In a liquid state according to molecular kinetic theory. II. Molecular physics. Kinetic model of an ideal gas

This video lesson is devoted to the topic “Basic provisions of the ICT. Structure of matter. Molecule". Here you will learn what molecular kinetic theory (MKT) studies in physics. Get acquainted with the three main provisions on which the ICT is based. You will learn what determines the physical properties of a substance and what an atom and a molecule are.

First, let's remember all the previous sections of physics that we studied, and understand that all this time we were considering the processes occurring with macroscopic bodies (or objects of the macrocosm). Now we will study their structure and the processes occurring inside them.

Definition. Macroscopic body- a body consisting of a large number of particles. For example: a car, a person, a planet, a billiard ball...

Microscopic body - a body consisting of one or more particles. For example: atom, molecule, electron... (Fig. 1)

Rice. 1. Examples of micro- and macro-objects, respectively

Having thus defined the subject of study of the MCT course, we should now talk about the main goals that the MCT course sets for itself, namely:

1. Study of processes occurring inside a macroscopic body (movement and interaction of particles)
2. Properties of bodies (density, mass, pressure (for gases)…)
3. Study of thermal phenomena (heating-cooling, changes in physical states of the body)

The study of these issues, which will take place throughout the entire topic, will now begin with the fact that we will formulate the so-called basic provisions of the ICT, that is, some statements whose truth has long been beyond doubt, and, starting from which, the entire further course will be built .

Let's look at them one by one:

All substances consist of a large number of particles - molecules and atoms.

Definition. Atom- the smallest particle of a chemical element. The dimensions of atoms (their diameter) are on the order of cm. It is worth noting that, unlike molecules, there are relatively few different types of atoms. All their varieties, which are currently known to man, are collected in the so-called periodic table (see Fig. 2)

Rice. 2. Periodic table of chemical elements (essentially varieties of atoms) by D. I. Mendeleev

Molecule- a structural unit of matter consisting of atoms. Unlike atoms, they are larger and heavier, and most importantly, they have a huge variety.

A substance whose molecules consist of one atom is called atomic, from a larger number - molecular. For example: oxygen, water, table salt () - molecular; helium silver (He, Ag) - atomic.

Moreover, it should be understood that the properties of macroscopic bodies will depend not only on the quantitative characteristics of their microscopic composition, but also on the qualitative one.

If in the structure of atoms a substance has a certain geometry ( crystal lattice), or, on the contrary, does not, then these bodies will have different properties. For example, amorphous bodies do not have a strict melting point. The most famous example is amorphous graphite and crystalline diamond. Both substances are made of carbon atoms.

Rice. 3. Graphite and diamond respectively

Thus, “how many atoms and molecules does matter consist of, in what relative arrangement, and what kind of atoms and molecules?” - the first question, the answer to which will bring us closer to understanding the properties of bodies.

All the particles mentioned above are in continuous thermal chaotic motion.

Just as in the examples discussed above, it is important to understand not only the quantitative aspects of this movement, but also the qualitative ones for various substances.

Molecules and atoms of solids undergo only slight vibrations relative to their constant position; liquid - also vibrate, but due to the large size of the intermolecular space, they sometimes change places with each other; Gas particles, in turn, move freely in space without practically colliding.

Particles interact with each other.

This interaction is electromagnetic in nature (interaction between the nuclei and electrons of an atom) and acts in both directions (both attraction and repulsion).

Here: d- distance between particles; a- particle size (diameter).

The concept of “atom” was first introduced by the ancient Greek philosopher and natural scientist Democritus (Fig. 4). In a later period, the Russian scientist Lomonosov actively wondered about the structure of the microworld (Fig. 5).

Rice. 4. Democritus

Rice. 5. Lomonosov

In the next lesson we will introduce methods of qualitative substantiation of the main provisions of ICT.

Bibliography

1. Myakishev G.Ya., Sinyakov A.Z. Molecular physics. Thermodynamics. - M.: Bustard, 2010.
2. Gendenshtein L.E., Dick Yu.I. Physics 10th grade. - M.: Ilexa, 2005.
3. Kasyanov V.A. Physics 10th grade. - M.: Bustard, 2010.

1. Elementy.ru ().
   
2. Samlib.ru ().
3. Youtube().

Homework

1. *Thanks to what force is it possible to do the experiment on measuring the size of an oil molecule, shown in the video tutorial?
2. Why does molecular kinetic theory not consider organic compounds?
3. Why is even a very small grain of sand an object of the macrocosm?
4. Forces of predominantly what nature act on particles from other particles?
5. How can you determine whether a certain chemical structure is a chemical element?

Any substance is considered by physics as a collection of smallest particles: atoms, molecules and ions. All these particles are in continuous chaotic motion and interact with each other through elastic collisions.

Atomic theory is the basis of molecular kinetic theory

Democritus

Molecular kinetic theory originated in Ancient Greece approximately 2,500 years ago. Its foundation is considered atomic hypothesis , whose authors were ancient Greek philosopher Leucippus and his student ancient Greek scientist Democritus from the city of Abdera.

Leucippus

Leucippus and Democritus assumed that all material things consist of indivisible tiny particles called atoms (from Greekἄτομος - indivisible). And the space between the atoms is filled with emptiness. All atoms have size and shape and are capable of movement. Proponents of this theory in the Middle Ages were Giordano Bruno, Galileo, Isaac Beckman and other scientists. The foundations of molecular kinetic theory were laid in the work “Hydrodynamics”, published in 1738. Its author was a Swiss physicist, mechanic and mathematician Daniel Bernoulli.

Basic principles of molecular kinetic theory

Mikhail Vasilievich Lomonosov

The closest thing to modern physics was the theory of the atomic structure of matter, which was developed by the great Russian scientist in the 18th century Mikhail Vasilievich Lomonosov. He argued that all substances are composed of molecules which he called corpuscles . And corpuscles, in turn, consist of atoms . Lomonosov's theory was called corpuscular .

But as it turns out, the atom is dividing. It consists of a positively charged nucleus and negative electrons. But in general it is electrically neutral.

Modern science calls atom the smallest part of a chemical element that is the carrier of its basic properties. Connected by interatomic bonds, atoms form molecules. A molecule can contain one or more atoms of the same or different chemical elements.

All bodies consist of a huge number of particles: atoms, molecules and ions. These particles move continuously and chaotically. Their movement does not have any specific direction and is called thermal movement . During their motion, particles interact with each other through absolutely elastic collisions.

We cannot observe molecules and atoms with the naked eye. But we can see the result of their actions.

Confirmation of the main provisions of the molecular kinetic theory are: diffusion , Brownian motion And change aggregate states of substances .

Diffusion

Diffusion in liquid

One of the proofs of the constant movement of molecules is the phenomenon diffusion .

In the process of movement, molecules and atoms of one substance penetrate between the molecules and atoms of another substance in contact with it. Molecules and atoms of the second substance behave in exactly the same way. in relation to the first. And after some time, the molecules of both substances are evenly distributed throughout the entire volume.

The process of penetration of molecules of one substance between molecules of another is called diffusion . We encounter the phenomenon of diffusion at home every day when we put a tea bag into a glass of boiling water. We observe how colorless boiling water changes its color. By throwing several manganese crystals into a test tube with water, you can see that the water turns pink. This is also diffusion.

The number of particles per unit volume is called concentration substances. During diffusion, molecules move from those parts of a substance where the concentration is higher to those parts where it is lower. The movement of molecules is called diffusion flow . As a result of diffusion, the concentrations in different parts of substances are equalized.

Diffusion can be observed in gases, liquids and solids. In gases it occurs at a faster rate than in liquids. We know how quickly odors spread in the air. The liquid in a test tube turns color much more slowly if ink is dropped into it. And if we put crystals of table salt at the bottom of a container with water and do not mix, then more than one day will pass before the solution becomes homogeneous.

Diffusion also occurs at the boundary of contacting metals. But its speed in this case is very low. If you coat copper with gold, at room temperature and atmospheric pressure, the gold will penetrate only a few microns into the copper after a few thousand years.

Lead from an ingot placed under a weight on a gold ingot will penetrate into it only to a depth of 1 cm in 5 years.

Diffusion in metals

Diffusion rate

The rate of diffusion depends on the cross-sectional area of ​​the flow, the difference in concentrations of substances, the difference in their temperatures or charges. Through a rod with a diameter of 2 cm, heat spreads 4 times faster than through a rod with a diameter of 1 cm. The higher the temperature difference between substances, the higher the rate of diffusion. During thermal diffusion, its speed depends on thermal conductivity material, and in the case of a flow of electric charges - from electrical conductivity .

Fick's law

Adolf Fick

In 1855, the German physiologist Adolf Eugen Fick made the first quantitative description of diffusion processes:

Where J - density diffusion flow of matter,

D - diffusion coefficient,

C - substance concentration.

Substance diffusion flux densityJ [cm -2 s -1 ] is proportional to the diffusion coefficientD [cm -2 s -1 ] and the concentration gradient taken with the opposite sign.

This equation is called Fick's first equation .

Diffusion, as a result of which the concentrations of substances are equalized, is called non-stationary diffusion . With such diffusion, the concentration gradient changes with time. And in case stationary diffusion this gradient remains constant.

Brownian motion

Robert Brown

This phenomenon was discovered by the Scottish botanist Robert Brown in 1827, studying under a microscope cytoplasmic grains suspended in water, isolated from pollen cells of a North American plant.Clarkia pulchella, he paid attention to the smallest solid grains. They trembled and moved slowly for no apparent reason. If the temperature of the liquid increased, the speed of the particles increased. The same thing happened when the particle size decreased. And if their size increased, the temperature of the liquid decreased or its viscosity increased, the movement of the particles slowed down. And these amazing “dances” of particles could be observed for an infinitely long time. Deciding that the reason for this movement was that the particles were alive, Brown replaced the grains with small particles of coal. The result was the same.

Brownian motion

To repeat Brown's experiments, it is enough to have the most ordinary microscope. The molecular size is too small. And it is impossible to examine them with such a device. But if we tint water in a test tube with watercolor paint and then look at it through a microscope, we will see tiny colored particles moving randomly. These are not molecules, but particles of paint suspended in water. And they are forced to move by water molecules that hit them from all sides.

This is the behavior of all particles visible through a microscope that are suspended in liquids or gases. Their random movement caused by the thermal movement of molecules or atoms is called Brownian motion . A Brownian particle is continuously subjected to impacts from the molecules and atoms that make up liquids and gases. And this movement does not stop.

But Brownian motion can involve particles as small as 5 microns (micrometers). If their size is larger, they are immobile. The smaller the size of a Brownian particle, the faster it moves. Particles smaller than 3 microns move translationally along all complex trajectories or rotate.

Brown himself could not explain the phenomenon he discovered. And only in the 19th century did scientists find the answer to this question: the movement of Brownian particles is caused by the influence of the thermal movement of molecules and atoms on them.

Three states of matter

The molecules and atoms that make up matter are not only in motion, but also interact with each other, mutually attracting or repelling.

If the distance between the molecules is comparable to their size, then they experience attraction. If it becomes smaller, then the repulsive force begins to dominate. This explains the resistance of physical bodies to deformation (compression or tension).

If the body is compressed, the distance between the molecules decreases, and repulsive forces will try to return the molecules to their original state. When stretching, the deformation of the body will interfere with the forces of attraction between the molecules.

Molecules interact not only within one body. Dip a piece of fabric into the liquid. We'll see that it gets wet. This is explained by the fact that liquid molecules are attracted to solid molecules more strongly than to each other.

Each physical substance, depending on temperature and pressure, can be in three states: solid, liquid or gaseous . They're called aggregate .

In gases the distance between molecules is large. Therefore, the forces of attraction between them are so weak that they perform chaotic and almost free movement in space. They change the direction of their movement, hitting each other or the walls of blood vessels.

In liquids molecules are located closer to each other than in a gas. The force of attraction between them is greater. The molecules in them no longer move freely, but oscillate chaotically around the equilibrium position. But they are able to jump in the direction of the action of an external force, changing places with each other. The result of this is fluid flow.

In solids The interaction forces between molecules are very strong due to the close distance between them. They cannot overcome the attraction of neighboring molecules, therefore they are only able to perform oscillatory movements around the equilibrium position.

Solids retain volume and shape. Liquid has no shape; it always takes the shape of the vessel in which it is currently located. But its volume remains the same. Gaseous bodies behave differently. They easily change both shape and volume, taking the shape of the vessel in which they were placed and occupying the entire volume provided to them.

However, there are also bodies that have a liquid structure, have little fluidity, but are still able to maintain their shape. Such bodies are called amorphous .

Modern physics also identifies a fourth state of matter - plasma .

Molecular kinetic theory(abbreviated MKT) is a theory that arose in the 19th century and considers the structure of matter, mainly gases, from the point of view of three main approximately correct provisions:

All bodies are made of particles: atoms, molecules And ions;

particles are in continuous chaotic movement (thermal);

particles interact with each other through perfectly elastic collisions.

MCT has become one of the most successful physical theories and has been confirmed by a number of experimental facts. The main evidence for the provisions of the ICT were:

Diffusion

Brownian motion

Change states of aggregation substances

A number of branches of modern physics have been developed on the basis of MCT, in particular, physical kinetics And statistical mechanics. In these branches of physics, not only molecular (atomic or ionic) systems are studied, which are not only in “thermal” motion, and interact not only through absolutely elastic collisions. The term molecular kinetic theory is practically no longer used in modern theoretical physics, although it is found in textbooks on general physics courses.

Ideal gas - mathematical model gas, which assumes that: 1) potential energy interactions molecules can be neglected in comparison with their kinetic energy; 2) the total volume of gas molecules is negligible. There are no forces of attraction or repulsion between the molecules, no collision of particles with each other or with the walls of the vessel absolutely elastic, and the interaction time between molecules is negligible compared to the average time between collisions. In the extended model of an ideal gas, the particles of which it consists also have the form of elastic spheres or ellipsoids, which makes it possible to take into account the energy of not only translational, but also rotational-vibrational motion, as well as not only central, but also non-central collisions of particles, etc.

There are classical ideal gases (its properties are derived from the laws of classical mechanics and are described Boltzmann statistics) and quantum ideal gas (properties are determined by the laws of quantum mechanics and described by statisticians Fermi - Dirac or Bose - Einstein)

Classical ideal gas

The volume of an ideal gas depends linearly on temperature at constant pressure

The properties of an ideal gas based on molecular kinetic concepts are determined based on the physical model of an ideal gas, in which the following assumptions are made:

In this case, the gas particles move independently of each other, the gas pressure on the wall is equal to the total momentum transferred during the collision of particles with the wall per unit time, internal energy- the sum of the energies of gas particles.

According to an equivalent formulation, an ideal gas is a gas that simultaneously obeys Boyle-Mariotte law And Gay Lussac , that is:

where is pressure and is absolute temperature. The properties of an ideal gas are described Mendeleev - Clapeyron equation

,

Where - , - weight, - molar mass.

Where - particle concentration, - Boltzmann constant.

For any ideal gas this is true Mayer's ratio:

Where - universal gas constant, - molar heat capacity at constant pressure, is the molar heat capacity at constant volume.

A statistical calculation of the molecular velocity distribution was performed by Maxwell.

Let's consider the result obtained by Maxwell in the form of a graph.

Gas molecules constantly collide as they move. The speed of each molecule upon collision changes. It can increase and decrease. However, the RMS speed remains unchanged. This is explained by the fact that in a gas at a certain temperature, a certain stationary velocity distribution of molecules that does not change over time is established, which obeys a certain statistical law. The speed of an individual molecule may change over time, but the proportion of molecules with speeds in a certain speed range remains unchanged.

The question cannot be asked: how many molecules have a certain speed. The fact is that, although the number of molecules is very large in any even small volume, the number of speed values ​​is arbitrarily large (like numbers in a sequential series), and it may happen that not a single molecule has a given speed.

Rice. 3.3

The problem of the velocity distribution of molecules should be formulated as follows. Let per unit volume n molecules. What fraction of molecules has speeds from v 1 to v 1 + Δ v? This is a statistical problem.

Based on Stern's experience, we can expect that the largest number of molecules will have some average speed, and the proportion of fast and slow molecules is not very large. The necessary measurements showed that the fraction of molecules related to the speed interval Δ v, i.e. , has the form shown in Fig. 3.3. Maxwell in 1859 theoretically defined this function based on the theory of probability. Since then it has been called the velocity distribution function of molecules or Maxwell's law.

Let us derive the velocity distribution function of ideal gas molecules

- speed interval near speed .

- the number of molecules whose velocities lie in the interval
.

- the number of molecules in the volume under consideration.

- angle of molecules whose velocities belong to the interval
.

- the fraction of molecules in a unit speed interval near the speed .

- Maxwell's formula.

Using Maxwell's statistical methods we obtain the following formula:

.

- mass of one molecule,
- Boltzmann constant.

The most probable speed is determined from the condition
.

Solving we get
;
.

Let's denote h/z
.

Then
.

Let's calculate the fraction of molecules in a given speed range near a given speed in a given direction.

.

.

- the fraction of molecules that have velocities in the range
,
,
.

Developing Maxwell's ideas, Boltzmann calculated the velocity distribution of molecules in a force field. Unlike the Maxwell distribution, in the Boltzmann distribution, instead of the kinetic energy of molecules, the sum of kinetic and potential energy appears.

In the Maxwell distribution:
.

In the Boltzmann distribution:
.

In a gravitational field

.

The formula for the concentration of ideal gas molecules is:

And respectively.

- Boltzmann distribution.

- concentration of molecules at the Earth's surface.

- concentration of molecules at height .

Heat capacity.

The heat capacity of a body is a physical quantity equal to the ratio

,
.

Heat capacity of one mole - molar heat capacity

.

Because
- process function
, That
.

Considering

;

;



.

- Mayer's formula.

That. the problem of calculating heat capacity comes down to finding .

.

For one mole:

, from here
.

Diatomic gas (O 2, N 2, Cl 2, CO, etc.).

(hard dumbbell model).

Total number of degrees of freedom:

.

Then
, That

;
.

This means that the heat capacity must be constant. At the same time, experience shows that heat capacity depends on temperature.

As the temperature decreases, first the vibrational degrees of freedom are “frozen,” and then the rotational degrees of freedom.

According to the laws of quantum mechanics, the energy of a harmonic oscillator with a classical frequency can only take on a discrete set of values

Polyatomic gases (H 2 O, CH 4, C 4 H 10 O, etc.).

;
;
;

Let's compare the theoretical data with the experimental ones.

It's clear that 2 atomic gases equals , but changes at low temperatures contrary to the theory of heat capacity.

Such a course of the curve from indicates a “freezing” of degrees of freedom. On the contrary, at high temperatures additional degrees of freedom are activated  these data cast doubt on the uniform distribution theorem. Modern physics makes it possible to explain the dependence from using quantum concepts.

Quantum statistics has eliminated difficulties in explaining the dependence of the heat capacity of gases (in particular diatomic gases) on temperature. According to the principles of quantum mechanics, the energy of rotational motion of molecules and the energy of vibration of atoms can only take discrete values. If the energy of thermal motion is significantly less than the difference in energies of neighboring energy levels (), then when molecules collide, rotational and vibrational degrees of freedom are practically not excited. Therefore, at low temperatures, the behavior of a diatomic gas is similar to the behavior of a monatomic gas. Since the difference between adjacent rotational energy levels is much smaller than between adjacent vibrational levels ( ), then with increasing temperature, rotational degrees of freedom are first excited. As a result, the heat capacity increases. With a further increase in temperature, vibrational degrees of freedom are also excited, and a further increase in heat capacity occurs. A. Einstein approximately believed that the vibrations of atoms in a crystal lattice were independent. Using a model of a crystal as a set of harmonic oscillators independently oscillating at the same frequency, he created a qualitative quantum theory of the heat capacity of a crystal lattice. This theory was subsequently developed by Debye, who took into account that the vibrations of atoms in a crystal lattice are not independent. Having considered the continuous frequency spectrum of oscillators, Debye showed that the main contribution to the average energy of a quantum oscillator is made by oscillations at low frequencies corresponding to elastic waves. Thermal excitation of a solid can be described in the form of elastic waves propagating in the crystal. According to the wave-particle duality of the properties of matter, elastic waves in a crystal are compared with quasiparticles–phonons having energy. A phonon is an elastic wave energy quantum, which is an elementary excitation that behaves like a microparticle. Just as the quantization of electromagnetic radiation led to the idea of ​​photons, so the quantization of elastic waves (as a result of thermal vibrations of molecules of solid bodies) led to the idea of ​​phonons. The energy of the crystal lattice consists of the energy of the phonon gas. Quasiparticles (in particular phonons) are very different from ordinary microparticles (electrons, protons, neutrons, etc.), since they are associated with the collective motion of many particles of the system.

Phonons cannot appear in a vacuum; they exist only in a crystal.

The phonon momentum has a peculiar property: when phonons collide in a crystal, their momentum can be transferred in discrete portions to the crystal lattice - the momentum is not conserved. Therefore, in the case of phonons we speak of quasi-momentum.

Phonons have zero spin and are bosons, and therefore the phonon gas obeys Bose–Einstein statistics.

Phonons can be emitted and absorbed, but their number is not kept constant.

The application of Bose–Einstein statistics to a phonon gas (a gas of independent Bose particles) led Debye to the following quantitative conclusion. At high temperatures, which are much higher than the characteristic Debye temperature (classical region), the heat capacity of solids is described by the law of Dulong and Petit, according to which the molar heat capacity of chemically simple bodies in the crystalline state is the same and does not depend on temperature. At low temperatures, when (quantum region), the heat capacity is proportional to the third power of thermodynamic temperature: The characteristic Debye temperature is equal to: , where is the limiting frequency of elastic vibrations of the crystal lattice.

The central concept of this topic is the concept of a molecule; the difficulty of its assimilation by schoolchildren is due to the fact that a molecule is an object that is not directly observable. Therefore, the teacher must convince tenth graders of the reality of the microworld, of the possibility of knowing it. In this regard, much attention is paid to the consideration of experiments that prove the existence and movement of molecules and make it possible to calculate their main characteristics (classical experiments of Perrin, Rayleigh and Stern). In addition, it is advisable to familiarize students with computational methods for determining the characteristics of molecules. When considering evidence of the existence and movement of molecules, students are told about Brown's observations of the random movement of small suspended particles, which did not stop during the entire observation period. At that time, no correct explanation was given for the cause of this movement, and only almost 80 years later A. Einstein and M. Smoluchowski built and J. Perrin experimentally confirmed the theory of Brownian motion. From considering Brown's experiments, it is necessary to draw the following conclusions: a) the movement of Brownian particles is caused by impacts of molecules of the substance in which these particles are suspended; b) Brownian motion is continuous and random, it depends on the properties of the substance in which the particles are suspended; c) the movement of Brownian particles makes it possible to judge the movement of the molecules of the medium in which these particles are located; d) Brownian motion proves the existence of molecules, their movement and the continuous and chaotic nature of this movement. Confirmation of this nature of the movement of molecules was obtained in the experiment of the French physicist Dunoyer (1911), who showed that gas molecules move in different directions and in the absence of collisions their movement is rectilinear. Currently, no one doubts the existence of molecules. Advances in technology have made it possible to directly observe large molecules. It is advisable to accompany the story about Brownian motion with a demonstration of a model of Brownian motion in a vertical projection using a projection lamp or overhead projector, as well as with a screening of the film fragment “Brownian motion” from the film “Molecules and Molecular Motion.” In addition, it is useful to observe Brownian motion in liquids using a microscope. The drug is made from a mixture of equal parts of two solutions: a 1% solution of sulfuric acid and a 2% aqueous solution of hyposulfite. As a result of the reaction, sulfur particles are formed, which are suspended in the solution. Two drops of this mixture are placed on a glass slide and the behavior of the sulfur particles is observed. The preparation can be made from a highly diluted solution of milk in water or from a solution of watercolor paint in water. When discussing the issue of the size of molecules, the essence of R. Rayleigh's experiment is considered, which consists of the following: a drop of olive oil is placed on the surface of water poured into a large vessel. The drop spreads over the surface of the water and forms a round film. Rayleigh suggested that when the drop stops spreading, its thickness becomes equal to the diameter of one molecule. Experiments show that molecules of different substances have different sizes, but to estimate the size of molecules they take a value equal to 10 -10 m. A similar experiment can be done in class. To demonstrate the calculation method for determining the sizes of molecules, an example is given of calculating the diameters of molecules of various substances from their densities and Avogadro's constant. It is difficult for schoolchildren to imagine the small sizes of molecules, so it is useful to give a number of comparative examples. For example, if all dimensions were increased so many times that the molecule was visible (i.e., up to 0.1 mm), then a grain of sand would turn into a hundred-meter rock, an ant would increase to the size of an ocean ship, and a person would be 1,700 km tall. The number of molecules in 1 mole of a substance can be determined from the results of an experiment with a monomolecular layer. Knowing the diameter of the molecule, you can find its volume and the volume of the amount of substance 1 mol, which is equal to where p is the density of the liquid. From this we determine Avogadro's constant. The calculation method consists in determining the number of molecules in the amount of 1 mole of a substance based on the known values ​​of the molar mass and the mass of one molecule of the substance. The value of Avogadro's constant, according to modern data, is 6.022169*10 23 mol -1. Students can be introduced to the calculation method for determining Avogadro’s constant by asking them to calculate it from the values ​​of the molar masses of different substances. Schoolchildren should be introduced to the Loschmidt number, which shows how many molecules are contained in a unit volume of gas under normal conditions (it is equal to 2.68799 * 10 -25 m -3). Tenth graders can independently determine the Loschmidt number for several gases and show that it is the same in all cases. By giving examples, you can give the children an idea of ​​how large the number of molecules per unit volume is. If you make a puncture in a rubber balloon so thin that 1,000,000 molecules come out through it every second, you will need approximately 30 billion. years for all the molecules to come out. One method for determining the mass of molecules is based on Perrin's experiment, which assumed that resin drops in water behave in the same way as molecules in the atmosphere. Perrin counted the number of droplets in different layers of the emulsion, using a microscope to isolate layers 0.0001 cm thick. The height at which there were two times fewer such droplets than at the bottom was equal to h = 3 * 10 -5 m. The mass of one drop of resin turned out to be equal to M = 8.5*10 -18 kg. If our atmosphere consisted only of oxygen molecules, then at an altitude of H = 5 km the oxygen density would be half that of the Earth’s surface. Write down the proportion m/M=h/H, from which the mass of the oxygen molecule m=5.1*10 -26 kg is found. Students are asked to independently calculate the mass of a hydrogen molecule, the density of which is half that of the Earth’s surface, at an altitude of H=80 km. Currently, the molecular masses have been refined. For example, for oxygen the value is set to 5.31*10 -26 kg, and for hydrogen - 0.33*10 -26 kg. When discussing the issue of the speed of movement of molecules, students are introduced to Stern's classical experiment. When explaining an experiment, it is advisable to create a model of it using the “Rotating disk with accessories” device. Several matches are fixed on the edge of the disk in a vertical position, and a tube with a groove is placed in the center of the disk. When the disk is motionless, a ball lowered into the tube, rolling down the chute, knocks down one of the matches. Then the disk is rotated at a certain speed, recorded by the tachometer. The newly launched ball will deviate from the original direction of movement (relative to the disk) and knock down a match located at some distance from the first one. Knowing this distance, the radius of the disk and the speed of the ball on the rim of the disk, you can determine the speed of the ball along the radius. After this, it is advisable to consider the essence of the Stern experiment and the design of its installation, using the film fragment “The Stern Experience” for illustration. Discussing the results of Stern's experiment, attention is drawn to the fact that there is a certain distribution of molecules by speed, as evidenced by the presence of a strip of deposited atoms of a certain width, and the thickness of this strip is different. In addition, it is important to note that molecules moving at high speeds settle closer to the location opposite the slit. The greatest number of molecules has the most probable speed. It is necessary to inform students that theoretically, the law of the distribution of molecules by speed was discovered by J. C. Maxwell. The velocity distribution of molecules can be modeled on a Galton board. Schoolchildren have already studied the issue of the interaction of molecules in the 7th grade; in the 10th grade, knowledge on this issue is deepened and expanded. It is necessary to emphasize the following points: a) intermolecular interaction is of an electromagnetic nature; b) intermolecular interaction is characterized by forces of attraction and repulsion; c) the forces of intermolecular interaction act at distances no greater than 2-3 molecular diameters, and at this distance only the attractive force is noticeable, the repulsive forces are practically zero; d) as the distance between molecules decreases, the interaction forces increase, and the repulsive force grows faster (proportional to r -9) than the attractive force (proportional to r -7 ). Therefore, as the distance between the molecules decreases, the attractive force first prevails, then at a certain distance r o the attractive force is equal to the repulsive force, and with further approach the repulsive force predominates. It is advisable to illustrate all of the above with a graph of the dependence of first the attractive force, the repulsive force, and then the resultant force on the distance. It is useful to construct a graph of the potential energy of interaction, which can later be used when considering the aggregate states of matter. The attention of tenth graders is drawn to the fact that the state of stable equilibrium of interacting particles corresponds to the equality of the resultant forces of interaction to zero and the smallest value of their mutual potential energy. In a solid body, the interaction energy of particles (binding energy) is much greater than the kinetic energy of their thermal motion, therefore the movement of particles of a solid body represents vibrations relative to the nodes of the crystal lattice. If the kinetic energy of the thermal motion of molecules is much greater than the potential energy of their interaction, then the movement of the molecules is completely random and the substance exists in a gaseous state. If kinetic energy thermal motion of particles is comparable to the potential energy of their interaction, then the substance is in a liquid state.

 § 2. Molecular physics. Thermodynamics

Basic provisions of molecular kinetic theory(MCT) are as follows.
1. Substances consist of atoms and molecules.
2. Atoms and molecules are in continuous chaotic motion.
3. Atoms and molecules interact with each other with forces of attraction and repulsion
The nature of the movement and interaction of molecules can be different; in this regard, it is customary to distinguish between 3 states of aggregation of matter: solid, liquid and gaseous. The interactions between molecules are strongest in solids. In them, the molecules are located in the so-called nodes of the crystal lattice, i.e. in positions at which the forces of attraction and repulsion between molecules are equal. The motion of molecules in solids is reduced to vibrational motion around these equilibrium positions. In liquids, the situation is different in that, having oscillated around some equilibrium positions, the molecules often change them. In gases, molecules are far from each other, so the interaction forces between them are very small and the molecules move forward, occasionally colliding with each other and with the walls of the vessel in which they are located.
 Relative molecular weight M r called the ratio of the mass m o of a molecule to 1/12 of the mass of a carbon atom m oc:

In molecular physics, the amount of a substance is usually measured in moles.
 Molem ν is the amount of a substance that contains the same number of atoms or molecules (structural units) as there are in 12 g of carbon. This number of atoms in 12 g of carbon is called Avogadro's number:

 Molar mass M = M r 10 −3 kg/mol is the mass of one mole of a substance. The number of moles in a substance can be calculated using the formula

 The basic equation of the molecular kinetic theory of an ideal gas:

Where m 0- mass of the molecule; n- concentration of molecules; Ṽ - root mean square speed of molecules.

 2.1. Gas laws

 The equation of state of an ideal gas is the Mendeleev-Clapeyron equation:

 Isothermal process(Boyle-Mariotte law):
For a given mass of gas at a constant temperature, the product of pressure and its volume is a constant:

In coordinates p−V isotherm is a hyperbola, and in coordinates V−T And p−T- straight (see Fig. 4)

 Isochoric process(Charles' law):
For a given mass of gas at a constant volume, the ratio of pressure to temperature in degrees Kelvin is a constant value (see Fig. 5).

 Isobaric process(Gay-Lussac's law):
For a given mass of gas at constant pressure, the ratio of gas volume to temperature in degrees Kelvin is a constant value (see Fig. 6).

 Dalton's law:
If there is a mixture of several gases in a vessel, then the pressure of the mixture is equal to the sum of the partial pressures, i.e. those pressures that each gas would create in the absence of the others.

 2.2. Elements of thermodynamics

 Internal body energy equal to the sum of the kinetic energies of the random motion of all molecules relative to the center of mass of the body and the potential energies of interaction of all molecules with each other.
 Internal energy of an ideal gas represents the sum of the kinetic energies of the random movement of its molecules; Since the molecules of an ideal gas do not interact with each other, their potential energy vanishes.
For an ideal monatomic gas, the internal energy is

 Quantity of heat Q is a quantitative measure of the change in internal energy during heat exchange without performing work.
 Specific heat- this is the amount of heat that 1 kg of a substance receives or gives up when its temperature changes by 1 K

 Work in thermodynamics:
work during isobaric expansion of a gas is equal to the product of the gas pressure and the change in its volume:

 Law of conservation of energy in thermal processes (first law of thermodynamics):
the change in the internal energy of a 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:

Application of the first law of thermodynamics to isoprocesses:
 A) isothermal process T = const ⇒ ∆T = 0.
In this case, the change in internal energy of an ideal gas

Hence: Q = A.
All the heat transferred to the gas is spent on doing work against external forces;

 b) isochoric process V = const ⇒ ∆V = 0.
In this case, the gas work

Hence, ∆U = Q.
All heat transferred to the gas is spent on increasing its internal energy;

 V) isobaric process p = const ⇒ ∆p = 0.
In this case:

 Adiabatic is a process that occurs without heat exchange with the environment:

In this case A = −∆U, i.e. The change in the internal energy of the gas occurs due to the work done by the gas on external bodies.
When a gas expands, it does positive work. The work A performed by external bodies on a gas differs from the work done by a gas only in sign:

 The amount of heat required to warm the body in a solid or liquid state within one state of aggregation, calculated by the formula

where c is the specific heat capacity of the body, m is the mass of the body, t 1 is the initial temperature, t 2 is the final temperature.
 The amount of heat required to melt a body at the melting point, calculated by the formula

where λ is the specific heat of fusion, m is the mass of the body.
 Amount of heat required for evaporation, calculated by the formula

where r is the specific heat of vaporization, m is the body mass.

In order to convert part of this energy into mechanical energy, heat engines are most often used. Heat engine efficiency is the ratio of the work A performed by the engine to the amount of heat received from the heater:

The French engineer S. Carnot came up with an ideal heat engine with an ideal gas as a working fluid. The efficiency of such a machine

Air, which is a mixture of gases, contains water vapor along with other gases. Their content is usually characterized by the term “humidity”. A distinction is made between absolute and relative humidity.
 Absolute humidity is called the density of water vapor in the air - ρ ([ρ] = g/m3). Absolute humidity can be characterized by the partial pressure of water vapor - p([p] = mmHg; Pa).
 Relative humidity (ϕ)- the ratio of the density of water vapor present in the air to the density of the water vapor that would have to be contained in the air at this temperature for the vapor to be saturated. Relative humidity can be measured as the ratio of the partial pressure of water vapor (p) to the partial pressure (p0) that saturated vapor has at that temperature:

The content of the article

MOLECULAR KINETIC THEORY– a branch of molecular physics that studies the properties of matter based on ideas about their molecular structure and certain laws of interaction between the atoms (molecules) that make up the substance. It is believed that particles of matter are in continuous, random motion and this movement is perceived as heat.

Until the 19th century A very popular basis for the doctrine of heat was the theory of caloric or some liquid substance flowing from one body to another. Heating of bodies was explained by an increase, and cooling by a decrease in the caloric content contained within them. The concept of atoms for a long time seemed unnecessary for the theory of heat, but many scientists even then intuitively connected heat with the movement of molecules. So, in particular, thought the Russian scientist M.V. Lomonosov. A lot of time passed before the molecular kinetic theory finally won in the minds of scientists and became an integral property of physics.

Many phenomena in gases, liquids and solids find a simple and convincing explanation within the framework of molecular kinetic theory. So pressure, exerted by a gas on the walls of the vessel in which it is enclosed, is considered as the total result of numerous collisions of rapidly moving molecules with the wall, as a result of which they transfer their momentum to the wall. (Recall that it is the change in momentum per unit time that, according to the laws of mechanics, leads to the appearance of force, and the force per unit surface of the wall is pressure). The kinetic energy of particle motion, averaged over their huge number, determines what is commonly called temperature substances.

The origins of the atomistic idea, i.e. The idea that all bodies in nature consist of the smallest indivisible particles, atoms, goes back to the ancient Greek philosophers - Leucippus and Democritus. More than two thousand years ago, Democritus wrote: “... atoms are countless in size and number, but they rush around the universe, whirling in a whirlwind, and thus everything complex is born: fire, water, air, earth.” A decisive contribution to the development of molecular kinetic theory was made in the second half of the 19th century. the works of remarkable scientists J.C. Maxwell and L. Boltzmann, who laid the foundations for a statistical (probabilistic) description of the properties of substances (mainly gases) consisting of a huge number of chaotically moving molecules. The statistical approach was generalized (in relation to any state of matter) at the beginning of the 20th century. in the works of the American scientist J. Gibbs, who is considered one of the founders of statistical mechanics or statistical physics. Finally, in the first decades of the 20th century. physicists realized that the behavior of atoms and molecules obeys the laws not of classical, but of quantum mechanics. This gave a powerful impetus to the development of statistical physics and made it possible to describe a number of physical phenomena that previously could not be explained within the framework of the usual concepts of classical mechanics.

Molecular kinetic theory of gases.

Each molecule flying towards the wall, when colliding with it, transfers its momentum to the wall. Since the speed of a molecule during an elastic collision with a wall varies from the value v before - v, the magnitude of the transmitted pulse is 2 mv. Force acting on the wall surface D S in time D t, is determined by the magnitude of the total momentum transmitted by all molecules reaching the wall during this period of time, i.e. F= 2mv n c D S/D t, where n c defined by expression (1). For pressure value p = F/D S in this case we find: p = (1/3)nmv 2.

To obtain the final result, you can abandon the assumption of the same speed of molecules by identifying independent groups of molecules, each of which has its own approximately the same speed. Then the average pressure value is found by averaging the square of the velocity over all groups of molecules or

This expression can also be represented in the form

It is convenient to give this formula a different form by multiplying the numerator and denominator under the square root sign by Avogadro's number

N a= 6.023·10 23.

Here M = mN A– atomic or molecular mass, value R = kN A= 8.318·10 7 erg is called the gas constant.

The average speed of molecules in a gas, even at moderate temperatures, turns out to be very high. So, for hydrogen molecules (H2) at room temperature ( T= 293K) this speed is about 1900 m/s, for nitrogen molecules in the air - about 500 m/s. The speed of sound in air under the same conditions is 340 m/s.

Considering that n = N/V, Where V– volume occupied by gas, N is the total number of molecules in this volume; it is easy to obtain consequences from (5) in the form of the well-known gas laws. To do this, the total number of molecules is represented as N = vN A, Where v is the number of moles of gas, and equation (5) takes the form

(8) pV = vRT,

which is called the Clapeyron–Mendeleev equation.

Given that T= const the gas pressure changes in inverse proportion to the volume it occupies (Boyle–Mariotte law).

In a closed vessel of a fixed volume V= const pressure changes directly proportional to the change in absolute gas temperature T. If the gas is in conditions where its pressure remains constant p= const, but the temperature changes (such conditions can be achieved, for example, if a gas is placed in a cylinder closed with a movable piston), then the volume occupied by the gas will change in proportion to the change in its temperature (Gay-Lussac's law).

Let there be a mixture of gases in the vessel, i.e. There are several different kinds of molecules. In this case, the magnitude of the momentum transferred to the wall by molecules of each type does not depend on the presence of molecules of other types. It follows that the pressure of a mixture of ideal gases is equal to the sum of the partial pressures that each gas would create separately if it occupied the entire volume. This is another of the gas laws - the famous Dalton's law.

Molecular mean free path . One of the first who, back in the 1850s, gave reasonable estimates of the average thermal velocity of molecules of various gases was the Austrian physicist Clausius. The unusually large values ​​of these velocities he obtained immediately aroused objections. If the speeds of molecules are really so high, then the smell of any odorous substance should spread almost instantly from one end of a closed room to the other. In fact, the spread of odor occurs very slowly and occurs, as is now known, through a process called gas diffusion. Clausius, and later others, were able to provide a convincing explanation for this and other gas transport processes (such as thermal conductivity and viscosity) using the concept of mean free path molecules , those. the average distance a molecule travels from one collision to another.

Each molecule in a gas experiences a very large number of collisions with other molecules. In the interval between collisions, the molecules move almost in a straight line, experiencing sharp changes in speed only at the moment of the collision itself. Naturally, the lengths of straight sections along the path of a molecule can be different, so it makes sense to talk only about a certain average free path of molecules.

During time D t the molecule goes through a complex zigzag path equal to v D t. There are as many kinks in the trajectory along this path as there are collisions. Let Z means the number of collisions that a molecule experiences per unit time. The mean free path is then equal to the ratio of the path length N 2, for example, a» 2.0·10 –10 m. Table 1 shows the values ​​of l 0 in µm (1 µm = 10 –6 m) calculated using formula (10) for some gases under normal conditions ( p= 1 atm, T=273K). These values ​​turn out to be approximately 100–300 times greater than the intrinsic diameter of the molecules.