Molecular physics – a branch of physics that studies the physical properties of bodies in various states of aggregation based on consideration of their molecular structure, the forces of interaction between the particles that form the body, and the nature of the thermal motion of these particles.

Numerous studies conducted by these scientists made it possible to formulate the main provisions of the molecular kinetic theory - MKT.

MKT explains the structure and properties of bodies based on the laws of motion and interaction of molecules that make up bodies .

The MCT is based on three important provisions, confirmed experimentally and theoretically.

1. All bodies consist of the smallest particles - atoms, molecules, which include even smaller elementary particles (electrons, protons, neutrons). The structure of any substance is discrete (discontinuous).
2. Atoms and molecules of matter are always in continuous chaotic motion.
3. Between the particles of any substance there are forces of interaction - attraction and repulsion. The nature of these forces is electromagnetic.

These provisions are confirmed empirically.

Experimental substantiation of the 1st position.

All bodies are made up of tiny particles. Firstly, this is evidenced by the possibility of division of matter (all bodies can be divided into parts).

The most striking experimental confirmation of the ideas of the molecular kinetic theory about the random motion of atoms and molecules is Brownian motion.

It was discovered by the English botanist R. Brown (1827). In 1827, the English botanist Brown, studying the internal structure of plants with a microscope, found that particles of solid matter in a liquid medium make continuous chaotic movement.

The thermal motion of particles suspended in a liquid (or gas) is calledBrownian motion.

Brownian particles move under the influence of random collisions of molecules. Due to the chaotic thermal motion of the molecules, these impacts never balance each other. As a result, the speed of a Brownian particle randomly changes in magnitude and direction, and its trajectory is a complex zigzag curve. The theory of Brownian motion was created by A. Einstein (1905). Einstein's theory was experimentally confirmed in the experiments of the French physicist J. Perrin (1908–1911).

The reason for Brownian motion is the continuous chaotic movement of liquid or gas molecules, which, randomly hitting a particle from all sides, set it in motion. The reason for the Brownian motion of a particle is that the impacts of molecules on it are not compensated. This means that Brownian motion is also an experimental substantiation of the 2nd position of the MKT.

The continuous movement of the molecules of any substance (solid, liquid, gaseous) is confirmed by numerous experiments on diffusion.

by diffusioncalled the phenomenon of spontaneous penetration of molecules of one substance into the gaps between the molecules of another. Those. it is the spontaneous mixing of substances.

If an odorous substance (perfume) is brought into the room, then after a while the smell of this substance will spread throughout the room. This indicates that the molecules of one substance without the influence of external forces penetrate into another. Diffusion is observed in both liquids and solids.

When studying the structure of matter, it was found that attractive and repulsive forces, called molecular forces, act simultaneously between molecules. These are electromagnetic forces.

The ability of solids to resist stretching, the special properties of the liquid surface lead to the conclusion that there are attractive forces.

The low compressibility of very dense gases and especially liquids and solids means that there are repulsive forces.

These forces act simultaneously. If this were not the case, then the bodies would not be stable: they would either shatter into particles or stick together.

Intermolecular interaction is the interaction of electrically neutral molecules and atoms.

The forces acting between two molecules depend on the distance between them. Molecules are complex spatial structures containing both positive and negative charges. If the distance between the molecules is large enough, then the forces of intermolecular attraction predominate. At short distances, repulsive forces predominate. Resultant force dependencies F and potential energy Ep interactions between molecules on the distance between their centers are qualitatively depicted in the figure. At some distance r = r 0, the interaction force vanishes. This distance can be conditionally taken as the diameter of the molecule. Potential interaction energy at r = r 0 is the minimum. To remove two molecules that are at a distance from each other r 0 , you need to give them additional energy E 0 . Value E 0 is called depth of the potential well or binding energy .

Between the electrons of one molecule and the nuclei of another, attractive forces act, which are conventionally considered negative (lower part of the graph). At the same time, repulsive forces act between the electrons of molecules and their nuclei, which are conditionally considered positive (upper part of the graph). At a distance equal to the size of the molecules, the resulting force is zero, i.e. attractive forces balance the repulsive forces. This is the most stable arrangement of molecules. As the distance increases, the attraction exceeds the repulsive force; as the distance between the molecules decreases, vice versa.

Atoms and molecules interact and therefore have potential energy.

Atoms and molecules are in constant motion, and therefore havekinetic energy.

Mass and size of molecules

Most substances consist of molecules, therefore, in order to explain the properties of macroscopic objects, explain and predict phenomena, it is important to know the basic characteristics of molecules.

moleculecalled the smallest stable particle of a given substance, which has its basic chemical properties.

A molecule is made up of even smaller particles called atoms, which in turn are made up of electrons and nuclei.

atomname the smallest particle of a given chemical element.

Molecule sizes very small.

The order of magnitude of the diameter of the molecule is 1 * 10 - 8 cm = 1 * 10 - 10 m

The order of magnitude of the volume of a molecule is 1 * 10 - 20 m 3

The fact that the sizes of molecules are small can also be judged from experience. In 1 liter (m 3) of pure water we will dilute 1 m 3 of green ink, we will dilute the ink 1,000,000 times. We will see that the solution has a green color and at the same time is homogeneous. This suggests that even when diluted 1,000,000 times, there are a large number of dye molecules in the water. This experiment shows how small the sizes of molecules are.

1 cm 3 of water contains 3.7 * 10 -8 molecules.

The order of magnitude of the mass of molecules is 1 * 10 -23 g \u003d 1 * 10 -26 kg

In molecular physics, it is customary to characterize the masses of atoms and molecules not by their absolute values ​​(in kg), but by relative dimensionless values ​​of relative atomic mass and relative molecular mass.

By international agreement, 1/12 of the mass of the carbon isotope 12 C (m 0C) is taken as a unit atomic mass m 0 :

m 0 \u003d 1/12 m 0С \u003d 1.66 * 10 -27

Relative molecular weight can be determined if the absolute value of the mass of the molecule (m mol in kg) is divided by the unit atomic mass.

M 0 \u003d m mol / 1/12 m 0С

Relative molecular (atomic) mass of a substance (from the periodic table)

7 14 N Nitrogen M 0 N = 14 M 0 N 2 = 28

The relative number of atoms or molecules contained in a substance is characterized by a physical quantity called the amount of substance.

Amount of substanceע – is the ratio of the number of molecules (atoms)Nin the bottom macroscopic body to the number of molecules in 0.012 kg of carbonN A

The amount of a substance is expressed in moles

One molethis is the amount of a substance in which there are as many molecules (atoms) as there are atoms in 0.012 kg of carbon.

A mole of any substance contains the same number of molecules. This number is called constant AvogadroN A\u003d 6.02 * 10 23 mol -1

The mass of one mole of a substance is called molar mass.

The number of molecules in a given mass of a substance:

Mass of a substance (any amount of substance):

Molar mass determination:

Video resource: Mass of molecules. The amount of substance.

(youtube)bfPw9aZJVqk&list=PLhOzgnnk_5jyM6NXfLniX5sX3rZTrpoea&index=18(/youtube)

The concept of temperature is one of the most important in molecular physics.

Temperature is a physical quantity that characterizes the degree of heating of bodies.

The random random movement of molecules is calledthermal motion.

The kinetic energy of thermal motion increases with increasing temperature. At low temperatures, the average kinetic energy of a molecule can be small. In this case, the molecules condense into a liquid or solid; in this case, the average distance between the molecules will be approximately equal to the diameter of the molecule. As the temperature rises, the average kinetic energy of the molecule becomes larger, the molecules fly apart, and a gaseous substance is formed.

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 through thermal contact is called amount of heat.

Consider an example. If you put a heated metal on ice, the ice will begin to melt, and the metal will cool until the temperatures of the bodies become the same. Upon contact between two bodies of different temperatures, heat exchange occurs, as a result of which the energy of the metal decreases, and the energy of ice increases.

Energy during heat transfer is always transferred from a body with a higher temperature to a body with a lower temperature. In the end, a state of the system of bodies sets in, in which there will be no heat exchange between the bodies of the system. Such a state is called thermal equilibrium.

Thermal equilibrium– this is such a state of a system of bodies in thermal contact, in which there is no heat transfer from one body to another, and all the macroscopic parameters of the bodies remain unchanged.

Temperature– this is a physical parameter that is the same for all bodies in thermal equilibrium. The possibility of introducing the concept of temperature follows from experience and is called the zeroth law of thermodynamics.

Bodies in thermal equilibrium have the same temperature.

To measure temperatures, the property of a liquid to change volume when heated (and cooled) is most often used.

The instrument used to measure temperature is calledthermometer.

To create a thermometer, it is necessary to choose a thermometric substance (for example, mercury, alcohol) and a thermometric quantity that characterizes the property of the substance (for example, the length of a mercury or alcohol column). Various designs of thermometers use a variety of physical properties of a substance (for example, a change in the linear dimensions of solids or a change in the electrical resistance of conductors when heated). Thermometers must be calibrated. 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 the heat exchange with the environment - this is a mixture of ice and water and a mixture of water and steam when boiling at normal atmospheric pressure.

Ordinary liquid thermometer consists of a small glass tank to which is attached a glass tube with a narrow internal channel. The reservoir and part of the tube are filled with mercury. The temperature of the medium in which the thermometer is immersed is determined by the position of the upper level of mercury in the tube. The divisions on the scale were agreed to be applied as follows. The number 0 is placed in the place of the scale where the level of the liquid column is set when the thermometer is lowered into melting snow (ice), the number 100 is placed in the place where the level of the liquid column is set when the thermometer is immersed in water vapor boiling at normal pressure (10 5 Pa). The distance between these marks is divided into 100 equal parts called degrees. This way of dividing the scale was introduced by Celsius. The Celsius degree is denoted as ºС.

By temperature Celsius scale The melting point of ice is assigned a temperature of 0 °C, and the boiling point of water is 100 °C. The change in the length of the liquid column in the capillaries of the thermometer by one hundredth of the length between the marks 0 °C and 100 °C is assumed to be 1 °C.

In a number of countries (USA) it is widely used Fahrenheit (T F), in which the freezing temperature of water is assumed to be 32 °F, and the boiling point of water is 212 °F. Hence,

Mercury thermometers used to measure temperature in the range from -30 ºС to +800 ºС. As well as liquid mercury and alcohol thermometers are used electrical and gas thermometers.

Electrical thermometer - resistance thermometer - it uses the dependence of the resistance of the metal on temperature.

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

To calibrate a constant volume gas thermometer, pressure can be measured at two temperatures (e.g. 0 °C and 100 °C), dots p 0 and p 100 on the chart, and then draw a straight line between them. Using the calibration curve thus obtained, temperatures corresponding to other pressures can be determined.

Gas thermometers are bulky and inconvenient for practical use: they are used as a precision standard for calibrating other thermometers.

The readings of thermometers filled with various thermometric bodies usually differ somewhat. To accurately determine the temperature does not depend on the substance filling the thermometer, we introduce thermodynamic temperature scale.

To introduce it, consider how the pressure of a gas depends on temperature when its mass and volume remain constant.

Thermodynamic temperature scale. Absolute zero.

Let's take a closed vessel with gas, and we will heat it, initially placing it in melting ice. We determine the gas temperature t with a thermometer, and the pressure p with a manometer. As the temperature of a gas increases, its pressure will increase. This dependence was found by the French physicist Charles. A plot of p versus t based on this experience is a straight line.

If we continue the graph to the region of low pressures, we can determine some "hypothetical" temperature at which the gas pressure would become equal to zero. Experience shows that this temperature is -273.15 °C and does not depend on the properties of the gas. It is impossible to experimentally obtain by cooling a gas in a state with zero pressure, since at very low temperatures all gases pass into liquid or solid states. The pressure of an ideal gas is determined by the impacts of randomly moving molecules on the walls of the vessel. This means that the decrease in pressure during cooling of the gas is explained by the decrease in the average energy of the translational motion of gas molecules E; the pressure of the gas will be zero when the energy of the translational motion of the molecules becomes zero.

The English physicist W. Kelvin (Thomson) put forward the idea that the obtained value of absolute zero corresponds to the cessation of the translational motion of the molecules of all substances. Temperatures below absolute zero cannot exist in nature. This is the limiting temperature at which the pressure of an ideal gas is zero.

The temperature at which the translational motion of molecules must stop is calledabsolute zero ( or zero Kelvin).

Kelvin in 1848 proposed using the point of zero gas pressure to build a new temperature scale - thermodynamic temperature scale(Kelvin scale). The temperature of absolute zero is taken as the reference point on this scale.

In the SI system, the unit of measure for temperature on the Kelvin scale is called kelvin and denoted by the letter K.

The size of the degree Kelvin is determined so that it coincides with the degree Celsius, i.e. 1K corresponds to 1ºС.

The temperature measured on the thermodynamic temperature scale is denoted T. It is called absolute temperature or thermodynamic temperature.

The Kelvin temperature scale is called absolute temperature scale . It turns out to be most convenient in the construction of physical theories.

In addition to the point of zero gas pressure, which is called absolute zero temperature , it suffices to accept one more fixed reference point. In the Kelvin scale, this point is triple point temperature of water(0.01 °C), in which all three phases are in thermal equilibrium - ice, water and steam. On the Kelvin scale, the temperature of the triple point is assumed to be 273.16 K.

Relationship between absolute temperature and scale temperature Celsius is expressed by the formula T = 273.16 +t, where t is the temperature in degrees Celsius.

More often they use the approximate formula T \u003d 273 + t and t \u003d T - 273

Absolute temperature cannot be negative.

Gas temperature is a measure of the average kinetic energy of molecular motion.

In the experiments of Charles, the dependence of p on t was found. The same relationship will be between p and T: i.e. between p and T is directly proportional.

On the one hand, the gas pressure is directly proportional to its temperature, on the other hand, we already know that the gas pressure is directly proportional to the average kinetic energy of the translational motion of molecules E (p = 2/3*E*n). So E is directly proportional to T.

The German scientist Boltzmann proposed to introduce the proportionality factor (3/2)k into the dependence of E on T

E = (3/2)kT

From this formula it follows that the average value of the kinetic energy of the translational motion of molecules does not depend on the nature of the gas, but is determined only by its temperature.

Since E \u003d m * v 2 / 2, then m * v 2 / 2 \u003d (3/2) kT

whence the root-mean-square velocity of gas molecules

The constant value k is called Boltzmann's constant.

In SI, it has the value k = 1.38 * 10 -23 J / K

If we substitute the value of E in the formula p \u003d 2/3 * E * n, then we get p = 2/3*(3/2)kT* n, reducing, we get p = n* k*T

The pressure of a gas does not depend on its nature, but is determined only by the concentration of moleculesnand gas temperature T.

The ratio p = 2/3*E*n establishes a relationship between microscopic (values ​​are determined using calculations) and macroscopic (values ​​can be determined from instrument readings) gas parameters, so it is commonly called the basic equation of the molecular - kinetic theory of gases.

DEFINITION

The equation underlying the molecular kinetic theory connects macroscopic quantities describing (for example, pressure) with the parameters of its molecules (and their velocities). This equation looks like:

Here, is the mass of a gas molecule, is the concentration of such particles per unit volume, and is the averaged square of the molecular velocity.

The basic equation of the MKT clearly explains how an ideal gas creates on the vessel walls surrounding it. Molecules all the time hit the wall, acting on it with a certain force F. Here it should be remembered: when a molecule hits an object, a force -F acts on it, as a result of which the molecule “bounces” from the wall. In this case, we consider the collisions of molecules with the wall to be absolutely elastic: the mechanical energy of the molecules and the wall is completely conserved without passing into . This means that only the molecules change during collisions, and the heating of the molecules and the wall does not occur.

Knowing that the collision with the wall was elastic, we can predict how the velocity of the molecule will change after the collision. The velocity modulus will remain the same as before the collision, and the direction of motion will change to the opposite with respect to the Ox axis (we assume that Ox is the axis that is perpendicular to the wall).

There are a lot of gas molecules, they move randomly and often hit the wall. Having found the geometric sum of forces with which each molecule acts on the wall, we find out the gas pressure force. To average the velocities of molecules, it is necessary to use statistical methods. That is why the basic MKT equation uses the averaged square of the molecular velocity , and not the square of the averaged velocity : the averaged velocity of randomly moving molecules is equal to zero, and in this case we would not get any pressure.

Now the physical meaning of the equation is clear: the more molecules are contained in the volume, the heavier they are and the faster they move, the more pressure they create on the walls of the vessel.

Basic MKT equation for the ideal gas model

It should be noted that the basic MKT equation was derived for the ideal gas model with the appropriate assumptions:

1. Collisions of molecules with surrounding objects are absolutely elastic. For real gases, this is not entirely true; some of the molecules still pass into the internal energy of the molecules and the wall.
2. The forces of interaction between molecules can be neglected. If the real gas is at high pressure and relatively low temperature, these forces become very significant.
3. We consider molecules to be material points, neglecting their size. However, the dimensions of the molecules of real gases affect the distance between the molecules themselves and the wall.
4. And, finally, the main equation of the MKT considers a homogeneous gas - and in reality we often deal with mixtures of gases. Such as, .

However, for rarefied gases, this equation gives very accurate results. In addition, many real gases at room temperature and at pressures close to atmospheric are very similar in properties to an ideal gas.

As is known from the laws, the kinetic energy of any body or particle. Replacing the product of the mass of each of the particles and the square of their speed in the equation we wrote down, we can represent it as:

Also, the kinetic energy of gas molecules is expressed by the formula , which is often used in problems. Here k is Boltzmann's constant, establishing the relationship between temperature and energy. k=1.38 10 -23 J/K.

The basic equation of the MKT underlies thermodynamics. It is also used in practice in astronautics, cryogenics and neutron physics.

Examples of problem solving

EXAMPLE 1

Exercise	Determine the speed of movement of air particles under normal conditions.
Decision	We use the basic MKT equation, considering air as a homogeneous gas. Since air is actually a mixture of gases, the solution to the problem will not be absolutely accurate. Gas pressure: We can notice that the product is a gas, since n is the concentration of air molecules (the reciprocal of volume), and m is the mass of the molecule. Then the previous equation becomes: Under normal conditions, the pressure is 10 5 Pa, the air density is 1.29 kg / m 3 - these data can be taken from the reference literature. From the previous expression we obtain air molecules:
Answer	m/s

EXAMPLE 2

Exercise	Determine the concentration of homogeneous gas molecules at a temperature of 300 K and 1 MPa. Consider the gas to be ideal.
Decision	Let's start the solution of the problem with the basic equation of the MKT: , as well as any material particles: . Then our calculation formula will take a slightly different form:

Basic provisions of molecular-kinetic theory.

Molecular-kinetic theory (MKT) deals with the study of the properties of substances, based on ideas about the particles of matter.

The ICT is based on three main principles:

1. All substances are composed of particles - molecules, atoms and ions.

2. Particles of matter are constantly and randomly moving.

3. Particles of matter interact with each other.

Random (chaotic) movement of atoms and molecules in a substance is called thermal movement, because the speed of movement of particles increases with increasing temperature. Experimental confirmation of the continuous motion of atoms and molecules in matter is Brownian motion and diffusion.

Particles of matter.

All substances and bodies in nature consist of atoms and molecules - groups of atoms. Such large bodies are called macroscopic. Atoms and molecules are microscopic bodies. Modern instruments (ion projectors, tunneling microscopes) make it possible to see images of individual atoms and molecules.
The basis of the structure of matter is atoms. Atoms also have a complex structure, they consist of elementary particles - protons, neutrons, which are part of the nucleus of an atom, electrons, and other elementary particles.
Atoms can combine into molecules, and there can be substances consisting only of atoms. Atoms as a whole are electrically neutral. Atoms that have too many or too few electrons are called ions. There are positive and negative ions.

The illustration shows examples of different substances having a structure, respectively, in the form of atoms, molecules and ions.

Forces of interaction between molecules.

At very small distances between molecules, repulsive forces act. Due to this, molecules do not penetrate into each other and pieces of matter never shrink to the size of one molecule. A molecule is a complex system consisting of individual charged particles: electrons and atomic nuclei. Although, in general, the molecules are electrically neutral, significant electrical forces act between them at short distances: the interaction of electrons and atomic nuclei of neighboring molecules occurs. If the molecules are located at distances exceeding their sizes by several times, then the interaction forces have practically no effect. Forces between electrically neutral molecules are short-range. At distances exceeding 2–3 molecular diameters, attractive forces act. As the distance between the molecules decreases, the force of attraction first increases, and then begins to decrease and decreases to zero, when the distance between two molecules becomes equal to the sum of the radii of the molecules. With a further decrease in the distance, the electron shells of the atoms begin to overlap, and rapidly increasing repulsive forces arise between the molecules.

Ideal gas. Basic equation of the MKT.

It is known that particles in gases, unlike liquids and solids, are located relative to each other at distances significantly exceeding their own dimensions. In this case, the interaction between molecules is negligible and the kinetic energy of molecules is much greater than the energy of intermolecular interaction. To clarify the most common properties inherent in all gases, a simplified model of real gases is used - an ideal gas. The main differences between an ideal gas and a real gas are:

1. Particles of an ideal gas are spherical bodies of very small sizes, practically material points.
2. There are no forces of intermolecular interaction between the particles.
3. Collisions of particles are absolutely elastic.

Real rarefied gases do indeed behave like an ideal gas. Let us use the ideal gas model to explain the origin of gas pressure. Due to thermal motion, gas particles from time to time hit the walls of the vessel. With each impact, the molecules act on the vessel wall with some force. Adding up with each other, the impact forces of individual particles form a certain pressure force that constantly acts on the wall. It is clear that the more particles are contained in the vessel, the more often they will hit the vessel wall, and the greater will be the pressure force, and hence the pressure. The faster the particles move, the harder they hit the vessel wall. Let's mentally imagine the simplest experiment: a rolling ball hits a wall. If the ball rolls slowly, then it will hit the wall with less force on impact than if it were moving fast. The larger the particle mass, the greater the impact force. The faster the particles move, the more often they hit the walls of the vessel. So, the force with which the molecules act on the wall of the vessel is directly proportional to the number of molecules contained in a unit volume (this number is called the concentration of molecules and is denoted by n), the mass of the molecule m o , the mean square of their velocities and the area of ​​the vessel wall. As a result, we obtain: the gas pressure is directly proportional to the concentration of particles, the mass of the particle, and the square of the particle's velocity (or their kinetic energy). The dependence of the pressure of an ideal gas on the concentration and on the average kinetic energy of the particles is expressed by the basic equation of the molecular-kinetic theory of an ideal gas. We have obtained the basic MKT equation for an ideal gas from general considerations, but it can be rigorously derived based on the laws of classical mechanics. Here is one of the forms of writing the main equation of the MKT:
P=(1/3) n m o V 2 .

Molecular Kinetic Theory(abbreviated MKT) - 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 up of particles. atoms, molecules and ions;

particles are in continuous chaotic movement (thermal);

particles interact with each other absolutely elastic collisions.

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

Diffusion

Brownian motion

Change aggregate states substances

Based on the MCT, a number of branches of modern physics have been developed, 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 not used in modern theoretical physics, although it is found in textbooks for general physics courses.

Ideal gas - mathematical model gas, which assumes that: 1) potential energy interactions molecules can be neglected compared to kinetic energy; 2) the total volume of gas molecules is negligible. Between molecules there are no forces of attraction or repulsion, collisions of particles between themselves and 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 is composed also have a shape in the form of elastic spheres or ellipsoids, which allows taking into account the energy of not only translational, but also rotational-oscillatory motion, as well as not only central, but also non-central collisions of particles, etc.

There are classical ideal gas (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, 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 energies of gas particles.

According to the equivalent formulation, an ideal gas is one that simultaneously obeys Boyle's Law - Mariotte and Gay Lussac , i.e:

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

,

where - , - weight,- molar mass.

where - particle concentration, -Boltzmann's constant.

For any ideal gas, Mayer's ratio:

where - universal gas constant, - molar heat capacity at constant pressure, - molar heat capacity at constant volume.

Statistical calculation of the distribution of velocities of molecules was performed by Maxwell.

Consider the result obtained by Maxwell in the form of a graph.

Gas molecules constantly collide as they move. The speed of each molecule changes upon collision. It can rise and fall. 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 does not change with time, which obeys a certain statistical law. The speed of an individual molecule can change over time, but the proportion of molecules with speeds in a certain range of speeds remains unchanged.

It is impossible to raise the question: how many molecules have a certain speed. The fact is that, although the number of molecules is very large in any even small volume, but the number of speed values ​​is arbitrarily large (as 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 distribution of molecules over velocities should be formulated as follows. Let in unit volume n molecules. What proportion of molecules has velocities from v 1 to v 1 + ∆ v? This is a statistical task.

Based on Stern's experience, it can be expected 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 , referred to the velocity interval Δ v, i.e. , has the form shown in Fig. 3.3. Maxwell in 1859 theoretically determined this function on the basis of probability theory. 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 the speed .

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

is the number of molecules in the considered volume.

- angle of molecules whose velocities belong to the interval
.

is the fraction of molecules in a unit velocity interval near the velocity .

- Maxwell's formula.

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

.

is the mass of one molecule,
is the Boltzmann constant.

The most probable speed is determined from the condition
.

Solving we get
;
.

Denote b/w
.

Then
.

Let us calculate the fraction of molecules in a given range of velocities near a given speed in a given direction.

.

.

is the proportion of molecules that have velocities in the interval
,
,
.

Developing Maxwell's ideas, Boltzmann calculated the velocity distribution of molecules in a force field. In contrast to the Maxwell distribution, the Boltzmann distribution uses the sum of kinetic and potential energies instead of the kinetic energy of molecules.

In the Maxwell distribution:
.

In the Boltzmann distribution:
.

In a gravitational field

.

The formula for the concentration of ideal gas molecules is:

and respectively.

is the Boltzmann distribution.

is the 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
, then
.

Considering

;

;



.

- Mayer's formula.

That. the problem of calculating the heat capacity is reduced to finding .

.

For one mole:

, hence
.

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

(hard dumbbell model).

Total number of degrees of freedom:

.

Then
, then

;
.

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

When the temperature is lowered, 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 theoretical data with experimental ones.

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

Such a course of the curve from testifies to the "freezing" of the degrees of freedom. On the contrary, at high temperatures, additional degrees of freedom are connected 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 the difficulties in explaining the dependence of the heat capacity of gases (in particular, diatomic gases) on temperature. According to the provisions of quantum mechanics, the energy of the rotational motion of molecules and the energy of vibrations of atoms can only take on discrete values. If the energy of thermal motion is much less than the difference between the energies of neighboring energy levels (), then the collision of molecules does not practically excite rotational and vibrational degrees of freedom. Therefore, at low temperatures, the behavior of a diatomic gas is similar to that of a monatomic one. Since the difference between neighboring rotational energy levels is much smaller than between neighboring 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 the atoms of the crystal lattice are independent. Using the model of a crystal as a set of harmonic oscillators independently oscillating with 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 as elastic waves propagating in a crystal. According to the corpuscular-wave dualism of the properties of matter, elastic waves in a crystal are compared with quasiparticles-phonons that have energy. A phonon is an energy quantum of an elastic wave, 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 the molecules of solids) led to the idea of ​​phonons. The energy of the crystal lattice is the sum 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 arise in a vacuum, they exist only in a crystal.

The momentum of a phonon has a peculiar property: when phonons collide in a crystal, their momentum can be transferred to the crystal lattice in discrete portions - the momentum is not conserved in this case. Therefore, in the case of phonons, one speaks of a 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 Dulong and Petit law, 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 the thermodynamic temperature: The characteristic Debye temperature is: , where is the limiting frequency of elastic vibrations of the crystal lattice.

The central concept of this topic is the concept of the molecule; the complexity of its assimilation by schoolchildren is due to the fact that the molecule is an object that is not directly observable. Therefore, the teacher must convince tenth-graders of the reality of the microcosm, of the possibility of its knowledge. In this regard, much attention is paid to the consideration of experiments that prove the existence and motion of molecules and make it possible to calculate their main characteristics (the classical experiments of Perrin, Rayleigh, and Stern). In addition, it is advisable to familiarize students with the calculation methods for determining the characteristics of molecules. When considering evidence for 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 time of observation. At that time, a correct explanation of the cause of this movement was not given, and only after almost 80 years A. Einstein and M. Smoluchovsky built, and J. Perrin experimentally confirmed the theory of Brownian movement. From the consideration of Brown's experiments, it is necessary to draw the following conclusions: a) the motion of Brownian particles is caused by impacts of the 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 motion and the continuous and chaotic nature of this motion. 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. At present, no one doubts the fact of 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 vertical projection using a projection lamp or a codoscope, as well as showing 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% sulfuric acid solution and a 2% aqueous solution of hyposulfite. As a result of the reaction, sulfur particles are formed, which are suspended in 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 is as follows: 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 the molecules of various substances have different sizes, but to estimate the size of the molecules they take a value equal to 10 -10 m. A similar experiment can be done in the class. To demonstrate the calculation method for determining the size of molecules, an example is given of calculating the diameters of molecules of various substances from their densities and the Avogadro constant. It is difficult for schoolchildren to imagine the small sizes of molecules; therefore, it is useful to give a number of examples of a comparative nature. For example, if all dimensions are increased so many times that the molecule is 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, a person would have a height of 1700 km. The number of molecules in the amount of substance 1 mol can be determined from the results of the 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 here, the Avogadro constant is determined. The calculation method consists in determining the number of molecules in the amount of 1 mol of a substance from the known values ​​of the molar mass and the mass of one molecule of the substance. The value of the Avogadro constant, according to modern data, is 6.022169 * 10 23 mol -1. Students can be introduced to the calculation method for determining the Avogadro constant by suggesting that it be calculated from the values ​​of the molar masses of various 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 guys an idea of ​​how large the number of molecules in a unit volume is. If a rubber balloon were to be pierced so thin that 1,000,000 molecules would escape through it every second, then approximately 30 billion molecules would be needed. years for all the molecules to come out. One of the methods for determining the mass of molecules is based on the experiment of Perrin, who proceeded from the fact that drops of resin in water behave in the same way as molecules in the atmosphere. Perrin counted the number of droplets in different layers of the emulsion, highlighting layers with a thickness of 0.0001 cm using a microscope. The height at which there are 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 \u003d 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 at the Earth's surface. The proportion m/M=h/H is recorded, from which the mass of an oxygen molecule m=5.1*10 -26 kg is found. Students are offered to independently calculate the mass of a hydrogen molecule, the density of which is half that of the Earth's surface, at a height of H = 80 km. At present, the values ​​of the masses of molecules have been refined. For example, oxygen is set to 5.31*10 -26 kg, and hydrogen is set to 0.33*10 -26 kg. When discussing the issue of the speeds of movement of molecules, students are introduced to the classical experiment of Stern. When explaining the experiment, it is advisable to create its model using the "Rotating disk with accessories" device. Several matches are fixed on the edge of the disk in a vertical position, in the center of the disk - a tube with a groove. When the disk is stationary, the ball lowered into the tube, rolling down the chute, knocks down one of the matches. Then the disk is brought into rotation at a certain speed, fixed 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, it is possible to determine the speed of the ball along the radius. After that, it is advisable to consider the essence of Stern's experiment and the design of its installation, using the film fragment "Stern's Experiment" as an illustration. When discussing the results of Stern's experiment, attention is drawn to the fact that there is a certain distribution of molecules over velocities, 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 speed settle closer to the place opposite the gap. 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 according to velocities was discovered by J. K. Maxwell. The velocity distribution of molecules can be modeled on the Galton board. The question of the interaction of molecules was already studied by schoolchildren 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 has an electromagnetic nature; b) intermolecular interaction is characterized by forces of attraction and repulsion; c) the forces of intermolecular interaction act at distances not greater than 2-3 molecular diameters, and at this distance only the attractive force is noticeable, the repulsive forces are practically equal to zero; d) as the distance between the molecules decreases, the interaction forces increase, and the repulsive force grows faster (in proportion to r -9) than the attractive force (in proportion to r -7 ). Therefore, when 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 prevails. It is expedient to illustrate all of the above with a graph of dependence on distance, first of the attractive force, the repulsive force, and then the resultant force. 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. Tenth-graders' attention 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, so the motion of solid body particles is 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 motion of the molecules is completely random and the substance exists in a gaseous state. If the kinetic energy thermal particle motion is comparable to the potential energy of their interaction, then the substance is in a liquid state.

According to the molecular kinetic theory, all substances consist of the smallest particles - molecules. Molecules are separated by gaps, are in continuous motion and interact with each other. A molecule is the smallest particle of a substance that has its chemical properties. Molecules consist of simpler particles - atoms of chemical elements. Molecules of different substances have different atomic composition.

Molecules have kinetic energy and at the same time potential energy of interaction. In the gaseous state, W kin >> W sweat. In liquid and solid states, the kinetic energy of particles is comparable to the energy of their interaction (Wkin ~Wpot).

Let us explain the three main provisions of the molecular-kinetic theory.

1. All substances are composed of molecules, i.e. have a discrete structure, the molecules are separated by gaps.

2. Molecules are in continuous random (chaotic) motion.

3. Between the molecules of the body there are forces interactions.

The molecular-kinetic theory is substantiated by numerous experiments and a huge number of physical phenomena.

The presence of gaps between molecules follows, for example, from experiments on mixing various liquids: the volume of a mixture is always less than the sum of the volumes of mixed liquids.

Here are some of the proofs of the random (chaotic) movement of molecules:

a) the desire of gas to occupy the entire volume provided to it (distribution of odorous gas throughout the room);

b) Brownian motion - the random movement of the smallest particles of matter visible in a microscope, which are in suspension and insoluble in it. This movement occurs under the influence of chaotic impacts of the molecules surrounding the liquid, which are in constant chaotic motion;

c) diffusion - mutual penetration of molecules of adjoining substances. During diffusion, the molecules of one body, being in continuous motion, penetrate into the gaps between the molecules of another body in contact with it and propagate between them. Diffusion manifests itself in all bodies - in gases, liquids and solids - but to varying degrees.

Diffusion in gases can be observed if a vessel with an odorous gas is opened indoors. After a while, the gas will spread throughout the room.

Diffusion in liquids is much slower than in gases. For example, let's pour a solution of copper sulphate into a glass, and then, very carefully, add a layer of water and leave the glass in a room with a constant temperature and where it is not subject to shaking. After some time, we will observe the disappearance of the sharp boundary between vitriol and water, and after a few days the liquids will mix, despite the fact that the density of vitriol is greater than the density of water. It also diffuses water with alcohol and other liquids.

Diffusion in solids is even slower than in liquids (from several hours to several years). It can be observed only in well ground bodies, when the distances between the surfaces of the ground bodies are close to the distances between molecules (10 -8 cm). In this case, the diffusion rate increases with increasing temperature and pressure.

Evidence of the force interaction of molecules:

a) deformation of bodies under the influence of force;

b) preservation of the form by solid bodies;

c) the surface tension of liquids and, as a consequence, the phenomenon of wetting and capillarity.

There are both attractive and repulsive forces between molecules. These forces are electromagnetic in nature.

Let us consider various cases of mutual arrangement of molecules and show which forces prevail. Let us introduce the following notation:

r – Distance between molecules.

d is the diameter of the molecule

F np – force of gravity

F om – repulsive force

→ - strive

Hence

r→∞=>F=0(forces are short-range)

r> d(≈2-3 diameters)=>F np > F om

r→d=>F np →0