Molecular physics

Basic concepts
The amount of a substance is measured in moles (n).
n is the number of moles
1 mole is equal to the amount of substance of a system containing as many particles as there are atoms in 0.012 kg of carbon. The number of molecules in one mole of a substance is numerically equal to the Avogadro constant N A .

NA \u003d 6.022 1023 1 / mol.

1 mole of any gas under normal conditions occupies a volume
V=2.24 10-2 m3.
M - molar mass (mass of a mole) - a value equal to the ratio of the mass of a substance m to the amount of substance n:

m o - the mass of one molecule, m - the mass of the taken amount of substance

is the number of molecules in a given volume.

Ideal gas. Basic equation of molecular-kinetic theory.

The basic equation of the molecular kinetic theory of gas is the equation:

,

P is the pressure of the gas on the walls of the vessel,
n is the concentration of molecules,

Root mean square velocity of molecules.

The gas pressure p can be determined by the formulas:

,

The average kinetic energy of the translational motion of molecules,

T is the absolute temperature,
K=1.38 10-23 J/K - Boltzmann's constant.

,

Where \u003d 8.31 J / mol × K, R is the universal gas constant
Т=373+t o С, t o С – temperature in Celsius.
For example, t=27 o C, T=273+27=300 K.
mixture of gases
If the volume V contains not one gas, but a mixture of gases, then the gas pressure p is determined by Dalton's law: the mixture of gases exerts a pressure on the walls equal to the sum of the pressures of each of the gases taken separately:

- pressure exerted on the walls by the 1st gas p1, the second p2, etc.

N is the number of moles of the mixture,

Clapeyron-Mendeleev equation, isoprocesses.

The state of an ideal gas is characterized by pressure p, volume V, temperature T.
[p]=Pascal (Pa), [V]=m3, [T]=Kelvin (K).
The equation of state for an ideal gas is:

, for one mole of gas const=R is the universal gas constant.

- the Mendeleev-Clapeyron equation.

If the mass m is constant, then the various processes occurring in gases can be described by laws arising from the Mendeleev-Clapeyron equation.

1. If m=const, T=const is an isothermal process.

Process equation:

Schedule of process:

2. If m=const, V=const is an isochoric process.

Process equation: .

Schedule of process:

3. If m=const, p=const is an isobaric process.

Process equation:

Schedule of process:

4. Adiabatic process - a process that proceeds without heat exchange with the environment. This is a very fast process of expanding or compressing a gas.

Saturated steam, humidity.

Absolute humidity is the pressure p of the water vapor contained in the air at a given temperature.
Relative humidity is the ratio of the pressure p of water vapor contained in the air at a given temperature to the pressure p0 of saturated water vapor at the same temperature:

p o - tabular value.
The dew point is the temperature at which water vapor in the air becomes saturated.

Thermodynamics

Thermodynamics studies the most general patterns of energy conversion, but does not consider the molecular structure of matter.
Any physical system consisting of a huge number of particles - atoms, molecules, ions and electrons, which perform random thermal motion and exchange energy when interacting with each other, is called a thermodynamic system. Such systems are gases, liquids and solids.

Internal energy.

A thermodynamic system has internal energy U. When a thermodynamic system passes from one state to another, its internal energy changes.
The change in the internal energy of an ideal gas is equal to the change in the kinetic energy of the thermal motion of its particles.
Change in internal energy D U during the transition of the system from one state to another does not depend on the process by which the transition was made.
For a monatomic gas:

- temperature difference at the end and beginning of the process.

The change in the internal energy of the system can occur due to two different processes: the performance of work A / on the system and the transfer of heat Q to it.

Work in thermodynamics.

The work depends on the process by which the transition of the system from one state to another was made. With isobaric process (p=const, m=const): ,

The difference between the volumes at the end and at the beginning of the process.

The work done on the system by external forces and the work done by the system against external forces are equal in magnitude and opposite in sign: .

First law of thermodynamics.

The law of conservation of energy in thermodynamics is called the first law of thermodynamics.
First law of thermodynamics:

A / - work done on the system by external forces,
A is the work done by the system

The difference between the internal energies of the final and initial states.

First law of thermodynamics.

The first law of thermodynamics is formulated as follows: The amount of heat (Q) communicated to the system goes to increase the internal energy of the system and to perform work on external bodies by the system.
Let us apply the first law of thermodynamics to various isoprocesses.
a) Isothermal process (T=const, m=const).
Since then , i.e. there is no change in internal energy, so:

- all the heat communicated to the system is expended on the work done by the system against external forces.

B) Isochoric process (V=const, m=const).
Since the volume does not change, the work of the system is 0 (A=0) and - all the heat communicated to the system is spent on changing the internal energy.
c) Isobaric process (p=const, m=const).

d) Adiabatic process (m=const, Q=0).

Work is done by the system by reducing the internal energy.

heat engine efficiency.

A heat engine is a periodically operating engine that performs work due to the amount of heat received from the outside. The heat engine must consist of three parts: 1) the working fluid - gas (or steam), with the expansion of which work is done; 2) a heater - a body in which, due to heat exchange, the working fluid receives the amount of heat Q1; 3) refrigerator (environment), taking away the amount of heat Q2 from the gas.
The heater periodically raises the gas temperature to T1, and the refrigerator lowers it to T2.
The ratio of the useful work A performed by the machine to the amount of heat received from the heater is called the efficiency of the machine h:

Efficiency of an ideal heat engine:

Т1 – heater temperature,
T2 is the temperature of the refrigerator.

- for an ideal heat engine.

TESTS

Answers and Solutions

1. A mole of any substance contains the same number of molecules, equal to Avogadro's number:
2. Let's write the Mendeleev-Clapeyron equation for two states with p=const and m=const, because the process of transition from one state to another is isobaric: (1) (2) Divide (1) by (2), we get: - equation of isobatic process.
3. 
4. To determine the temperature, we apply the Mendeleev-Clapeyron equation. From the graph: for state A - , for state B - . , from the first equation -, then - .
5. mixture pressure . We write the equation of the isothermal process:, - gas pressure after expansion.
6. To solve the problem, we write down the first law of thermodynamics. For isobaric process:. For isochoric process:. Because Cp is the specific heat at constant pressure, CV is the heat capacity at constant volume. Because , , i.e.
7. - The first law of thermodynamics. By the condition Q=A, i.e. delta U\u003d 0, which means that the process proceeds at a constant temperature (the process is isothermal).
8. A 1 - numerically equal to the area of ​​\u200b\u200bthe figure A 1 B,. Because less than the other areas, then the work A 1 is minimal.

An online course can be certified.

The course deals with the key concepts and methods of thermodynamics and molecular physics as part of the general physics course given to students of the Moscow Institute of Physics and Technology. First of all, the basic thermodynamic quantities, concepts and postulates are introduced. The main thermodynamic relations are considered. Separate lectures are devoted to the theory of phase transitions, the van der Waals gas model, and surface phenomena. The basic concepts of statistical physics are given: micro- and macro-state of the system, partition function, distribution functions, etc. The distributions of Maxwell, Boltzmann, Gibss are discussed. Elements of the theory of heat capacity of gases are presented. Expressions are derived for fluctuations of the main thermodynamic quantities. The description of molecular processes in gases is given: processes of transfer, diffusion and thermal conductivity.

About the course

The online course contains a discussion of basic physics issues, analysis of problems, demonstrations of physical experiments, without which a deep understanding of general physics is impossible. To successfully master the online course, it is desirable for the student to know the course of general physics: "Mechanics" and to master the basics of mathematical analysis, to know the basics of linear algebra and probability theory.

Format

The online course contains theoretical material, demonstrations of key thermodynamic experiments necessary for a correct understanding of phenomena, analysis of solutions to typical problems, exercises and tasks for self-solving

The seventh, thirteenth and eighteenth weeks contain control tasks for checking.

Course program

Week 1
Basic concepts of molecular physics and thermodynamics: the subject of research, its characteristic features. Problems of molecular physics. Equations of state. The pressure of an ideal gas as a function of the kinetic energy of the molecules. Relationship between the temperature of an ideal gas and the kinetic energy of its molecules. Laws of ideal gases. Equations of state for an ideal gas. Quasi-static, reversible and irreversible thermodynamic processes. Zero start of thermodynamics. Work, heat, internal energy. First law of thermodynamics. Heat capacity. Heat capacity of ideal gases at constant volume and constant pressure, Mayer's equation. Adiabatic and polytropic processes. Polytropic equation for an ideal gas. Adiabatic and polytropic processes. Independence of the internal energy of an ideal gas from volume.

Week 2
The second law of thermodynamics. Formulations of the second beginning. Thermal machine. Determination of the efficiency of a heat engine. Carnot cycle. Carnot's theorem. Clausius inequality. The maximum efficiency of the Carnot cycle compared to other thermodynamic cycles. Refrigeration machine. Chiller efficiency. Heat pump. The efficiency of a heat pump operating on the Carnot cycle. The relationship between the efficiency factors of a heat pump and a chiller.

Week 3
Thermodynamic definition of entropy. Entropy increase law. Entropy of an ideal gas. Entropy in reversible and irreversible processes. Adiabatic expansion of an ideal gas into a vacuum. The combined equation of the first and second laws of thermodynamics. Third law of thermodynamics. Change in entropy and heat capacity as the temperature approaches absolute zero.

Week 4
Thermodynamic functions. Properties of thermodynamic functions. Maximum and minimum work. Transformations of thermodynamic functions. Maxwell's relations. Dependence of internal energy on volume. Dependence of heat capacity on volume. The ratio between CP and CV. Thermophysical properties of solids. Thermodynamics of deformation of solids. Temperature change during adiabatic stretching of an elastic rod. Thermal expansion as a consequence of the anharmonicity of oscillations in the lattice. Coefficient of linear expansion of the rod.

Week 5
Conditions of thermodynamic equilibrium. Phase transformations. Phase transitions of the first and second kind. chemical potential. Phase equilibrium condition. Curve of phase equilibrium. Clausius–Clapeyron equation. Diagram of the state of a two-phase system "liquid-steam". Dependence of heat of phase transition on temperature. Critical point. Triple point. State diagram "ice-water-steam". surface phenomena. Surface thermodynamics. Free energy of the surface. edge angles. Wetting and non-wetting. Laplace formula. Dependence of vapor pressure on liquid surface curvature. Boiling. The role of nuclei in the formation of a new phase.

Week 6
Van der Waals gas as a model of a real gas. Van der Waals gas isotherms. metastable states. superheated liquid and supercooled vapor. Maxwell's rule and the lever rule. Critical parameters and reduced van der Waals gas equation of state. Internal energy of van der Waals gas. Van der Waals gas adiabatic equation. Entropy of the van der Waals gas. The speed of sound in gases. The rate at which gas flows out of an orifice. Joule-Thomson effect. Adiabatic expansion, throttling. Getting low temperatures.

Week 7
Checking

Week 8
Dynamic and statistical regularities. Macroscopic and microscopic states. phase space. Elements of the theory of probability. normalization condition. Mean values ​​and dispersion. Binomial distribution law. Poisson distribution. Gaussian distribution.

Week 9
Maxwell distributions. Distribution of particles by velocity components and absolute values ​​of velocity. Most probable, mean and rms speeds. Maxwell's energy distributions. The average number of impacts of molecules colliding per unit time with a single area. Average energy of molecules escaping into vacuum through a small hole in a vessel.

Week 10
Boltzmann distribution in a uniform force field. barometric formula. Micro and macro states. Statistical weight of a macrostate. Statistical definition of entropy. Entropy in mixing gases. Gibbs paradox. Representation of the Gibbs distribution. Partition function and its use to find internal energy. Statistical temperature.

Week 11
fluctuations. Average values ​​of energy and dispersion (root-mean-square fluctuation) of particle energy. Fluctuations of thermodynamic quantities. Temperature fluctuation in a fixed volume. Volume fluctuation in isothermal and adiabatic processes. Fluctuations of additive physical quantities. Dependence of fluctuations on the number of particles constituting the system.

Week 12
Heat capacity. Classical theory of heat capacities. The law of uniform distribution of thermal motion energy over degrees of freedom. Heat capacity of crystals (Dulong–Petit law). Elements of the quantum theory of heat capacities. Characteristic temperatures. Dependence of heat capacity on temperature.

Week 13
Collisions. Effective gas-kinetic cross section. Free path length. Distribution of molecules over free path lengths. The number of collisions between molecules. Transport phenomena: viscosity, thermal conductivity and diffusion. Fick and Fourier laws. Coefficients of viscosity, thermal conductivity and diffusion in gases.

Week 14
Brownian motion. Mobility. Einstein-Smoluchowski law. Relationship between particle mobility and diffusion coefficient. Transport phenomena in rarefied gases. Knudsen effect. Effusion. The flow of a rarefied gas through a straight pipe.

Week 15
Checking

Learning Outcomes

As a result of studying the discipline "Thermodynamics", the student must:

• Know:
  • basic concepts used in molecular physics, thermodynamics;
  • the meaning of physical quantities used in molecular physics, thermodynamics;
  • equations of state for ideal gas and van der Waals gas;
  • distributions of Boltzmann and Maxwell, the law of uniform distribution of energy over degrees of freedom;
  • zero, first, second and third laws of thermodynamics, Clausius's inequality, entropy increase law;
  • conditions of stable thermodynamic equilibrium;
  • the Clausius-Clapeyron equation;
  • Laplace formula;
  • equations describing transfer processes (diffusion, viscosity, thermal conductivity);
• Be able to:
  • use the basic provisions of the molecular-kinetic theory of gases to solve problems;
  • use the laws of molecular physics and thermodynamics in describing the equilibrium states of thermal processes and transfer processes;
• Own:
  • methods for calculating the parameters of the state of matter;
  • methods for calculating work, the amount of heat and internal energy;

Formed competencies

• the ability to analyze scientific problems and physical processes, to use in practice the fundamental knowledge gained in the field of natural sciences (OK-1)
• the ability to master new issues, terminology, methodology and master scientific knowledge, self-study skills (OK-2)
• the ability to apply in their professional activities the knowledge gained in the field of physical and mathematical disciplines (PC-1)
• the ability to understand the essence of the tasks set in the course of professional activity, and to use the appropriate physical and mathematical apparatus to describe and solve them (PC-3)
• the ability to use knowledge in the field of physical and mathematical disciplines for the further development of disciplines in accordance with the training profile (PC-4)
• ability to apply the theory and methods of mathematics, physics and computer science to build qualitative and quantitative models (PC-8)

Molecular physics and thermodynamics are essentially two different in their approaches, but closely related sciences that deal with the same thing - the study of the macroscopic properties of physical systems, but with completely different methods.

Molecular physics Molecular physics or molecular kinetic theory is based on certain ideas about the structure of matter. – To establish the laws of behavior of macroscopic systems consisting of a huge number of particles, various models of matter are used in molecular physics, for example, ideal gas models. Molecular physics is a statistical theory, physics, that is, a theory that considers the behavior of systems consisting of a huge number of particles (atoms, molecules), based on probabilistic models. It seeks, on the basis of a statistical approach, to establish a connection between the experimentally measured macroscopic quantities (pressure, volume, temperature, etc.) and the values ​​of the microscopic characteristics of the particles included in the microscopic characteristics of the system (mass, momentum, energy, etc.) .

Thermodynamics In contrast to the molecular-kinetic theory, thermodynamics, when studying the thermodynamic properties of macroscopic systems, does not rely on any ideas about the molecular structure of a substance. Thermodynamics is a phenomenological science. - It draws conclusions about the properties of matter on the basis of laws established by experience, such as the law of conservation of energy. Thermodynamics operates only with macroscopic quantities (pressure, temperature, volume, etc.), which are introduced on the basis of a physical experiment.

Both approaches - thermodynamic and statistical - do not contradict, but complement each other. Only the combined use of thermodynamics and molecular kinetic theory can give the most complete picture of the properties of systems consisting of a large number of particles.

Molecular physics Molecular-kinetic theory is the study of the structure and properties of matter based on the concept of the existence of atoms and molecules as the smallest particles of chemical substances.

Molecular-Kinetic Theory Main provisions of MKT 1. All substances - liquid, solid and gaseous - are formed from the smallest particles - molecules, which themselves consist of atoms ("elementary molecules"). Molecules of a chemical substance can be simple and complex, i.e., consist of one or more atoms. Molecules and atoms are electrically neutral particles. Under certain conditions, molecules and atoms can acquire an additional electrical charge and turn into positive or negative ions. 2. Atoms and molecules are in continuous chaotic motion, which is called thermal motion 3. Particles interact with each other by forces that are electrical in nature. The gravitational interaction between particles is negligible.

Molecular-kinetic theory The most striking experimental confirmation of the ideas of the molecular-kinetic theory about the random motion of atoms and molecules is Brownian motion. Brownian motion is the thermal motion of the smallest microscopic particles suspended in a liquid or gas. It was discovered by the English botanist R. Brown in 1827. Brownian particles move under the influence of random collisions of molecules. Due to the chaotic thermal motion of the molecules, these impacts never cancel each other out. As a result, the speed of a Brownian particle randomly changes in magnitude and direction, and its trajectory is a complex zigzag curve (Fig.). The theory of Brownian motion was created by A. Einstein in 1905. Einstein's theory was experimentally confirmed in the experiments of the French physicist J. Perrin, carried out in 1908–1911.

Molecular-Kinetic Theory The constant chaotic motion of the molecules of a substance also manifests itself in another easily observable phenomenon - diffusion. Diffusion is the phenomenon of penetration of two or more adjoining substances of a friend. - The process proceeds most rapidly in a gas if it is a gas that is heterogeneous in composition. Diffusion leads to the formation of a homogeneous mixture, regardless of the density of the components. So, if in two parts of the vessel, separated by a partition, there are oxygen O 2 and hydrogen H 2, then after the removal of the partition, the process of interpenetration of the other's gases begins, leading to the formation of an explosive mixture - explosive gas. This process also occurs when a light gas (hydrogen) is in the upper half of the vessel, and a heavier one (oxygen) is in the lower half.

Molecular Kinetic Theory - Similar processes in liquids proceed much more slowly. The interpenetration of two liquids of dissimilar liquids into each other, the dissolution of solids in liquids (for example, sugar in water) and the formation of homogeneous solutions are examples of diffusion processes in liquids. In real conditions, diffusion in liquids and gases is masked by faster mixing processes, for example, due to the occurrence of convection currents.

Molecular Kinetic Theory - The slowest diffusion process occurs in solids. However, experiments show that when solids come into contact of well-cleaned surfaces of two metals, after a long time, atoms of another metal are found in each of them. Diffusion and Brownian motion - Diffusion and Brownian motion are related phenomena. The interpenetration of contacting substances of a friend and the random movement of the smallest particles suspended in a liquid or gas occur due to the chaotic thermal movement of molecules.

Molecular Kinetic Theory The forces acting between two molecules The forces acting between two molecules depend on the distance between them. Molecules are complex spatial structures containing both positive and negative charges. If the distance between the molecules is large enough, then the forces of intermolecular attraction predominate. At short distances, repulsive forces predominate.

Molecular Kinetic Theory At a certain distance r = r 0 the interaction force vanishes. This distance can be conditionally taken as the diameter of the molecule. The potential energy of interaction at r = r 0 is minimal. To remove two molecules that are at a distance r 0 from each other, you need to give them additional energy E 0. The value of E 0 is called the depth of the potential well or the binding energy. Molecules are extremely small. Simple monatomic molecules are about 10–10 m in size. Complex polyatomic molecules can be hundreds or thousands of times larger.

Molecular-Kinetic Theory The kinetic energy of thermal motion increases with increasing temperature At low temperatures, the average kinetic energy of a molecule can be less than the depth of the potential well E 0. In this case, the molecules condense into a liquid or solid; in this case, the average distance between the molecules will be approximately equal to r 0. As the temperature rises, the average kinetic energy of the molecule becomes greater than E 0, the molecules fly apart, and a gaseous substance is formed

Molecular-Kinetic Theory Aggregate states of matter In solids, molecules perform random vibrations around fixed centers (equilibrium positions) in solids. These centers can be located in space in an irregular manner (amorphous bodies) or form ordered bulk structures (crystalline bodies). Therefore, solids retain both shape and volume.

Molecular-Kinetic Theory Aggregate states of matter In liquids, molecules have much greater freedom for thermal motion. They are not tied to specific centers and can move throughout the volume. This explains the fluidity of liquids. Closely spaced liquid molecules can also form ordered structures containing several molecules. This phenomenon is called short-range order, in contrast to the long-range order characteristic of crystalline bodies. Therefore, liquids do not retain their shape, but retain their volume.

Molecular-kinetic theory Aggregate states of matter In gases, the distances between molecules are usually much greater than their sizes. The forces of interaction between molecules at such large distances are small, and each molecule moves along a straight line until the next collision with another molecule or with the vessel wall. - The average distance between air molecules under normal conditions is about 10–8 m, i.e., ten times greater than the size of the molecules. The weak interaction between molecules explains the ability of gases to expand and fill the entire volume of the vessel. In the limit, when the interaction tends to zero, we come to the concept of an ideal gas. Therefore, gases do not retain either shape or volume.

Molecular-kinetic theory Amount of substance In molecular-kinetic theory, the amount of substance is considered to be proportional to the number of substance particles. The unit of quantity of a substance is called a mole (mole). A mole is the amount of a substance that contains as many particles (molecules) as there are atoms 0.012 kg of carbon 12 C. (A carbon molecule consists of one atom) Thus, one mole of any substance contains the same number of particles (molecules ). This number is called Avogadro's constant NA: NA = 6.02 1023 mol–1. Avogadro's constant is one of the most important constants in molecular kinetic theory.

Molecular-kinetic theory The amount of a substance ν is defined as the ratio of the number N of particles (molecules) of a substance to the Avogadro constant NA: The mass of one mole of a substance is usually called the molar mass M The molar mass is equal to the product of the mass m 0 of one molecule of a given substance by the Avogadro constant: M = NA · m 0 Molar mass is expressed in kilograms per mole (kg/mol). For substances whose molecules consist of one atom, the term atomic mass is often used. 1/12 of the mass of an atom of the carbon isotope 12 C (with a mass number of 12) is taken as a unit of mass of atoms and molecules. This unit is called the atomic mass unit (a.m.u.): 1 a.m. e.m. = 1.66 10–27 kg. This value almost coincides with the mass of a proton or neutron. The ratio of the mass of an atom or molecule of a given substance to 1/12 of the mass of a carbon atom 12 C is called the relative mass.

Molecular Kinetic Theory The simplest model considered by molecular kinetic theory is the ideal gas model: 1. In the ideal gas kinetic model, molecules 1. are considered as perfectly elastic balls interacting with each other and with the walls only during elastic collisions. 2. The total volume of all molecules is assumed to be small compared 2. with the volume of the vessel containing the gas. The ideal gas model describes the behavior of real gases quite well in a wide range of pressures and temperatures. The task of the molecular kinetic theory is to establish a relationship between microscopic (mass, microscopic speed, kinetic energy of molecules) and macroscopic parameters (pressure, volume, macroscopic temperature parameters).

Molecular Kinetic Theory As a result of each collision between molecules and molecules with walls, the velocities of molecules can change in magnitude and in direction; on the time intervals between successive collisions, the molecules move uniformly and rectilinearly. In the ideal gas model, it is assumed that all collisions occur according to the laws of elastic impact, i.e., they obey the laws of Newtonian mechanics. Using the ideal gas model, we calculate the gas pressure on the vessel wall. In the process of interaction of a molecule with the vessel wall, forces arise between them that obey Newton's third law. As a result, the projection υx of the velocity of the molecule, perpendicular to the wall, changes its sign to the opposite, while the projection υy of the velocity, parallel to the wall, remains unchanged (Fig.).

Molecular Kinetic Theory The formula for the average pressure of a gas on the wall of a vessel is written as This equation establishes the relationship between the pressure p of an ideal gas, the mass of the molecule m 0, the concentration of molecules n, the average value of the square of the velocity and the average kinetic energy of the translational motion of the molecules. This is the basic equation of the molecular kinetic theory of gases. Thus, the pressure of a gas is equal to two thirds of the average kinetic energy of the translational motion of molecules contained in a unit volume.

Molecular-Kinetic Theory The basic equation of the MCT of gases includes the product of the concentration of molecules n and the average kinetic energy of translational motion. In this case, the pressure is proportional to the average kinetic energy. Questions arise: how can one experimentally change the average kinetic energy of the motion of molecules in a vessel of constant volume? What physical quantity must be changed in order to change the average kinetic energy? Experience shows that temperature is such a quantity.

Molecular-Kinetic Theory Temperature The concept of temperature is closely related to the concept of thermal equilibrium. Bodies in contact with each other can exchange energy. The energy transferred from one body to another during thermal contact is called the amount of heat Q. Thermal equilibrium is such a state of a system of bodies in thermal contact in which there is no heat transfer from one body to another, and all macroscopic parameters of the bodies remain unchanged. Temperature is a physical parameter that is the same for the temperature of all bodies in thermal equilibrium. The possibility of introducing the concept of temperature follows from experience and is called the zeroth law of thermodynamics.

Molecular-Kinetic Theory Temperature To measure temperature, physical instruments are used - thermometers, in which the temperature value is judged by a change in some physical parameter. To create a thermometer, it is necessary to choose a thermometric substance (for example, mercury, alcohol) and a thermometric quantity that characterizes the property of the substance (for example, the length of a mercury or alcohol column). Various designs of thermometers use a variety of physical properties of a substance (for example, a change in the linear dimensions of solids or a change in the electrical resistance of conductors when heated). Thermometers must be calibrated.

Molecular-kinetic theory A special place in physics is occupied by gas thermometers (Fig.), in which the thermometric substance is a rarefied gas (helium, air) in a vessel of constant volume (V = const), and the thermometric quantity is the gas pressure p. Experience shows that the gas pressure (at V = const) increases with increasing temperature, measured in Celsius.

Molecular Kinetic Theory To calibrate a constant volume gas thermometer, you can measure the pressure at two temperatures (for example, 0 °C and 100 °C), plot the points p 0 and p 100 on a graph, and then draw a straight line between them (Fig. ). Using the calibration curve thus obtained, temperatures corresponding to other pressures can be determined. By extrapolating the graph to the area of ​​low pressures, it is possible to extrapolate the graph to the area of ​​low pressures to determine some "hypothetical" temperature at which the gas pressure would become equal to zero. Experience shows that this temperature is equal to -273.15 °C and does not depend on the properties of the gas. In practice, it is impossible to obtain a gas in a state with zero pressure by cooling, since at very low temperatures all gases pass into a liquid or solid state.

Molecular-kinetic theory The English physicist W. Kelvin (Thomson) in 1848 suggested using the point of zero gas pressure to build a new temperature scale (the Kelvin scale). In this scale, the temperature unit is the same as in the Celsius scale, but the zero point is shifted: TK = TC + 273.15. In the SI system, the temperature unit on the Kelvin scale is called kelvin and denoted by the letter K. For example, room temperature TC \u003d 20 ° С on the Kelvin scale is equal to TK \u003d 293.15 K.

Molecular Kinetic Theory The Kelvin temperature scale is called the absolute temperature scale. It turns out to be the most convenient temperature scale for constructing physical theories. There is no need to tie the Kelvin scale to two fixed points - the melting point of ice and the boiling point of water at normal atmospheric pressure, as is customary in the Celsius scale. In addition to the point of zero gas pressure, which is called the absolute zero of temperature, it is enough to take one more fixed reference point as the absolute zero of temperature. In the Kelvin scale, the temperature of the triple point of water (0.01 ° C) is used as such a point, in which all three phases are in thermal equilibrium - ice, water and steam. On the Kelvin scale, the temperature of the triple point is assumed to be 273.16 K.

Molecular-kinetic theory Thus, the pressure of a rarefied gas in a vessel of constant volume V changes in direct proportion to its absolute temperature: p ~ T. T ν in a given vessel to the volume V of the vessel where N is the number of molecules in the vessel, NA is the Avogadro constant, n = N / V is the concentration of molecules (i.e., the number of molecules per unit volume of the vessel).

Molecular Kinetic Theory Combining these proportionality relations, we can write: p = nk. T, where k is some constant value that is universal for all gases. It is called the Boltzmann constant, in honor of the Austrian physicist L. Boltzmann, one of the creators of the MKT. The Boltzmann constant is one of the fundamental physical constants. Its numerical value in SI: k = 1.38 10–23 J/K.

Molecular Kinetic Theory Comparing the ratios p = nk. T with the basic equation of the MKT gases, you can get: The average kinetic energy of the chaotic movement of gas molecules is directly proportional to the absolute temperature. Thus, temperature is a measure of the average kinetic energy of the translational motion of molecules. It should be noted that the average kinetic energy of the translational motion of a molecule does not depend on its mass. A Brownian particle suspended in a liquid or gas has the same average kinetic energy as an individual molecule, whose mass is many orders of magnitude less than the mass of a Brownian particle.

Molecular-kinetic theory This conclusion also applies to the case when the vessel contains a mixture of chemically non-interacting gases whose molecules have different masses. In a state of equilibrium, the molecules of different gases will have the same average kinetic energies of thermal motion, determined only by the temperature of the mixture. The pressure of the mixture of gases on the walls of the vessel will be the sum of the partial pressures of each gas: p = p 1 + p 2 + p 3 + ... = (n 1 + n 2 + n 3 + ...)k. T In this ratio, n 1, n 2, n 3, … are the concentrations of molecules of various gases in the mixture. This relation expresses, in the language of molecular kinetic theory, the Dalton law experimentally established at the beginning of the 19th century: the pressure in a mixture of the Dalton law of chemically non-interacting gases is equal to the sum of their partial pressures.

Molecular-kinetic theory Equation of state of an ideal gas Relation p = nk. T can be written in another form that establishes a relationship between the macroscopic parameters of the gas - volume V, pressure p, temperature T and the amount of substance ν = m / M. M - This relation is called the ideal gas equation of state or the Clapeyron–Mendeleev ideal gas equation of state – The product of the Avogadro constant NA and the Boltzmann constant k is called the universal gas constant and is denoted by the letter R. Its numerical value in SI is: R = k ∙NA = 8.31 J/mol·K.

Molecular-kinetic theory Equation of state of an ideal gas - If the gas temperature is Tn = 273.15 K (0 ° C), and the pressure pn = 1 atm = 1.013 105 Pa, then they say that the gas is under normal conditions. As follows from the equation of state for an ideal gas, one mole of any gas under normal conditions occupies the same volume V 0 \u003d 0.0224 m 3 / mol \u003d 22.4 dm 3 / mol. This statement is called Avogadro's law.

Molecular-Kinetic Theory Isoprocesses Gas can participate in various thermal processes, in which all parameters describing its state (p, V and T) can change. If the process proceeds slowly enough, then at any moment the system is close to its equilibrium state. Such processes are called quasi-static. In the usual quasi-static time scale for us, these processes can proceed not very slowly. For example, rarefaction and compression of gas in a sound wave, occurring hundreds of times per second, can be considered as a quasi-static process. Quasi-static processes can be depicted on a state diagram (for example, in p, V coordinates) as a certain trajectory, each point of which represents an equilibrium state. Of interest are processes in which one of the parameters (p, V or T) remains unchanged. Such processes are called isoprocesses.

Isothermal process (T = const) An isothermal process is a quasi-static process that occurs at a constant temperature T. It follows from the equation of state of an ideal gas that at a constant temperature T and T, a constant amount of substance ν in the vessel, the product of the pressure p of the gas and its p volume V must remain permanent: p. V = const

Isothermal process (T = const) On the plane (p, V), isothermal processes are represented at various temperatures T by a family of hyperbolas p ~ 1 / V, which are called isotherms. The equation of the isothermal process was obtained from the experiment by the English physicist R. Boyle (1662) and independently by the French physicist E. Mariotte (1676). Therefore, the equation is called the Boyle–Mariotte law. T3 > T2 > T1

Isochoric process (V = const) An isochoric process is a process of quasi-static heating or cooling of a gas at a constant volume V and provided that the amount of substance ν in the vessel remains unchanged. As follows from the ideal gas equation of state, under these conditions, the gas pressure p changes in direct proportion to its absolute temperature: p ~ T or = const

Isochoric process (V = const) On the plane (p, T), isochoric processes for a given amount of matter ν for different values ​​of volume V are represented by a family of straight lines called isochores. Large values ​​of volume correspond to isochores with a smaller slope with respect to the temperature axis (Fig.). The dependence of gas pressure on temperature was studied experimentally by the French physicist J. Charles (1787). Therefore, the equation of the isochoric process is called Charles' law. V3 > V2 > V1

Isobaric process (p = const) An isobaric process is a quasi-static process that occurs at a constant pressure p. The equation of the isobaric process for a certain constant amount of substance ν has the form: where V 0 is the volume of gas at a temperature of 0 °C. The coefficient α is equal to (1/273, 15) K– 1. Its α is called the temperature coefficient of volumetric expansion of gases.

Isobaric process (p = const) On the plane (V, T), isobaric processes at different values ​​of pressure p are depicted by a family of straight lines (Fig.), which are called isobars. The dependence of gas volume on temperature at constant pressure was experimentally investigated by the French physicist J. Gay-Lussac (1862). Therefore, the equation of the isobaric process is called the Gay-Lussac law. p3 > p2 > p1

Isoprocesses The experimentally established laws of Boyle -Mariotte, Charles and Gay-Lussac find -Mariotte, Charles and Gay-Lussac explanation in the molecular-kinetic theory of gases. They are a consequence of the ideal gas equation of state.

Thermodynamics Thermodynamics is the science of thermal phenomena. In contrast to the molecular-kinetic theory, which draws conclusions on the basis of ideas about the molecular structure of a substance, thermodynamics proceeds from the most general laws of thermal processes and the properties of macroscopic systems. The conclusions of thermodynamics are based on a set of experimental facts and do not depend on our knowledge of the internal structure of matter, although in a number of cases thermodynamics uses molecular kinetic models to illustrate its conclusions.

Thermodynamics Thermodynamics considers isolated systems of bodies that are in a state of thermodynamic equilibrium. This means that all observed macroscopic processes have ceased in such systems.

Thermodynamics If a thermodynamic system has been exposed to an external influence, it will eventually move into another equilibrium state. Such a transition is called a thermodynamic process. If the process proceeds slowly enough (infinitely slow in the limit), then the system at each moment of time is close to the equilibrium state. Processes consisting of a sequence of equilibrium states are called quasi-static.

Thermodynamics. Internal energy One of the most important concepts of thermodynamics is the internal energy of a body. All macroscopic bodies have energy contained within the bodies themselves. From the point of view of the MKT, the internal energy of a substance is the sum of the kinetic energy of all atoms and molecules and the potential energy of their interaction with each other. In particular, the internal energy of an ideal gas is equal to the sum of the kinetic energies of all gas particles in continuous and random thermal motion. From this follows Joule's law, confirmed by numerous experiments: The internal energy of an ideal gas depends only on its temperature and does not depend on volume

Thermodynamics. The internal energy of the MKT leads to the following expression for the internal energy of one mole of an ideal monatomic gas (helium, neon, etc.), the molecules of which perform only translational motion: Since the potential energy of the interaction of molecules depends on the distance between them, in the general case, the internal energy U of the body depends along with the temperature T, it also depends on the volume V: T U = U (T, V) Thus, the internal energy U of the body is uniquely determined by the macroscopic parameters characterizing the state of the body. It does not depend on how the given state was realized. It is customary to say that internal energy is a state function.

Thermodynamics. Ways to change the internal energy The internal energy of a body can change if the external forces acting on it do work (positive or negative). work For example, if the gas is compressed in a cylinder under the piston, then external forces do some positive work A "on the gas. At the same time, pressure forces, A" acting on the piston from the gas, do work A = -A "

Thermodynamics. Methods for changing internal energy The internal energy of a body can change not only as a result of the work done, but also as a result of heat transfer. During thermal contact of bodies, the internal energy of one of them can increase, while the other can decrease. In this case, one speaks of a heat flow from one body to another. The amount of heat Q received by the body, The amount of heat Q is the change in the internal energy of the body as a result of heat transfer.

Thermodynamics. Ways to change internal energy The transfer of energy from one body to another in the form of heat can only occur if there is a temperature difference between them. The heat flow is always directed from a hot body to a cold one. The amount of heat Q is an energy quantity. In SI, the amount of heat is measured in units of mechanical work - joules (J).

Thermodynamics. The first law of thermodynamics the energy flows between the selected thermodynamic system and the surrounding bodies are conditionally depicted. The value of Q > 0 if the thermal flow Q > 0 is directed towards the thermodynamic system. The value A > 0 if the system performs positive work A > 0 on the surrounding bodies. If the system exchanges heat with surrounding bodies and does work (positive or negative), then the state of the system changes, the state of the system changes, i.e., its macroscopic parameters (temperature, pressure, volume) change.

Thermodynamics. The first law of thermodynamics Since the internal energy U is uniquely determined by macroscopic parameters characterizing the state of the system, it follows that the processes of heat transfer and work are accompanied by a change in the internal energy of the system ΔU.

Thermodynamics. The first law of thermodynamics The first law of thermodynamics is a generalization of the law of conservation and transformation of energy for a thermodynamic system. It is formulated as follows: The change ΔU of the internal energy of a non-isolated thermodynamic system is equal to the difference between the amount of heat Q transferred to the system and the work A performed by the system on external bodies. ΔU = Q - A The relation expressing the first law of thermodynamics is often written in a different form: Q = ΔU + A The amount of heat received by the system goes to change its internal energy and perform work on external bodies.

Thermodynamics. The first law of thermodynamics Let us apply the first law of thermodynamics to isoprocesses in gases. In an isochoric process (V = const), the gas does no work, A = 0. Therefore, Q = ΔU = U (T 2) - U (T 1). Here U (T 1) and U (T 2) are the internal energies of the gas in the initial and final states. The internal energy of an ideal gas depends only on temperature (Joule's law). During isochoric heating, heat is absorbed by the gas (Q > 0), and its internal energy increases. During cooling, heat is given off to external bodies (Q 0 - heat is absorbed by the gas, and the gas does positive work. With isobaric compression Q

Thermal engines. Thermodynamic cycles. Carnot cycle A heat engine is a device capable of converting the received amount of heat into mechanical work. Mechanical work in heat engines is performed in the process of expansion of a certain substance, which is called the working fluid. As a working fluid, gaseous substances (gasoline vapors, air, water vapor) are usually used. The working body receives (or gives away) thermal energy in the process of heat exchange with bodies that have a large supply of internal energy. These bodies are called thermal reservoirs. Really existing heat engines (steam engines, internal combustion engines, etc.) operate cyclically. The process of heat transfer and conversion of the received amount of heat into work is periodically repeated. To do this, the working fluid must perform a circular process or a thermodynamic cycle, in which the initial state is periodically restored.

Thermal engines. Thermodynamic cycles. Carnot cycle A common feature of all circular processes is that they cannot be carried out by bringing the working fluid into thermal contact with only one thermal reservoir. They need at least two. A heat reservoir with a higher temperature is called a heater, and a heat reservoir with a lower temperature is called a refrigerator. Making a circular process, the working fluid receives from the heater a certain amount of heat Q 1 > 0 and gives the cooler the amount of heat Q 2

Thermal engines. Thermodynamic cycles. Carnot cycle The work A performed by the working fluid per cycle is equal to the amount of heat Q received per cycle. The ratio of work A to the amount of heat Q 1 received by the working fluid per cycle from the heater is called the efficiency η of the heat engine:

Thermal engines. Thermodynamic cycles. The Carnot cycle The coefficient of efficiency indicates what part of the thermal energy received by the working fluid from the "hot" thermal reservoir has turned into useful work. The rest (1 - η) was "uselessly" transferred to the refrigerator. (1 – η) The efficiency of a heat engine is always less than one (η 0, A > 0, Q 2 T 2

Thermal engines. Thermodynamic cycles. Carnot cycle In 1824, the French engineer S. Carnot considered a circular process consisting of two isotherms and two adiabats, which played an important role in the development of the theory of thermal processes. It is called the Carnot cycle (Fig. 3. 11. 4).

Thermal engines. Thermodynamic cycles. Carnot cycle The Carnot cycle is performed by the gas in the cylinder under the piston. In the isothermal section (1–2), the gas is brought into thermal contact with a hot thermal reservoir (heater) having a temperature T 1. The gas expands isothermally, doing work A 12, while a certain amount of heat Q 1 = A 12 is supplied to the gas. Further in the adiabatic section (2–3), the gas is placed in an adiabatic shell and continues to expand in the absence of heat transfer. In this section, the gas performs work A 23 > 0. The temperature of the gas during adiabatic expansion drops to the value T 2. In the next isothermal section (3–4), the gas is brought into thermal contact with a cold thermal reservoir (refrigerator) at a temperature T 2

Irreversibility of thermal processes. The second law of thermodynamics. The first law of thermodynamics - the law of conservation of energy for thermal processes - establishes a relationship between the amount of heat Q received by the system, the change ΔU of its internal energy and the work A performed on external bodies: Q = ΔU + A According to this law, energy cannot be created or destroyed; it is transferred from one system to another and is transformed from one form into another. Processes that violate the first law of thermodynamics have never been observed. On fig. devices prohibited by the first law of thermodynamics are shown. Cyclically operating heat engines prohibited by the first law of thermodynamics: 1 - perpetual motion machine of the 1st kind, performing work without consuming energy from the outside; 2 - heat engine with efficiency η > 1

Irreversibility of thermal processes. The second law of thermodynamics. The first law of thermodynamics does not establish the direction of thermal processes. The first law of thermodynamics processes. However, as experience shows, many thermal processes can proceed only in one direction. Such processes are called irreversible. For example, during thermal contact of two bodies with different temperatures, the heat flow is always directed from a warmer body to a colder one. A spontaneous process of heat transfer from a body with a low temperature to a body with a higher temperature is never observed. Therefore, the process of heat transfer at a finite temperature difference is irreversible. Reversible processes are the processes of transition of a system from one equilibrium state to another, which can be carried out in the opposite direction through the same sequence of intermediate equilibrium states. In this case, the system itself and the surrounding bodies return to their original state. Processes in which the system always remains in a state of equilibrium are called quasi-static. All quasi-static processes are reversible. All reversible processes are quasi-static.

Irreversibility of thermal processes. The second law of thermodynamics. The processes of converting mechanical work into internal energy of the body are irreversible due to the presence of friction, diffusion processes in gases and liquids, gas mixing processes in the presence of an initial pressure difference, etc. All real processes are irreversible, but they can approach reversible arbitrarily close processes. Reversible processes are idealizations of real processes. The first law of thermodynamics cannot distinguish reversible from irreversible processes. It simply requires a certain energy balance from the thermodynamic process and does not say anything about whether such a process is possible or not.

Irreversibility of thermal processes. The second law of thermodynamics. The direction of spontaneously occurring processes establishes the second law of thermodynamics. It can be formulated in thermodynamics as a ban on certain types of thermodynamic processes. The English physicist W. Kelvin gave the following formulation of the second law in 1851: the second law In a cyclically operating heat engine, a process is impossible, the only result of which would be the conversion into mechanical work of the entire amount of heat received from a single heat reservoir.

Irreversibility of thermal processes. The second law of thermodynamics. The German physicist R. Clausius gave a different formulation of the second law of thermodynamics: A process is impossible, the only result of which would be the transfer of energy by heat transfer from a body with a low temperature to a body with a higher temperature. On fig. the processes forbidden by the second law, but not forbidden by the first law of thermodynamics, are depicted. These processes correspond to two formulations of the second law of thermodynamics. 1 - perpetual motion machine of the second kind; 2 - spontaneous transfer of heat from a cold body to a warmer one (ideal refrigerator)

Molecular physics. Thermodynamics.

1.Statistical and thermodynamic methods

2.Molecular-kinetic theory of ideal gases

2.1 Basic definitions

2.2.Experimental laws of ideal gas

2.3 Equation of state of ideal gas (Clapeyron-Mendeleev equation

2.4.Basic equation of the molecular kinetic theory of an ideal gas

2.5 Maxwell distribution

2.6 Boltzmann distribution

3. Thermodynamics

3.1. Internal energy. The law of uniform distribution of energy over degrees of freedom

3.2. The first law of thermodynamics

3.3. Work of gas when changing its volume

3.4 Heat capacity

3.5. First law of thermodynamics and isoprocesses

3.5.1 Isochoric process (V = const)

3.5.2. Isobaric process (p = const)

3.5.3 Isothermal process (T = const)

3.5.4. Adiabatic process (dQ = 0)

3.5.5. Polytropic processes

3.6.Circular process (cycle). Reversible and irreversible processes. Carnot cycle.

3.7.Second law of thermodynamics

3.8 Real gases

3.8.1. Forces of intermolecular interaction

3.8.2 Van der Waals equation

3.8.3 Internal energy of a real gas

3.8.4. Joule-Thomson effect. Liquefaction of gases.

1.Statistical and thermodynamic methods

Molecular physics and thermodynamics - branches of physics that studymacroscopic processes associated with the huge number of atoms and molecules contained in the bodies. To study these processes, two fundamentally different (but mutually complementary) methods are used: statistical (molecular-kinetic) andthermodynamic.

Molecular physics - a branch of physics that studies the structure and properties of matter based on molecular kinetic concepts based on the fact that all bodies consist of molecules in continuous chaotic motion. The processes studied by molecular physics are the result of the combined action of a huge number of molecules. The laws of behavior of a huge number of molecules are studied usingstatistical method , which is based on what propertiesmacroscopic system are determined by the properties of the particles of the system, the features of their motion and the averaged values ​​of the dynamic characteristics of these particles (speed, energy, etc.). For example, the temperature of a body is determined by the average speed of the chaotic movement of its molecules, and one cannot speak of the temperature of one molecule.

Thermodynamics - branch of physics that studies the general properties of macroscopic systems instate of thermodynamic equilibrium , and transition processes between these states. Thermodynamics does not consider microprocesses , which underlie these transformations, but is based on two principles of thermodynamics - fundamental laws established experimentally.

Statistical methods of physics cannot be used in many areas of physics and chemistry, while thermodynamic methods are universal. However, statistical methods make it possible to establish the microscopic structure of a substance, while thermodynamic methods only establish relationships between macroscopic properties. Molecular-kinetic theory and thermodynamics complement each other, forming a single whole, but differing in research methods.

2.Molecular-kinetic theory of ideal gases

2.1 Basic definitions

The object of study in molecular-kinetic theory is a gas. It is believed that gas molecules, making random movements, are not bound by interaction forces and therefore they move freely, striving, as a result of collisions, to scatter in all directions, filling the entire volume provided to them. Thus, the gas takes on the volume of the vessel that the gas occupies.

Ideal gas is a gas for which: the intrinsic volume of its molecules is negligible compared to the volume of the vessel; there are no interaction forces between gas molecules; collisions of gas molecules with each other and with the walls of the vessel are absolutely elastic. For many real gases, the ideal gas model describes well their macroproperties.

Thermodynamic system - a set of macroscopic bodies that interact and exchange energy both among themselves and with other bodies (the external environment).

State of the system- a set of physical quantities (thermodynamic parameters, state parameters) , which characterize the properties of the thermodynamic system:temperature, pressure, specific volume.

Temperature- physical quantity characterizing the state of thermodynamic equilibrium of a macroscopic system. In the SI system, the use is allowed thermodynamic and practical temperature scale .In the thermodynamic scale, the triple point of water (the temperature at which ice, water and steam at a pressure of 609 Pa are in thermodynamic equilibrium) is considered equal to T = 273.16 degrees Kelvin[K]. In a practical scale, the freezing and boiling points of water at a pressure of 101300 Pa are considered equal, respectively, t \u003d 0 and t \u003d 100 degrees Celsius [C].These temperatures are related by the relation

The temperature T = 0 K is called zero Kelvin, according to modern concepts, this temperature is unattainable, although it is possible to approach it arbitrarily close.

Pressure - physical quantity determined by the normal force F acting from the side of the gas (liquid) on a single area placed inside the gas (liquid) p = F/S, where S is the area size. The unit of pressure is pascal [Pa]: 1 Pa is equal to the pressure created by a force of 1 N, uniformly distributed over a surface normal to it with an area of ​​1 m 2 (1 Pa = 1 N / m 2).

Specific volumeis the volume per unit mass v = V/m = 1/r, where V is the volume of mass m, r is the density of a homogeneous body. Since v ~ V for a homogeneous body, the macroscopic properties of a homogeneous body can be characterized by both v and V.

Thermodynamic process - any change in a thermodynamic system that leads to a change in at least one of its thermodynamic parameters.Thermodynamic equilibrium- such a state of a macroscopic system, when its thermodynamic parameters do not change over time.Equilibrium processes - processes that proceed in such a way that the change in thermodynamic parameters over a finite period of time is infinitesimal.

isoprocesses are equilibrium processes in which one of the main parameters of the state remains constant.isobaric process - a process occurring at constant pressure (in coordinates V,t he is portrayedisobar ). Isochoric process- a process occurring at a constant volume (in coordinates p,t he is portrayedisochore ). Isothermal process - a process occurring at a constant temperature (in coordinates p,V he is portrayedisotherm ). adiabatic processis a process in which there is no heat exchange between the system and the environment (in coordinates p,V he is portrayedadiabatic ).

Constant (number) Avogadro - the number of molecules in one mole N A \u003d 6.022. 10 23 .

Normal conditions: p = 101300 Pa, T = 273.16 K.