Modern ideas about mkt. Fundamentals of molecular kinetic theory

As a rule, we understand the world through so-called macroscopic bodies (Greek “macro” - large). These are all the bodies that surround us: houses, cars, water in a glass, water in the ocean, etc. We were interested in what was happening to these bodies and around them. Now we will also be interested in what happens inside bodies. A section of physics called MCT will help us answer this question.
MKT – molecular kinetic theory. It explains physical phenomena and properties of bodies from the point of view of their internal microscopic structure. This theory is based on three statements:

All bodies consist of small particles, between which there are gaps.
Particles of bodies constantly and randomly move.
Particles of bodies interact with each other: they attract and repel.

These statements are called the fundamental principles of the ICT. All of them are confirmed by numerous experiments.

With a macroscopic approach, we are interested in the bodies themselves: their size, volume, mass, energy, and so on. Take a look at the picture on the left. For example, when studying water splashes macroscopically, we will measure their size, volume, and mass.

With a microscopic approach, we are also interested in size, volume, mass and energy. However, not the bodies themselves, but those particles from which they consist: molecules, ions and atoms. This is exactly what the top picture symbolizes. But you should not think that molecules, ions and atoms can be seen with a magnifying glass. This drawing is just an artistic hyperbole. These particles can be seen only with the help of special, so-called electron microscopes.

MCT was not always a scientific theory. Having originated before our era, molecular (or, as it was called before, atomic) theory remained only a convenient hypothesis for more than two thousand years! And only in the 20th century it turns into a full-fledged physical theory. Here's how the famous physicist E. Rutherford talks about it:

“Not a single physicist or chemist can close his eyes to the enormous role that the atomic hypothesis currently plays in science. ... By the end of the 19th century, its ideas permeated a very large area of ​​physics and chemistry. The idea of ​​atoms became more and more concrete. ... The simplicity and usefulness of atomic views in explaining a wide variety of phenomena in physics and chemistry naturally raised the authority of this theory in the eyes of scientists. A tendency arose to consider the atomic hypothesis no longer as a useful working hypothesis, for which it is very difficult to find direct and convincing evidence, but as a. one of the firmly established facts of nature.

But there was also no shortage of scientists and philosophers who pointed out the unfoundedness of this theory, on which, however, so much was built. We can agree with the usefulness of the idea of ​​molecules to explain these experiments, but what confidence do we have that atoms really exist and are not just a fiction, a figment of our imagination? It must be said, however, that this lack of direct evidence has not at all shaken the faith of the vast majority of people of science in the granular structure of matter.

The denial of atomic theory has never contributed and will never contribute to the discovery of new facts. The great advantage of the atomic theory is that it gives us, so to speak, a tangible concrete idea of ​​matter, which not only serves us to explain many phenomena, but also renders us enormous service as a working hypothesis."

There are two methods for studying the properties of matter: molecular kinetic and thermodynamic.

The molecular kinetic theory interprets the properties of bodies that are directly observed experimentally (pressure, temperature, etc.) as the total result of the action of molecules. In doing so, she uses the statistical method, being interested not in the movement of individual molecules, but only in the average values ​​that characterize the movement of a huge collection of particles. Hence its other name – statistical physics.

Thermodynamics studies the macroscopic properties of bodies without being interested in their microscopic picture. Thermodynamics is based on several fundamental laws (called the principles of thermodynamics), established on the basis of a generalization of a large body of experimental facts. Thermodynamics and molecular-kinetic theory mutually complement each other, forming essentially a single whole.

Molecular kinetic theory called the doctrine of the structure and properties of matter based on the idea of ​​​​the existence of atoms and molecules as the smallest particles of a chemical substance. The molecular kinetic theory is based on three main principles:

• All substances - liquid, solid and gaseous - are formed from tiny particles - molecules, which themselves consist of atoms(“elementary molecules”). The molecules of a chemical substance can be simple or complex and consist of one or more atoms. Molecules and atoms are electrically neutral particles. Under certain conditions, molecules and atoms can acquire additional electrical charge and turn into positive or negative ions (anions and cations, respectively).
• Atoms and molecules are in continuous chaotic movement and interaction, the speed of which depends on temperature, and the nature of which depends on the state of aggregation of the substance.
• Particles interact with each other by forces that are electrical in nature. The gravitational interaction between particles is negligible.

Atom– the smallest chemically indivisible particle of an element (iron, helium, oxygen atom). Molecule- the smallest particle of a substance that retains its chemical properties. The molecule consists of one or more atoms (water - H 2 O - 1 oxygen atom and 2 hydrogen atoms). And he– an atom or molecule that has one or more electrons extra (or electrons missing).

Molecules are extremely small in size. Simple monatomic molecules have a size of the order of 10–10 m. Complex polyatomic molecules can have sizes hundreds and thousands of times larger.

The random chaotic movement of molecules is called thermal motion. The kinetic energy of thermal motion increases with increasing temperature. At low temperatures, molecules condense into a liquid or solid. As the temperature increases, the average kinetic energy of a molecule becomes greater, the molecules fly apart, and a gaseous substance is formed.

In solids, molecules undergo random vibrations around fixed centers (equilibrium positions). These centers can be located in space in an irregular manner (amorphous bodies) or form ordered volumetric structures (crystalline bodies).

In liquids, molecules have much greater freedom for thermal movement. They are not tied to specific centers and can move throughout the entire volume of liquid. This explains the fluidity of liquids.

In gases, the distances between molecules are usually much larger 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 wall of the container. The average distance between air molecules under normal conditions is about 10 –8 m, that is, hundreds of 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 arrive at the idea of ​​an ideal gas.

Ideal gas is a gas whose molecules do not interact with each other, with the exception of elastic collision processes, and are considered material points.

In molecular kinetic theory, the amount of matter is considered to be proportional to the number of particles. The unit of quantity of a substance is called a mole (mole). Mole- this is the amount of substance containing the same number of particles (molecules) as there are atoms in 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: N A = 6.022·10 23 mol –1.

Avogadro's constant is one of the most important constants in molecular kinetic theory. Quantity of substance is defined as the ratio of the number N particles (molecules) of matter to Avogadro's constant N A, or as the ratio of mass to molar mass:

The mass of one mole of a substance is usually called molar mass M. Molar mass is equal to the product of mass m 0 of one molecule of a given substance per Avogadro’s constant (that is, per the number of particles in one mole). Molar mass is expressed in kilograms per mole (kg/mol). For substances whose molecules consist of a single atom, the term atomic mass is often used. In the periodic table, molar mass is indicated in grams per mole. Thus we have another formula:

Where: M- molar mass, N A – Avogadro’s number, m 0 – mass of one particle of matter, N– the number of particles of a substance contained in the mass of a substance m. In addition, you will need the concept concentrations(number of particles per unit volume):

Let us also recall that the density, volume and mass of a body are related by the following formula:

If the problem involves a mixture of substances, then we talk about the average molar mass and average density of the substance. As when calculating the average speed of uneven movement, these values ​​are determined by the total masses of the mixture:

Do not forget that the total amount of a substance is always equal to the sum of the amounts of substances included in the mixture, and you need to be careful with the volume. Gas mixture volume Not equal to the sum of the volumes of gases included in the mixture. So, 1 cubic meter of air contains 1 cubic meter of oxygen, 1 cubic meter of nitrogen, 1 cubic meter of carbon dioxide, etc. For solids and liquids (unless otherwise specified in the condition), we can assume that the volume of the mixture is equal to the sum of the volumes of its parts.

Basic equation of MKT ideal gas

As they move, gas molecules continually collide with each other. Because of this, the characteristics of their movement change, therefore, when speaking about impulses, velocities, and kinetic energies of molecules, we always mean the average values ​​of these quantities.

The number of collisions of gas molecules under normal conditions with other molecules is measured millions of times per second. If we neglect the size and interaction of molecules (as in the ideal gas model), then we can assume that between successive collisions the molecules move uniformly and rectilinearly. Naturally, when approaching the wall of the vessel in which the gas is located, the molecule also experiences a collision with the wall. All collisions of molecules with each other and with the walls of the container are considered absolutely elastic collisions of balls. When it collides with a wall, the momentum of the molecule changes, which means that a force acts on the molecule from the side of the wall (remember Newton’s second law). But according to Newton's third law, with exactly the same force directed in the opposite direction, the molecule acts on the wall, exerting pressure on it. The totality of all impacts of all molecules on the wall of the vessel leads to the appearance of gas pressure. Gas pressure is the result of collisions of molecules with the walls of the container. If there is no wall or any other obstacle for the molecules, then the very concept of pressure loses its meaning. For example, it is completely unscientific to talk about pressure in the center of the room, because there the molecules do not press on the wall. Why then, when we place a barometer there, are we surprised to find that it shows some kind of pressure? Right! Because the barometer itself is the very wall on which the molecules press.

Since pressure is a consequence of the impacts of molecules on the wall of a vessel, it is obvious that its value should depend on the characteristics of individual molecules (on the average characteristics, of course, you remember that the speeds of all molecules are different). This dependence is expressed the basic equation of the molecular kinetic theory of an ideal gas:

Where: p- gas pressure, n- concentration of its molecules, m 0 - mass of one molecule, v kv - root mean square speed (note that the equation itself contains the square of the root mean square speed). The physical meaning of this equation is that it establishes a connection between the characteristics of the entire gas (pressure) and the parameters of the movement of individual molecules, that is, the connection between the macro- and microworld.

Corollaries from the basic MKT equation

As already noted in the previous paragraph, the speed of thermal movement of molecules is determined by the temperature of the substance. For an ideal gas, this dependence is expressed by simple formulas for root mean square speed movement of gas molecules:

Where: k= 1.38∙10 –23 J/K – Boltzmann constant, T– absolute temperature. Let’s immediately make a reservation that in future in all problems you should, without hesitation, convert the temperature into kelvins from degrees Celsius (except for problems on the heat balance equation). Law of Three Constants:

Where: R= 8.31 J/(mol∙K) – universal gas constant. The next important formula is the formula for average kinetic energy of translational motion of gas molecules:

It turns out that the average kinetic energy of the translational motion of molecules depends only on temperature and is the same at a given temperature for all molecules. And finally, the most important and frequently used consequences from the basic MKT equation are the following formulas:

Temperature measurement

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.

Thermal equilibrium- this is 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 all bodies in thermal equilibrium.

To measure temperature, physical instruments are used - thermometers, in which the temperature value is judged by a change in any physical parameter. To create a thermometer, you must select 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 thermometer designs use various 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. To do this, they are brought into thermal contact with bodies whose temperatures are considered given. Most often, simple natural systems are used in which the temperature remains unchanged despite heat exchange with the environment - a mixture of ice and water and a mixture of water and steam when boiling at normal atmospheric pressure. On the Celsius temperature scale, the melting point of ice is assigned a temperature of 0°C, and the boiling point of water: 100°C. The change in the length of the liquid column in the capillaries of the thermometer per one hundredth of the length between the marks of 0°C and 100°C is taken equal to 1°C.

The English physicist W. Kelvin (Thomson) in 1848 proposed using the point of zero gas pressure to construct a new temperature scale (Kelvin scale). In this scale, the temperature unit is the same as in the Celsius scale, but the zero point is shifted:

In this case, a temperature change of 1ºC corresponds to a temperature change of 1 K. Temperature changes on the Celsius and Kelvin scales are equal. In the SI system, the unit of temperature measured on the Kelvin scale is called kelvin and denoted by the letter K. For example, room temperature T C = 20°C on the Kelvin scale is T K = 293 K. The Kelvin temperature scale is called the absolute temperature scale. It turns out to be most convenient when constructing physical theories.

Equation of state of an ideal gas or Clapeyron-Mendeleev equation

Equation of state of an ideal gas is another consequence of the basic MKT equation and is written in the form:

This equation establishes a relationship between the main parameters of the state of an ideal gas: pressure, volume, amount of substance and temperature. It is very important that these parameters are interconnected; changing any of them will inevitably lead to changing at least one more. That is why this equation is called the equation of state of an ideal gas. It was discovered first for one mole of gas by Clapeyron, and subsequently generalized to the case of a larger number of moles by Mendeleev.

If the gas temperature is T n = 273 K (0°C), and pressure p n = 1 atm = 1 10 5 Pa, then they say that the gas is at normal conditions.

Gas laws

Solving problems for calculating gas parameters is greatly simplified if you know which law and which formula to apply. So, let's look at the basic gas laws.

1. Avogadro's law. One mole of any substance contains the same number of structural elements, equal to Avogadro's number.

2. Dalton's law. The pressure of a mixture of gases is equal to the sum of the partial pressures of the gases included in this mixture:

The partial pressure of a gas is the pressure it would produce if all the other gases suddenly disappeared from the mixture. For example, air pressure is equal to the sum of the partial pressures of nitrogen, oxygen, carbon dioxide and other impurities. In this case, each of the gases in the mixture occupies the entire volume provided to it, that is, the volume of each of the gases is equal to the volume of the mixture.

3. Boyle-Mariotte law. If the mass and temperature of the gas remain constant, then the product of the gas pressure and its volume does not change, therefore:

A process occurring at a constant temperature is called isothermal. Note that this simple form of the Boyle-Marriott law only holds if the mass of the gas remains constant.

4. Gay-Lussac's law. Gay-Lussac's law itself is not of particular value when preparing for exams, so we will give only a corollary from it. If the mass and pressure of the gas remain constant, then the ratio of the volume of the gas to its absolute temperature does not change, therefore:

A process that occurs at constant pressure is called isobaric or isobaric. Note that this simple form of Gay-Lussac's law only holds if the mass of the gas remains constant. Don't forget about converting temperature from degrees Celsius to Kelvin.

5. Charles's law. Like Gay-Lussac’s law, Charles’s law in its exact formulation is not important for us, so we will only give a corollary from it. If the mass and volume of the gas remain constant, then the ratio of the gas pressure to its absolute temperature does not change, therefore:

A process occurring at constant volume is called isochoric or isochoric. Note that this simple form of Charles's law only holds if the mass of the gas remains constant. Don't forget about converting temperature from degrees Celsius to Kelvin.

6. Universal gas law (Clapeyron). At a constant mass of a gas, the ratio of the product of its pressure and volume to temperature does not change, therefore:

Please note that the mass must remain the same, and do not forget about kelvins.

So, there are several gas laws. We list the signs that you need to use one of them when solving a problem:

1. Avogadro's law applies to all problems involving the number of molecules.
2. Dalton's law applies to all problems involving a mixture of gases.
3. Charles's law is used in problems where the volume of gas remains constant. Usually this is either stated explicitly, or the problem contains the words “gas in a closed vessel without a piston.”
4. Gay-Lussac's law is applied if the gas pressure remains unchanged. Look for the words “gas in a vessel closed by a movable piston” or “gas in an open vessel” in the problems. Sometimes nothing is said about the vessel, but according to the condition it is clear that it communicates with the atmosphere. Then it is assumed that atmospheric pressure always remains unchanged (unless otherwise stated in the condition).
5. Boyle-Marriott law. This is where it's most difficult. It’s good if the problem says that the temperature of the gas is constant. It’s a little worse if the word “slow” is present in the condition. For example, a gas is slowly compressed or slowly expanded. It is even worse if it is said that the gas is closed by a heat-non-conducting piston. Finally, it’s really bad if nothing is said about the temperature, but from the condition it can be assumed that it does not change. Usually in this case, students apply the Boyle-Marriott law out of despair.
6. Universal gas law. It is used if the mass of the gas is constant (for example, the gas is in a closed vessel), but according to the condition it is clear that all other parameters (pressure, volume, temperature) change. In general, you can often use the Clapeyron-Mendeleev equation instead of the universal law; you will get the correct answer, only you will write two extra letters in each formula.

Graphic representation of isoprocesses

In many branches of physics, it is convenient to depict the dependence of quantities on each other graphically. This makes it easier to understand the relationships between parameters occurring in a process system. This approach is very often used in molecular physics. The main parameters describing the state of an ideal gas are pressure, volume and temperature. The graphical method for solving problems consists of depicting the relationship of these parameters in various gas coordinates. There are three main types of gas coordinates: ( p; V), (p; T) And ( V; T). Note that these are just the basic (most common types of coordinates). The imagination of the writers of problems and tests is not limited, so you can come across any other coordinates. So, let us depict the main gas processes in the main gas coordinates.

Isobaric process (p = const)

An isobaric process is a process that occurs at constant pressure and mass of gas. As follows from the equation of state of an ideal gas, in this case the volume changes in direct proportion to the temperature. Graphs of the isobaric process in coordinates R–V; V–T And R–T have the following form:

V–T coordinates is directed exactly to the origin, but this graph can never start directly from the origin, since at very low temperatures the gas turns into a liquid and the dependence of volume on temperature changes.

Isochoric process (V = const)

An isochoric process is the process of heating or cooling a gas at a constant volume and provided that the amount of substance in the vessel remains unchanged. As follows from the equation of state of an ideal gas, under these conditions the gas pressure changes in direct proportion to its absolute temperature. Graphs of an isochoric process in coordinates R–V; R–T And V–T have the following form:

Please note that the continuation of the graph in p–T coordinates is directed exactly to the origin, but this graph can never start directly from the origin, since gas turns into liquid at very low temperatures.

Isothermal process (T = const)

An isothermal process is a process that occurs at a constant temperature. From the equation of state of an ideal gas it follows that at a constant temperature and a constant amount of substance in the vessel, the product of the gas pressure and its volume must remain constant. Graphs of an isothermal process in coordinates R–V; R–T And V–T have the following form:

Note that when performing tasks on graphs in molecular physics Not special accuracy is required in plotting coordinates along the corresponding axes (for example, so that the coordinates p 1 and p 2 two states of gas in the system p(V) coincided with the coordinates p 1 and p 2 of these states in the system p(T). Firstly, these are different coordinate systems in which different scales can be chosen, and secondly, this is an unnecessary mathematical formality that distracts from the main thing - the analysis of the physical situation. The main requirement: that the quality of the graphs be correct.

Nonisoprocesses

In problems of this type, all three main gas parameters change: pressure, volume and temperature. Only the mass of the gas remains constant. The simplest case is if the problem is solved “head-on” using the universal gas law. It’s a little more difficult if you need to find an equation for a process that describes a change in the state of a gas, or analyze the behavior of gas parameters using this equation. Then you need to act like this. Write down this equation of the process and the universal gas law (or the Clapeyron-Mendeleev equation, whichever is more convenient for you) and consistently eliminate unnecessary quantities from them.

Change in quantity or mass of a substance

In essence, there is nothing complicated in such tasks. You just need to remember that the gas laws are not satisfied, since the formulations of any of them say “at constant mass.” Therefore, we act simply. We write the Clapeyron-Mendeleev equation for the initial and final states of the gas and solve the problem.

Baffles or pistons

In problems of this type, gas laws are again applied, and the following remarks must be taken into account:

• Firstly, gas does not pass through the partition, that is, the mass of gas in each part of the vessel remains unchanged, and thus the gas laws are satisfied for each part of the vessel.
• Secondly, if the partition is heat-non-conducting, then when the gas is heated or cooled in one part of the vessel, the temperature of the gas in the second part will remain unchanged.
• Thirdly, if the partition is movable, then the pressures on both sides are equal at any given moment in time (but this pressure, equal on both sides, can change over time).
• And then we write gas laws for each gas separately and solve the problem.

Gas laws and hydrostatics

The specificity of the problems is that in the pressure it will be necessary to take into account the “add-on weights” associated with the pressure of the liquid column. What options might there be:

• A container containing gas is submerged under water. The pressure in the vessel will be equal to: p = p atm + ρgh, Where: h– immersion depth.
• Horizontal the tube is closed from the atmosphere by a column of mercury (or other liquid). The gas pressure in the tube is exactly equal to: p = p atm atmospheric, since a horizontal column of mercury does not exert pressure on the gas.
• Vertical the gas tube is closed on top with a column of mercury (or other liquid). Gas pressure in the tube: p = p atm + ρgh, Where: h– height of the mercury column.
• A vertical narrow tube containing gas is turned with the open end down and is sealed with a column of mercury (or other liquid). Gas pressure in the tube: p = p atm – ρgh, Where: h– height of the mercury column. The “–” sign is used because mercury does not compress, but stretches the gas. Students often ask why the mercury does not flow out of the tube. Indeed, if the tube were wide, the mercury would flow down the walls. And so, since the tube is very narrow, surface tension does not allow the mercury to rupture in the middle and let air in, and the gas pressure inside (less than atmospheric) keeps the mercury from flowing out.

Once you have been able to correctly record the gas pressure in the tube, apply one of the gas laws (usually Boyle-Mariotte, since most of these processes are isothermal, or the universal gas law). Apply the chosen law for gas (in no case for liquid) and solve the problem.

Thermal expansion of bodies

As the temperature rises, the intensity of the thermal movement of particles of a substance increases. This causes the molecules to more “actively” repel each other. Because of this, most bodies increase in size when heated. Don't make the typical mistake; atoms and molecules themselves do not expand when heated. Only the empty spaces between molecules increase. The thermal expansion of gases is described by Gay-Lussac's law. The thermal expansion of liquids obeys the following law:

Where: V 0 – volume of liquid at 0°C, V- at a temperature t, γ – coefficient of volumetric expansion of the liquid. Please note that all temperatures in this topic must be taken in degrees Celsius. The coefficient of volumetric expansion depends on the type of liquid (and on temperature, which is not taken into account in most problems). Please note that the numerical value of the coefficient, expressed in 1/°C or 1/K, is the same, since heating a body by 1°C is the same as heating it by 1 K (and not by 274 K).

For expansion of solids Three formulas are used to describe the change in linear dimensions, area and volume of a body:

Where: l 0 , S 0 , V 0 – length, surface area and volume of the body at 0°C, respectively, α – coefficient of linear expansion of the body. The coefficient of linear expansion depends on the type of body (and on temperature, which is not taken into account in most problems) and is measured in 1/°C or 1/K.

Successful, diligent and responsible implementation of these three points will allow you to show an excellent result at the CT, the maximum of what you are capable of.

Found a mistake?

If you think you have found an error in the training materials, please write about it by email. You can also report an error on the social network (). In the letter, indicate the subject (physics or mathematics), the name or number of the topic or test, the number of the problem, or the place in the text (page) where, in your opinion, there is an error. Also describe what the suspected error is. Your letter will not go unnoticed, the error will either be corrected, or you will be explained why it is not an error.

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?

Molecular kinetic theory (MKT) is a doctrine that explains thermal phenomena in macroscopic bodies and the internal properties of these bodies by the movement and interaction of atoms, molecules and ions that make up the bodies. The MCT structure of matter is based on three principles:

1. Matter consists of particles - molecules, atoms and ions. The composition of these particles includes smaller elementary particles. A molecule is the smallest stable particle of a given substance. The molecule has the basic chemical properties of a substance. A molecule is the limit of division of a substance, that is, the smallest part of a substance that is capable of maintaining the properties of this substance. An atom is the smallest particle of a given chemical element.
2. The particles that make up matter are in continuous chaotic (disorderly) motion.
3. Particles of matter interact with each other - they attract and repel.

These basic provisions are confirmed experimentally and theoretically.

Composition of the substance

Modern instruments make it possible to observe images of individual atoms and molecules. Using an electron microscope or an ion projector (microscope), you can image individual atoms and estimate their sizes. The diameter of any atom is of the order of d = 10 -8 cm (10 -10 m). Molecules are larger than atoms. Since molecules are made up of several atoms, the greater the number of atoms in a molecule, the larger its size. The sizes of molecules range from 10 -8 cm (10 -10 m) to 10 -5 cm (10 -7 m).

Chaotic particle movement

The continuous chaotic movement of particles is confirmed by Brownian motion and diffusion. Random motion means that molecules do not have any preferred paths and their movements have random directions. This means that all directions are equally probable.

Diffusion(from Latin diffusion - spreading, spreading) - a phenomenon when, as a result of the thermal movement of a substance, spontaneous penetration of one substance into another occurs (if these substances come into contact).

Mutual mixing of substances occurs due to the continuous and random movement of atoms or molecules (or other particles) of the substance. Over time, the depth of penetration of molecules of one substance into another increases. The depth of penetration depends on temperature: the higher the temperature, the greater the speed of movement of the particles of the substance and the faster the diffusion occurs.

Diffusion is observed in all states of matter - in gases, liquids and solids. An example of diffusion in gases is the spread of odors in the air in the absence of direct mixing. Diffusion in solids ensures the connection of metals during welding, soldering, chrome plating, etc. Diffusion occurs much faster in gases and liquids than in solids.

The existence of stable liquid and solid bodies is explained by the presence of intermolecular interaction forces (forces of mutual attraction and repulsion). The same reasons explain the low compressibility of liquids and the ability of solids to resist compressive and tensile deformations.

The forces of intermolecular interaction are of an electromagnetic nature—they are forces of electrical origin. The reason for this is that molecules and atoms consist of charged particles with opposite signs of charges - electrons and positively charged atomic nuclei. In general, molecules are electrically neutral. In terms of its electrical properties, a molecule can be approximately considered as an electric dipole.

The force of interaction between molecules has a certain dependence on the distance between the molecules. This dependence is shown in Fig. 1.1. Shown here are the projections of interaction forces onto a straight line that passes through the centers of the molecules.

Rice. 1.1. Dependence of intermolecular forces on the distance between interacting atoms.

As we see, as the distance between molecules r decreases, the force of attraction F r pr increases (red line in the figure). As already mentioned, the forces of attraction are considered to be negative, therefore, as the distance decreases, the curve goes down, that is, into the negative zone of the graph.

Attractive forces act as two atoms or molecules approach each other, as long as the distance r between the centers of the molecules is in the region of 10 -9 m (2-3 molecular diameters). As this distance increases, the attractive forces weaken. Attractive forces are short-range forces.

Where a– coefficient depending on the type of attractive forces and the structure of interacting molecules.

With further approach of atoms or molecules at distances between the centers of the molecules of the order of 10 -10 m (this distance is comparable to the linear dimensions of inorganic molecules), repulsive forces F r from (blue line in Fig. 1.1) appear. These forces appear due to the mutual repulsion of positively charged atoms in the molecule and decrease with increasing distance r even faster than the attractive forces (as can be seen on the graph - the blue line tends to zero more “steeply” than the red one).

Where b– coefficient depending on the type of repulsive forces and the structure of interacting molecules.

At a distance r = r 0 (this distance is approximately equal to the sum of the radii of the molecules), the attractive forces balance the repulsive forces, and the projection of the resulting force F r = 0. This state corresponds to the most stable arrangement of interacting molecules.

In general, the resulting force is:

For r > r 0, the attraction of molecules exceeds repulsion; for r< r 0 – отталкивание молекул превосходит их притяжение.

The dependence of the interaction forces between molecules on the distance between them qualitatively explains the molecular mechanism of the appearance of elastic forces in solids.

When a solid body is stretched, the particles move away from each other at distances exceeding r 0 . In this case, attractive forces of molecules appear, which return the particles to their original position.

When a solid body is compressed, the particles approach each other at distances smaller than the distance r 0 . This leads to an increase in repulsive forces, which return the particles to their original position and prevent further compression.

If the displacement of molecules from equilibrium positions is small, then the interaction forces grow linearly with increasing displacement. On the graph, this segment is shown as a thick, light green line.

Therefore, at small deformations (millions of times greater than the size of the molecules), Hooke's law is satisfied, according to which the elastic force is proportional to the deformation. At large displacements, Hooke's law does not apply.

MOLECULAR KINETIC THEORY
a branch of molecular physics that examines many properties of substances based on the concept of the rapid chaotic movement of a huge number of atoms and molecules of which these substances are composed. The molecular kinetic theory focuses not on the differences between individual types of atoms and molecules, but on the common features of their behavior. Even the ancient Greek philosophers, who were the first to express atomistic ideas, believed that atoms were in continuous motion. D. Bernoulli tried to give a quantitative analysis of this movement in 1738. A fundamental contribution to the development of molecular kinetic theory was made in the period from 1850 to 1900 by R. Clausius in Germany, L. Boltzmann in Austria and J. Maxwell in England. These same physicists laid the foundations of statistical mechanics, a more abstract discipline that studies the same subject as molecular kinetic theory, but without constructing detailed, and therefore less general, models. Deepening of the statistical approach at the beginning of the 20th century. associated mainly with the name of the American physicist J. Gibbs, who is considered one of the founders of statistical mechanics. Revolutionary ideas were also introduced into this science by M. Planck and A. Einstein. In the mid-1920s, classical mechanics finally gave way to new, quantum mechanics. It gave impetus to the development of statistical mechanics, which continues to this day.
MOLECULAR KINETIC THEORY OF HEAT
It is known that heated bodies, when cooling, give up part of their heat to colder bodies. Until the 19th century It was believed that heat is a kind of liquid (caloric) flowing from one body to another. One of the main achievements of physics of the 19th century. What happened was that heat began to be considered simply as one of the forms of energy, namely the kinetic energy of atoms and molecules. This idea applies to all substances - solid, liquid and gaseous. Particles of a heated body move faster than those of a cold body. For example, the sun's rays, heating our skin, cause its molecules to vibrate faster, and we feel these vibrations as heat. In a cold wind, air molecules, colliding with molecules on the surface of our body, take away energy from them, and we feel cold. In all cases, when heat is transferred from one body to another, the movement of particles in the first of them slows down, in the second it accelerates, and the energy of the particles of the second body increases exactly as much as the energy of the particles of the first decreases. Many familiar thermal phenomena can be directly explained using molecular kinetic theory. Since heat is generated by the random movement of molecules, it is possible to increase the temperature of a body (increase the heat reserve in it) not through the supply of heat, but, for example, through friction: molecules of rubbing surfaces, colliding with each other, begin to move more intensely, and the temperature of the surfaces increases . For the same reason, a piece of iron heats up when it is struck with a hammer. Another thermal phenomenon is an increase in gas pressure when heated. As the temperature rises, the speed of movement of the molecules increases, they hit the walls of the vessel in which the gas is located more often and harder, which manifests itself in an increase in pressure. The gradual evaporation of liquids is explained by the fact that their molecules one after another pass into the air, while the fastest of them evaporate first, and those that remain have less energy on average. This is why when liquids evaporate from a wet surface, it cools. The mathematical apparatus, built on the molecular kinetic theory, makes it possible to analyze these and many other effects based on the equations of molecular motion and the general principles of probability theory. Let's assume that we raised the rubber ball to a certain height and then released it from our hands. The ball will hit the floor and then bounce several times, each time to a lower height than before, because upon impact some of its kinetic energy is converted into heat. This type of impact is called partially elastic. A piece of lead does not bounce off the floor at all - at the first impact, all its kinetic energy is converted into heat, and the temperature of the piece of lead and the floor rises slightly. Such an impact is called absolutely inelastic. An impact in which all the kinetic energy of a body is conserved without being converted into heat is called absolutely elastic. In gases, when atoms and molecules collide with each other, only an exchange of their velocities occurs (we are not considering here the case when, as a result of collisions, gas particles interact and enter into chemical reactions); the total kinetic energy of the entire set of atoms and molecules cannot be converted into heat, since it already is. The continuous movement of atoms and molecules of a substance is called thermal motion. In liquids and solids the picture is more complex: in addition to kinetic energy, it is also necessary to take into account the potential energy of particle interaction.
Thermal movement in air. If air is cooled to a very low temperature, it will turn into liquid, and the volume of liquid formed will be very small. For example, when 1200 cm3 of atmospheric air is liquefied, 2 cm3 of liquid air is obtained. The main assumption of atomic theory is that the sizes of atoms and molecules hardly change when the aggregate state of a substance changes. Consequently, in atmospheric air the molecules must be separated from each other at distances much greater than in a liquid. Indeed, out of 1200 cm3 of atmospheric air, more than 1198 cm3 is occupied by empty space. Air molecules move chaotically in this space at very high speeds, constantly colliding with each other like billiard balls.
Gas or steam pressure. Consider a rectangular vessel, per unit volume of which there are n gas molecules of mass m each. We will be interested only in those molecules that hit one of the walls of the vessel. Let us choose the x axis so that it is perpendicular to this wall and consider a molecule whose velocity component v along the axis we have chosen is equal to vx. When a molecule hits the wall of a container, its momentum in the x-axis direction will change by -2mvx. In accordance with Newton's third law, the same will be the impulse transferred to the wall. It can be shown that if all molecules move at the same speeds, then per unit wall area of ​​1 s (1/2) nvx molecules collide. To verify this, consider a boundary layer of gas near one of the walls, filled with molecules with the same values ​​of v and vx (Fig. 1). Let us assume that the thickness of this layer is so small that most molecules fly through it without collisions. Molecule A will reach the wall at time t = l /vx; by this time exactly half of the molecules from the boundary layer will hit the wall (the other half is moving away from the wall). Their number is determined by the gas density and the volume of the boundary layer with area A and thickness l: N = (1/2) nAl. Then the number of molecules hitting a unit area in 1 s will be N/At = (1/2) nvx, and the total momentum transferred to this area in 1 s will be equal to (1/2) nvx × 2mvx = nmvx2. In fact, the component vx is not the same for different molecules, so the value vx2 should be replaced by its average value

and">

We obtain the same relation if, instead of the random movement of molecules in all directions, we consider the movement of one sixth of their number perpendicular to each of the six faces of a rectangular vessel, assuming that each molecule has kinetic energy
Boyle's Law - Mariotte. In formula (1), n ​​does not denote the total number of molecules, but the number of molecules per unit volume. If the same number of molecules is placed in half the volume (without changing the temperature), then the value of n will double, and the pressure will also double if v2 does not depend on density. In other words, at constant temperature, gas pressure is inversely proportional to volume. The English physicist R. Boyle and the French physicist E. Mariotte experimentally established that at low pressures this statement is true for any gas. Thus, the Boyle-Mariotte law can be explained by making the reasonable assumption that at low pressures the speed of molecules does not depend on n.
Dalton's law. If the vessel contains a mixture of gases, i.e. There are several different types of molecules, then the momentum transferred to the wall by molecules of each type does not depend on whether molecules of other types are present. Thus, according to molecular kinetic theory, the pressure of a mixture of two or more ideal gases is equal to the sum of the pressures that each gas would create if it occupied the entire volume. This is Dalton's law, which governs gas mixtures at low pressures.
Molecular speeds. Formula (1) allows us to estimate the average speed of gas molecules. Thus, atmospheric pressure at sea level is approximately 106 dyne/cm2 (0.1 MPa), and the mass of 1 cm3 of air is 0.0013 g. Substituting these values ​​into formula (1), we obtain a very large value for the speed of molecules:

At high altitudes above sea level, where the atmosphere is very thin, air molecules can travel great distances in a second without colliding with each other. A different picture is observed at the Earth's surface: in 1 s, each molecule collides with other molecules on average approx. 800 million times. It describes a highly curved trajectory, and in the absence of air currents after one second with a high probability it ends up at a distance of only 1-2 cm from the place where it was at the beginning of this second.
Avogadro's law. As we have already said, air at room temperature has a density of approximately 0.0013 g/cm3 and creates a pressure MOLECULAR KINETIC THEORY of 106 dynes/cm2. Hydrogen gas, whose density at room temperature is only 0.00008 g/cm3, also creates a pressure of 106 dynes/cm2. According to formula (1), gas pressure is proportional to the number of molecules per unit volume and their average kinetic energy. In 1811, the Italian physicist A. Avogadro put forward a hypothesis according to which equal volumes of different gases at the same temperature and pressure contain the same number of molecules. If this hypothesis is correct, then from relation (1) we obtain that for different gases under the above conditions, the value (1/2) mv2 is the same, i.e. the average kinetic energy of the molecules is the same. This conclusion is quite consistent with the molecular kinetic theory
(see also HEAT).
The mass of 1 cm3 of hydrogen is small not because there are fewer molecules present in a given volume, but because the mass of each hydrogen molecule is several times less than the mass of a molecule of nitrogen or oxygen - the gases that mainly make up air. It has been established that the number of molecules of any gas in 1 cm3 at 0 ° C and normal atmospheric pressure is 2.687 * 10 19.
Average free path. An important quantity in the molecular kinetic theory of gases is the average distance traveled by a molecule between two collisions. This quantity is called the mean free path and is denoted by L. It can be calculated as follows. Let's imagine that molecules are spheres of radius r; then their centers upon collision will be at a distance 2r from each other. During its movement, the molecule “touches” all molecules within a cross section of area p (2r)2 and, moving a distance L, it “touches” all molecules in the volume 4pr2L, so that the average number of molecules it collides with will be equal to 4pr2Ln . To find L, you need to take this number equal to 1, whence

From this relationship one can directly find the radius of the molecule if the value of L is known (it can be found from measurements of gas viscosity; see below). The value of r turns out to be of the order of 10-8 cm, which is consistent with the results of other measurements, and L for typical gases under normal conditions ranges from 100 to 200 molecular diameters. The table shows L values ​​for atmospheric air at different altitudes above sea level.
VELOCITY DISTRIBUTION OF MOLECULES
In the middle of the 19th century. not only the development of molecular kinetic theory took place, but also the formation of thermodynamics. Some concepts of thermodynamics turned out to be useful for molecular kinetic theory - first of all, absolute temperature and entropy.
Thermal equilibrium. In thermodynamics, the properties of substances are considered mainly based on the idea that any system tends to a state with the highest entropy and, having reached such a state, cannot spontaneously leave it. This idea is consistent with the molecular kinetic description of gas behavior. A collection of gas molecules has a certain total energy that can be distributed between individual molecules in a huge number of ways. Whatever the initial distribution of energy, if the gas is left to its own devices, the energy will quickly be redistributed and the gas will reach a state of thermal equilibrium, i.e. to the state with the highest entropy. Let's try to formulate this statement more strictly. Let N (E) dE be the number of gas molecules with kinetic energy in the range from E to E + dE. Regardless of the initial distribution of energy, the gas, left to its own devices, will come to a state of thermal equilibrium with a characteristic function N (E) corresponding to the steady-state temperature. Instead of energies, we can consider the velocities of molecules. Let us denote by f (v) dv the number of molecules with velocities ranging from v to v + dv. There is always a certain number of molecules in a gas with velocities in the range from v to v + dv. Already a moment later, none of these molecules will have a speed that lies in the specified interval, since they will all undergo one or more collisions. But other molecules with velocities that previously differed significantly from v will, as a result of collisions, acquire velocities lying in the interval from v to v + dv. If the gas is in a stationary state, then the number of molecules that will acquire speed v, after a sufficiently large period of time, will be equal to the number of molecules whose speed will cease to be equal to v. Only in this case can the function n(v) remain constant. This number, of course, depends on the velocity distribution of gas molecules. The form of this distribution in a gas at rest was established by Maxwell: if there are N molecules in total, then the number of molecules with velocities in the interval from v to v + dv is equal to

where parameter b depends on temperature (see below).
Gas laws. The above estimates for the average speed of air molecules at sea level corresponded to ordinary temperature. According to the molecular kinetic theory, the kinetic energy of all gas molecules is the heat that it possesses. At higher temperatures, the molecules move faster and the gas contains more heat. As follows from formula (1), if the volume of a gas is constant, then with increasing temperature its pressure increases. This is exactly how all gases behave (Charles' law). If a gas is heated at constant pressure, it will expand. It has been established that at low pressure for any gas of volume V containing N molecules, the product of pressure and volume is proportional to the absolute temperature:

where T is the absolute temperature, k is a constant. From Avogadro's law it follows that the value of k is the same for all gases. It is called Boltzmann's constant and is equal to 1.38*10 -14 erg/K. Comparing expressions (1) and (3), it is easy to notice that the total energy of translational motion of N molecules, equal to (1/2) Nmv2, is proportional to the absolute temperature and is equal to

On the other hand, having integrated expression (2), we obtain that the total energy of translational motion of N molecules is equal to 3Nm / 4b 2. Hence

Substituting expression (5) into formula (2), you can find the distribution of molecules by speed at any temperature T. The molecules of many common gases, for example nitrogen and oxygen (the main components of atmospheric air), consist of two atoms, and their molecule resembles a dumbbell in shape . Each such molecule not only moves forward with enormous speed, but also rotates very quickly. In addition to the energy of translational motion, N molecules have the energy of rotational motion NkT, so the total energy of N molecules is equal to (5/2) NkT.
Experimental verification of the Maxwell distribution. In 1929, it became possible to directly determine the velocity distribution of gas molecules. If you make a small hole or cut a narrow slit in the wall of a vessel containing gas or vapor at a certain temperature, the molecules will fly out through them, each at their own speed. If the hole leads into another vessel from which the air has been evacuated, then most of the molecules will have time to fly a distance of several centimeters before the first collision. In the installation schematically shown in Fig. 2, there is a vessel V containing gas or vapor, the molecules of which fly out through the slit S1; S2 and S3 - slots in the transverse plates; W1 and W2 are two disks mounted on a common shaft R. Several radial slots are cut into each disk. Slit S3 is located so that, if there were no disks, molecules flying out of slit S1 and passing through slit S2 would also fly through slit S3 and fall on detector D. If one of the slits of disk W1 is opposite slit S2, then the molecules that fly through through the slots S1 and S2, will also pass through the slot of the disk W1, but they will be delayed by the disk W2 mounted on the shaft R so that its slots do not coincide with the slots of the disk W1. If the disks are stationary or rotate slowly, then the molecules from the vessel V do not enter the detector D. If the disks rotate rapidly at a constant speed, then some of the molecules pass through both disks. It is not difficult to understand which molecules will be able to overcome both obstacles - those that will cover the distance from W1 to W2 in the time required to shift the disk slit W2 to the desired angle. For example, if all the slits of disk W2 are rotated at an angle of 2° relative to the slits of disk W1, then the molecules that fly from W1 to W2 during the rotation of disk W2 by 2° will enter the detector. By changing the rotation frequency of the shaft with disks, it is possible to measure the velocities of molecules escaping from the vessel V and construct their distribution. The distribution obtained in this way agrees well with the Maxwellian one.

Saturated vapor pressure. If you pour some water into a large closed vessel that contains air but no water vapor, some of it will immediately evaporate and particles of steam will begin to spread throughout the vessel. If the volume of the vessel is very large compared to the volume of water, then evaporation will continue until all the water turns into steam. If a lot of water is poured, then not all of it will evaporate; the evaporation rate will gradually decrease and eventually the process will stop - the volume of the vessel will become saturated with water vapor. From the standpoint of molecular kinetic theory, this is explained as follows. From time to time, one or another water molecule located in a liquid medium near the surface receives enough energy from neighboring molecules to escape into the vapor-air environment. Here it collides with other similar molecules and with air molecules, describing a very intricate zigzag trajectory. In its movement, it also hits the walls of the vessel and the surface of the water; in this case, it can bounce off the water or be absorbed by it. While water evaporates, the number of vapor molecules it captures from the air-steam environment remains less than the number of molecules leaving the water. But there comes a moment when these values ​​are equalized - equilibrium is established, and the steam pressure reaches saturation. In this state, the number of molecules per unit volume of vapor above the liquid remains constant (of course, if the temperature is constant). The same picture is observed for solids, but for most bodies, vapor pressure becomes noticeable only at high temperatures.
VIBRATIONS OF ATOMS IN SOLIDS AND LIQUIDS
When examining a well-preserved ancient Greek or Roman gem under a microscope, you can see that its details remain as clear as they apparently were when the gem first left the hands of the master who made it. It is clear that over a huge period of time, only very few atoms were able to “break out” from the surface of the stone from which the gem was made - otherwise its details would have lost clarity over time. Most atoms of a solid can only perform oscillatory movements relative to a certain fixed position, and with increasing temperature the average frequency of these oscillations and their amplitude only increase. When a substance begins to melt, the behavior of its molecules becomes similar to the behavior of liquid molecules. If in a solid body each particle vibrates in a small volume occupying a fixed position in space, then in a liquid this volume itself moves slowly and randomly, and the vibrating particle moves with it.
THERMAL CONDUCTIVITY OF GAS
In any unevenly heated body, heat is transferred from its warmer parts to its colder ones. This phenomenon is called thermal conductivity. Using molecular kinetic theory, we can find the rate at which a gas conducts heat. Consider a gas enclosed in a rectangular vessel, the upper surface of which has a higher temperature than the lower. The temperature of the gas in the vessel gradually decreases when moving from the upper to the lower layers - there is a temperature gradient in the gas. Let us consider a thin horizontal layer of gas AB, having a temperature T (Fig. 3), and an adjacent layer CD with a slightly higher temperature, T ў. Let the distance between AB and CD be equal to the mean free path L. According to formula (4), the average energy of a molecule in the AB layer is proportional to the temperature T, and in the CD layer - to the temperature T." Consider a molecule from the AB layer that collides with another molecule at point A, after which it moves without collisions to point C; with a high probability it will fall into the CD layer with an energy corresponding to the AB layer. And vice versa, a molecule from the CD layer moving without collisions from point D to point B will with a high probability fall into. layer AB with higher energy corresponding to the layer CD, from where it flew out. It is clear that during such collisions more energy is transferred from CD to AB than from AB to CD - there is a continuous flow of heat from the warmer layer to the colder one. observed for all layers in the gas.

Where Cv is the heat capacity of n molecules contained in a unit volume. When moving from CD to AB, located at a distance L from each other, the temperature decreases by (T" - T) and if dT/dz is the temperature gradient in the direction perpendicular to the plane FG, then

Substituting the temperature difference, expressed through the gradient, into formula (7), we find that the total energy transferred through a unit area in 1 s is equal to

The value of K, described by the expression K = (1/3)CvcL,
is called the thermal conductivity coefficient of the gas.
GAS VISCOSITY
If you measure the speed of the river flow at different depths, you will find that the water is almost motionless at the bottom, and the closer to the surface, the faster it moves. Thus, in a river flow there is a velocity gradient similar to the temperature gradient discussed above; Moreover, due to viscosity, each layer located above carries with it the neighboring one lying below it. This picture is observed not only in liquids, but also in gases. Using molecular kinetic theory, we will try to determine the viscosity of the gas. Let us assume that the gas flows from left to right and that in the horizontal layer CD in Fig. 3, the flow velocity is greater than in layer AB, located directly below CD. Let, as before, the distance between the planes be equal to the mean free path. Gas molecules move quickly throughout the volume along chaotic trajectories, but this chaotic movement is superimposed by the directed movement of the gas. Let u be the speed of gas flow in the AB layer (in the direction from A to B), and u" be the slightly higher speed in the CD layer (in the direction from C to D). In addition to the momentum caused by the chaotic movement, the molecule in the AB layer has momentum mu, and in the CD layer - by the momentum muў. Molecules passing from AB to CD without collisions transfer the momentum mu corresponding to the AB layer to the CD layer, while particles falling from CD to AB mix with molecules from AB and bring with them. impulse mu". Consequently, from CD to AB through a unit area of ​​the plane FG in 1 s an impulse equal to

Since the rate of change of momentum is equal to force, we have obtained an expression for the force per unit area with which one layer acts on another: the slower layer slows down the faster one, and the latter, on the contrary, dragging the slower layer along with it, accelerates it. Similar forces act between adjacent layers throughout the entire volume of flowing gas. If du/dz is the velocity gradient in the gas in the direction perpendicular to FG, then

The value nm in formula (8) is the mass of gas per unit volume; if we denote this quantity by r, then the force per unit area will be equal to

where coefficient (1/3)rLc is the gas viscosity. Two conclusions follow from the last two sections of the article. The first is that the ratio of viscosity to thermal conductivity is r/Cv. The second follows from the previously given expression for L and consists in the fact that the viscosity of a gas depends only on its temperature and does not depend on pressure and density. The correctness of both conclusions has been confirmed experimentally with high accuracy.
see also
HEAT ;
STATISTICAL MECHANICS;
THERMODYNAMICS.
LITERATURE
Girschfeld J., Curtiss Ch., Bird R. Molecular theory of gases and liquids. M., 1961 Frenkel Ya.I. Kinetic theory of liquids. L., 1975 Kikoin A.K., Kikoin I.K. Molecular physics. M., 1976

Collier's Encyclopedia. - Open Society. 2000 .

See what "MOLECULAR KINETIC THEORY" is in other dictionaries:

- (abbreviated MKT) theory of the 19th century, which considered the structure of matter, mainly gases, from the point of view of three main approximately correct provisions: all bodies consist of particles: atoms, molecules and ions; particles are in continuous... ... Wikipedia

- (abbreviated MKT) a theory that considers the structure of matter from the point of view of three main approximately correct provisions: all bodies consist of particles whose size can be neglected: atoms, molecules and ions; particles are in continuous... ... Wikipedia