownian motion). The higher the temperature of the body becomes, the more actively the molecules begin to move in it (due to the possession of greater kinetic energy).

During the process of heat conduction Active participation accept atoms, electrons, molecules. It is carried out in bodies, whose different parts temperature is not the same.

In the case of the ability of a substance to conduct heat, we can talk about the presence quantitative characteristics. AT this case this role is played by the thermal conductivity coefficient. Such a characteristic demonstrates the amount of heat that will pass through unit indicators of area and length per unit of time. In this case, a change in body temperature by exactly 1 K is observed.

Thermal conductivity- this is a type of heat transfer in which there is a direct transfer of energy from particles (molecules, atoms) of a more heated part of the body to particles of its less heated part.

Consider a series of experiments with heating a solid, liquid and gas.

Radiant heat transfer.

Radiant heat transfer- this is heat transfer, in which energy is transferred by various beams.

It can be Sun rays, as well as the rays emitted by heated bodies around us.

So, for example, sitting near a fire, we feel how heat is transferred from the fire to our body. However, the cause of such heat transfer cannot be either thermal conductivity (which is very small for the air between the flame and the body), or convection (since convection flows are always directed upwards). Here, the third type of heat transfer takes place - radiant heat transfer.

Take a small, smoked on one side, flask.

Insert a glass tube bent at a right angle through the cork into it. In this tube, which has a narrow channel, we introduce a colored liquid. Having fixed the scale on the tube, we get the device - thermoscope. This device allows you to detect even a slight heating of the air in a smoked flask.

If a piece of metal heated to high temperature, then the liquid column will move to the right. Obviously, the air in the flask heated up and expanded. The rapid heating of air in a thermoscope can only be explained by the transfer of energy from a heated body to it. As in the case of a fire, the energy here was transferred not by thermal conductivity and not convective heat transfer. The energy in this case was transferred with the help of invisible rays emitted by a heated body. These rays are called thermal radiation.

Radiant heat transfer can take place in a complete vacuum. This distinguishes it from other types of heat transfer.

All bodies radiate energy: both strongly heated and weakly, for example, the human body, a stove, an electric light bulb. But the higher the temperature of the body, the stronger its thermal radiation. The radiated energy, having reached other bodies, is partially absorbed by them, and partially reflected. When absorbed, the energy of thermal radiation is converted into the internal energy of the bodies, and they heat up.

Light and dark surfaces absorb energy differently. So, if in an experiment with a thermoscope, turn the flask to a heated body, first smoked, and then bright side, then the liquid column in the first case will move to greater distance than in the second (see the figure above). It follows from this that bodies with a dark surface absorb energy better (and therefore heat up more) than bodies with a light or specular surface.

Bodies with a dark surface not only absorb better, but also radiate energy better.

The ability to absorb radiation energy in different ways finds wide application in tech. For example, Balloons and the wings of airplanes are often painted silver so that they are less heated by the sun's rays.

If you need to use solar energy(for example, to heat some appliances installed on artificial satellites), then these devices are painted in a dark color.