Experimental substantiation of the main provisions of the molecular-kinetic theory (MKT) of the structure of matter. Mass and size of molecules. Avogadro constant. Provisions of the molecular kinetic theory Provisions of the MKT and experimental substantiation

Molecular-kinetic theory is a branch of physics that studies the properties of various states of matter, based on the concept of the existence of molecules and atoms as the smallest particles of matter. The ICT is based on three main principles:

1. All substances consist of the smallest particles: molecules, atoms or ions.

2. These particles are in continuous chaotic motion, the speed of which determines the temperature of the substance.

3. Between the particles there are forces of attraction and repulsion, the nature of which depends on the distance between them.

The main provisions of the MKT are confirmed by many experimental facts. The existence of molecules, atoms and ions has been proven experimentally, molecules have been sufficiently studied and even photographed using electron microscopes. The ability of gases to expand indefinitely and occupy the entire volume provided to them is explained by the continuous chaotic movement of molecules. The elasticity of gases, solids and liquids, the ability of liquids to wet some solids, the processes of coloring, gluing, maintaining the shape of solids, and much more indicate the existence of forces of attraction and repulsion between molecules. The phenomenon of diffusion - the ability of the molecules of one substance to penetrate into the gaps between the molecules of another - also confirms the basic provisions of the MKT. The phenomenon of diffusion explains, for example, the spread of odors, the mixing of dissimilar liquids, the process of dissolving solids in liquids, the welding of metals by melting them or by pressure. A confirmation of the continuous chaotic motion of molecules is also Brownian motion - the continuous chaotic motion of microscopic particles that are insoluble in a liquid.

The movement of Brownian particles is explained by the chaotic movement of fluid particles that collide with microscopic particles and set them in motion. It has been experimentally proved that the speed of Brownian particles depends on the temperature of the liquid. The theory of Brownian motion was developed by A. Einstein. The laws of motion of particles are of a statistical, probabilistic nature. There is only one known way to reduce the intensity of Brownian motion - a decrease in temperature. The existence of Brownian motion convincingly confirms the motion of molecules.

Any substance consists of particles, therefore the amount of substance v is considered to be proportional to the number of particles, i.e. structural elements contained in the body.

The unit of quantity of a substance is the mole. A mole is the amount of a substance that contains as many structural elements of any substance as there are atoms in 12 g of C12 carbon. The ratio of the number of molecules of a substance to the amount of a substance is called the Avogadro constant:

The Avogadro constant shows how many atoms and molecules are contained in one mole of a substance. Molar mass - the mass of one mole of a substance, equal to the ratio of the mass of the substance to the amount of the substance:

Molar mass is expressed in kg/mol. Knowing the molar mass, you can calculate the mass of one molecule:

The molar mass is related to the relative molecular mass Mg. Relative molecular weight is a value equal to the ratio of the mass of a molecule of a given substance to 1/12 of the mass of a C12 carbon atom. If the chemical formula of a substance is known, then its relative mass can be determined using the periodic table, which, when expressed in kilograms, shows the magnitude of the molar mass of this substance.

Molecular Kinetic Theory (MKT)- this 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. At the heart of the MCT of the structure of matter are three provisions:

1. Matter is made up 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. A 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 able to maintain 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 (random) motion.
3. Particles of matter interact with each other - attract and repel.

These basic provisions are confirmed experimentally and theoretically.

The composition of the substance

Modern instruments make it possible to observe images of individual atoms and molecules. An electron microscope or an ion projector (microscope) can be used to image individual atoms and estimate their size. The diameter of any atom is of the order 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 motion of particles

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

Diffusion(from the 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 are in contact).

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

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 air in the absence of direct mixing. Diffusion in solids ensures the connection of metals during welding, soldering, chrome plating, etc. In gases and liquids, diffusion occurs much faster than in solids.

The existence of stable liquid and solid bodies is explained by the presence of forces of intermolecular interaction (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 electromagnetic in nature - these are forces of electrical origin. The reason for this is that molecules and atoms are composed of charged particles with opposite charge signs - electrons and positively charged atomic nuclei. In general, molecules are electrically neutral. According to the electrical properties, the molecule can be approximately considered as an electric dipole.

The strength of interaction between molecules has a certain dependence on the distance between molecules. This dependence is shown in Fig. 1.1. Shown here are the projections of the interaction forces on 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 you can see, as the distance between molecules r decreases, the attractive force 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, while 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 forces of attraction weaken. Attractive forces are short-range forces.

where a is a coefficient depending on the type of attractive forces and the structure of the interacting molecules.

With further approach of atoms or molecules at distances between the centers of molecules of the order of 10 -10 m (this distance is comparable with the linear dimensions of inorganic molecules), repulsive forces F r from appear (blue line in Fig. 1.1). 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 is a coefficient depending on the type of repulsive forces and the structure of the 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 the interacting molecules.

In general, the resulting force is:

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

The dependence of the interaction forces of 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 . At the same time, 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 chart, this segment is shown as a thickened light green line.

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

1.Experimental substantiation of the main provisions of the molecular-kinetic theory of the structure of matter. Mass and size of molecules.

Molecular-kinetic theory is a branch of physics that studies the properties of various states of matter, based on the concept of the existence of molecules and atoms as the smallest particles of matter. The ICT is based on three main principles:

1. All substances consist of the smallest particles: molecules, atoms or ions.

2. These particles are in continuous chaotic motion, the speed of which determines the temperature of the substance.

3. Between the particles there are forces of attraction and repulsion, the nature of which depends on the distance between them.

The main provisions of the MKT are confirmed by many experimental facts. The existence of molecules, atoms and ions has been proven experimentally, molecules have been sufficiently studied and even photographed using electron microscopes. The ability of gases to expand indefinitely and occupy the entire volume provided to them is explained by the continuous chaotic movement of molecules. The elasticity of gases, solids and liquids, the ability of liquids to wet some solids, the processes of coloring, gluing, maintaining the shape of solids, and much more indicate the existence of forces of attraction and repulsion between molecules. The phenomenon of diffusion - the ability of the molecules of one substance to penetrate into the gaps between the molecules of another - also confirms the basic provisions of the MKT. The phenomenon of diffusion explains, for example, the spread of odors, the mixing of dissimilar liquids, the process of dissolving solids in liquids, the welding of metals by melting them or by pressure. A confirmation of the continuous chaotic motion of molecules is also Brownian motion - the continuous chaotic motion of microscopic particles that are insoluble in a liquid.

The movement of Brownian particles is explained by the chaotic movement of fluid particles that collide with microscopic particles and set them in motion. It has been experimentally proved that the speed of Brownian particles depends on the temperature of the liquid. The theory of Brownian motion was developed by A. Einstein. The laws of motion of particles are of a statistical, probabilistic nature. There is only one known way to reduce the intensity of Brownian motion - a decrease in temperature. The existence of Brownian motion convincingly confirms the motion of molecules.

Any substance consists of particles, therefore the amount of substance v is considered to be proportional to the number of particles, i.e. structural elements contained in the body.

The unit of quantity of a substance is the mole. A mole is the amount of a substance that contains as many structural elements of any substance as there are atoms in 12 g of C12 carbon. The ratio of the number of molecules of a substance to the amount of a substance is called the Avogadro constant:

The Avogadro constant shows how many atoms and molecules are contained in one mole of a substance. Molar mass - the mass of one mole of a substance, equal to the ratio of the mass of the substance to the amount of the substance:

Molar mass is expressed in kg/mol. Knowing the molar mass, you can calculate the mass of one molecule:

The average mass of molecules is usually determined by chemical methods, the Avogadro constant has been determined with high accuracy by several physical methods. The masses of molecules and atoms are determined with a considerable degree of accuracy using a mass spectrograph.

The masses of molecules are very small. For example, the mass of a water molecule:

The molar mass is related to the relative molecular mass Mg. Relative molecular weight is a value equal to the ratio of the mass of a molecule of a given substance to 1/12 of the mass of a C12 carbon atom. If the chemical formula of a substance is known, then its relative mass can be determined using the periodic table, which, when expressed in kilograms, shows the magnitude of the molar mass of this substance.

Molecular-kinetic theory is a branch of physics that studies the properties of various states of matter, based on the concept of the existence of molecules and atoms as the smallest particles of matter. The ICT is based on three main principles:

1. All substances consist of the smallest particles: molecules, atoms or ions.

2. These particles are in continuous chaotic motion, the speed of which determines the temperature of the substance.

3. Between the particles there are forces of attraction and repulsion, the nature of which depends on the distance between them.

The main provisions of the MKT are confirmed by many experimental facts. The existence of molecules, atoms and ions has been proven experimentally, molecules have been sufficiently studied and even photographed using electron microscopes. The ability of gases to expand indefinitely and occupy the entire volume provided to them is explained by the continuous chaotic movement of molecules. The elasticity of gases, solids and liquids, the ability of liquids to wet some solids, the processes of coloring, gluing, maintaining the shape of solids, and much more indicate the existence of forces of attraction and repulsion between molecules. The phenomenon of diffusion - the ability of the molecules of one substance to penetrate into the gaps between the molecules of another - also confirms the basic provisions of the MKT. The phenomenon of diffusion explains, for example, the spread of odors, the mixing of dissimilar liquids, the process of dissolving solids in liquids, the welding of metals by melting them or by pressure. A confirmation of the continuous chaotic motion of molecules is also Brownian motion - the continuous chaotic motion of microscopic particles that are insoluble in a liquid.

The movement of Brownian particles is explained by the chaotic movement of fluid particles that collide with microscopic particles and set them in motion. It has been experimentally proved that the speed of Brownian particles depends on the temperature of the liquid. The theory of Brownian motion was developed by A. Einstein. The laws of motion of particles are of a statistical, probabilistic nature. There is only one known way to reduce the intensity of Brownian motion - a decrease in temperature. The existence of Brownian motion convincingly confirms the motion of molecules.

Any substance consists of particles, therefore the amount of substance v is considered to be proportional to the number of particles, i.e. structural elements contained in the body.

The unit of quantity of a substance is the mole. A mole is the amount of a substance that contains as many structural elements of any substance as there are atoms in 12 g of C12 carbon. The ratio of the number of molecules of a substance to the amount of a substance is called the Avogadro constant:

The Avogadro constant shows how many atoms and molecules are contained in one mole of a substance. Molar mass - the mass of one mole of a substance, equal to the ratio of the mass of the substance to the amount of the substance:

Molar mass is expressed in kg/mol. Knowing the molar mass, you can calculate the mass of one molecule:

The average mass of molecules is usually determined by chemical methods, the Avogadro constant has been determined with high accuracy by several physical methods. The masses of molecules and atoms are determined with a considerable degree of accuracy using a mass spectrograph.

The masses of molecules are very small. For example, the mass of a water molecule:

The molar mass is related to the relative molecular mass Mg. Relative molecular weight is a value equal to the ratio of the mass of a molecule of a given substance to 1/12 of the mass of a C12 carbon atom. If the chemical formula of a substance is known, then its relative mass can be determined using the periodic table, which, when expressed in kilograms, shows the magnitude of the molar mass of this substance.

Molecular-kinetic theory is substantiated Let us give some of the proofs of the chaotic chaotic movement of molecules: a The desire of gas to occupy the entire volume provided to it, the spread of odorous gas throughout the room; b Brownian motion is the random movement of the smallest particles of matter visible in a microscope that are in suspension and insoluble in it. 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 odorous ...

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EXPERIMENTAL SUBSTANTIATION OF THE MOLECULAR-KINETIC THEORY

According to the molecular kinetic theory, all substances consist of the smallest particles - molecules. Molecules are in constant 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 E kin and at the same time the potential energy of interaction E sweat . In a gaseous state E kin > E sweat . In liquid and solid states, the kinetic energy of particles is comparable to the energy of their interaction.

Three main points 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 of interaction.

Molecular-kinetic theory is substantiated

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.

1. Diffusion.

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 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 (Fig. 1). At small distances between molecules, repulsive forces predominate. As the distance r between molecules increases, both the attractive and repulsive forces decrease, with the repulsive forces decreasing faster. Therefore, for some value of r 0 (distance between molecules) the forces of attraction and repulsion are mutually balanced.

Rice. one. Attractive and repulsive forces.

If we agree to assign a positive sign to the repulsive forces, and a negative sign to the attractive forces, and to perform an algebraic addition of the repulsive and attractive forces, then we get the graph shown in Figure 2.

Rice. 2. Algebraic addition of repulsive and attractive forces.

Rice. 3. The dependence of the potential energy of the interaction of molecules on the distance between them.

Figure 3 shows a graph of the dependence of the potential energy of the interaction of molecules on the distance between them. Distance r 0 between molecules corresponds to the minimum of their potential energy (Fig. 3). To change the distance between molecules in one direction or another, it is required to expend work against the prevailing forces of attraction or repulsion. At shorter distances (Fig. 2) the curve rises steeply; this region corresponds to a strong repulsion of molecules (due mainly to the Coulomb repulsion of approaching nuclei). Molecules attract at large distances.

Distance r0 corresponds to a stable equilibrium mutual position of molecules. Figure 2 shows that as the distance between molecules increases, the prevailing forces of attraction restore the equilibrium position, and when the distance between them decreases, the balance is restored by the prevailing repulsive forces.

Modern experimental methods of physics (X-ray diffraction analysis, observations with an electron microscope, and others) made it possible to observe the microstructure of substances.

2. Avogadro's number.

The number of grams of a substance equal to the molecular weight of that substance is called a gram molecule or a mole. For example, 2 g of hydrogen is a gram molecule of hydrogen; 32 grams of oxygen make up a gram-molecule of oxygen. The mass of one mole of a substance is called the molar mass of that substance.

Denoted by m . For hydrogen ; for oxygen ; for nitrogen etc.

The number of molecules contained in one mole of different substances is the same and is called the Avogadro number (N A).

Avogadro's number is extremely large. To feel its colossality, imagine that a number of pinheads (each about 1 mm in diameter) was poured into the Black Sea, equal to Avogadro's number. At the same time, it would turn out that there is no longer room for water in the Black Sea: it would not only be filled to the brim, but also with a large excess of these pinheads. An avogadrum number of pinheads could cover an area equal, for example, to the territory of France, with a layer about 1 km thick. And such a huge number of individual molecules is contained in only 18 g of water; in 2 g of hydrogen, etc.

It was found that in 1 cm 3 any gas under normal conditions (i.e. at 0 0 C and pressure 760 mm. rt. Art.) contains 2,710 19 molecules.

If we take a number of bricks equal to this number, then, being tightly packed, these bricks would cover the surface of the entire land of the Earth with a layer 120 m high. The kinetic theory of gases allows us to calculate only the mean free path of a gas molecule (i.e., the average distance that passes molecule from collision to collision with other molecules) and the diameter of the molecule.

We present some results of these calculations.

The diameters of individual molecules are small quantities. When magnified a million times, the molecules would be the size of a dot in the typographic type of this book. Denote by m - the mass of gas (any substance). Then the relationgives the number of moles of the gas.

The number of gas molecules n can be expressed:

(1).

Number of molecules per unit volume n 0 will be equal to:

(2) , where: V is the volume of gas.

The mass of one molecule m 0 can be determined by the formula:

(3) .

The relative mass of the molecule m rel is called the value equal to the ratio of the absolute mass of the molecule m 0 to 1/12 of the mass of a carbon atom m oc.

(4), where m oc = 210 -26 kg.

3. Ideal gas equation and isoprocesses.

Using the equation of state of an ideal gas, one can study processes in which the mass of the gas and one of the three parameters - pressure, volume, or temperature - remain unchanged. Quantitative relationships between two gas parameters for a fixed value of the third parameter are called gas laws.

Processes occurring at a constant value of one of the parameters are called isoprocesses (from the Greek "isos" - equal). True, in reality, no process can proceed with a strictly fixed value of any parameter. There are always certain influences that violate the constancy of temperature, pressure or volume. Only under laboratory conditions is it possible to maintain the constancy of one or another parameter with good accuracy, but in existing technical devices and in nature this is practically impossible.

An isoprocess is an idealized model of a real process that only approximates reality.

The process of changing the state of the thermodynamic system of macroscopic bodies at a constant temperature is called isothermal.

To maintain the temperature of the gas constant, it is necessary that it be able to exchange heat with a large system - a thermostat. Otherwise, during compression or expansion, the temperature of the gas will change. Atmospheric air can serve as a thermostat if its temperature does not noticeably change throughout the process.

According to the equation of state of an ideal gas, in any state with a constant temperature, the product of the gas pressure and its volume remains constant: pV=const at T=const. For a gas of a given mass, the product of the pressure of the gas and its volume is constant if the temperature of the gas does not change.

This law was experimentally discovered by the English scientist R. Boiler (1627 - 1691) and somewhat later by the French scientist E Mariotte (1620 -1684). Therefore, it is called the Boyle-Mariotte law.

Boyle's law - Mariotte is valid for any gases, as well as their mixtures, for example, for air. Only at pressures several hundred times greater than atmospheric pressure does the deviation from this law become significant.

The dependence of gas pressure on volume at constant temperature is graphically represented by a curve called an isotherm. A gas isotherm depicts the inverse relationship between pressure and volume. A curve of this kind is called a hyperbola in mathematics.

Different constant temperatures correspond to different isotherms. As the temperature rises, the pressure according to the equation of state increases if V=const. Therefore, the isotherm corresponding to a higher temperature T 2 , lies above the isotherm corresponding to the lower temperature T 1 .

An isothermal process can be approximately considered the process of slow compression of air during the expansion of gas under the pump piston when pumping it out of the vessel. True, the temperature of the gas changes in this case, but in the first approximation this change can be neglected.

The process of changing the state of a thermodynamic system at constant pressure is called isobaric (from the Greek "baros" - weight, heaviness).

According to the equation, in any state of a gas with constant pressure, the ratio of the gas volume to its temperature remains constant: =const at p=const.

For a gas of a given mass, the ratio of volume to temperature is constant if the pressure of the gas does not change.

This law was established experimentally in 1802 by the French scientist J. Gay-Lussac (1778 - 1850) and is called Gay-Lussac's law.

According to the equation, the volume of gas depends linearly on temperature at constant pressure: V=const T.

This dependence is graphically represented by a straight line, which is called an isobar. Different pressures correspond to different isobars. With increasing pressure, the volume of gas at a constant temperature decreases according to the Boyle-Mariotte law. Therefore, the isobar corresponding to the higher pressure p 2 , lies below the isobar corresponding to the lower pressure p 1 .

At low temperatures, all isobars of an ideal gas converge at the point T=0. But this does not mean that the volume of real gas really vanishes. All gases with strong cooling turn into a liquid, and the equation of state is not applicable to liquids.

The process of changing the state of a thermodynamic system at a constant volume is called isochoric (from the Greek "horema" - capacity).

It follows from the equation of state that in any state of a gas with a constant volume, the ratio of gas pressure to its temperature remains unchanged: =const at V=const.

For a gas of a given mass, the ratio of pressure to temperature is constant if the volume does not change.

This gas law was established in 1787 by the French physicist J. Charles (1746 - 1823) and is called Charles's law. According to the equation:

Const at V=const gas pressure linearly depends on temperature at constant volume: p=const T.

This dependence is represented by a straight line, called the isochore.

Different volumes correspond to different isochores. With an increase in the volume of a gas at a constant temperature, its pressure, according to the Boyle-Mariotte law, decreases. Therefore, the isochore corresponding to a larger volume V 2 , lies below the isochore corresponding to the smaller volume V 1 .

According to the equation, all isochores start at the point T=0.

So the pressure of an ideal gas at absolute zero is zero.

The increase in gas pressure in any container or in a light bulb when heated is an isochoric process. The isochoric process is used in constant volume gas thermostats.

4. Temperature.

Any macroscopic body or group of macroscopic bodies is called a thermodynamic system.

Thermal or thermodynamic equilibrium is such a state of a thermodynamic system in which all its macroscopic parameters remain unchanged: volume, pressure do not change, heat transfer does not occur, there are no transitions from one state of aggregation to another, etc. Under constant external conditions, any thermodynamic system spontaneously passes into a state of thermal equilibrium.

Temperature is a physical quantity that characterizes the state of thermal equilibrium of a system of bodies: all bodies of the system that are in thermal equilibrium with each other have the same temperature.

Absolute zero temperature - the limiting temperature at which the pressure of an ideal gas at constant volume must be zero or the volume of an ideal gas at constant pressure must be equal to zero.

Thermometer - a device for measuring temperature. Typically, thermometers are calibrated on the Celsius scale: the temperature of water crystallization (ice melting) corresponds to 0 ° C, its boiling point is 100 ° C.

Kelvin introduced an absolute temperature scale, according to which zero temperature corresponds to absolute zero, the temperature unit on the Kelvin scale is equal to degrees Celsius: [T] = 1 K (Kelvin).

Relationship between temperature in energy units and temperature in degrees Kelvin:

where k \u003d 1.38 * 10 -23 J/K - Boltzmann's constant.

The relationship between the absolute scale and the Celsius scale:

T = t + 273, where t is the temperature in degrees Celsius.

The average kinetic energy of the random motion of gas molecules is proportional to the absolute temperature:

Taking into account equality (1), the basic equation of the molecular kinetic theory can be written as follows: p = nkT .

Basic equations of the molecular-kinetic theory of an ideal gas for pressure.

A gas is called ideal if:

1) the own volume of gas molecules is negligible compared to the volume of the vessel;

2) there are no interaction forces between gas molecules;

3) collisions of gas molecules with the walls of the vessel are absolutely elastic.

Real gases (for example, oxygen and helium) under conditions close to normal, as well as at low pressures and high temperatures, are close to ideal gases. Particles of an ideal gas in the intervals between collisions move uniformly and rectilinearly. The gas pressure on the walls of the vessel can be considered as a series of rapidly following impacts of gas molecules against the wall. Let's look at how to calculate the pressure caused by individual impacts. Let us imagine that a series of separate and frequent impacts occurs on a certain surface. Find such an average constant force , which, acting during the time t during which individual impacts occurred, will produce the same effect as all these impacts in their totality. In this case, the momentum of this average force during the time t must be equal to the sum of the impulses of all those impacts that the surface received during this time, i.e.

Where t 1 , t 2 , t 3 ... t n - the time of interaction of the first, second, ..., n-th molecules with the wall (i.e., the duration of the impact); f 1 , f 2 , f 3 ... f n is the impact force of the molecules on the wall. From this formula follows:

(7).

The average pressure force caused by a number of individual impacts on a certain surface is numerically equal to the sum of the impulses of all impacts received by this surface per unit time is called the isochore.

5. Velocities of gas molecules.

Formula (12) can be written as:

(15), where (mass of gas).

From expression (15) we calculate the mean square velocity of gas molecules:

(16) .

Knowing that (R is the universal gas constant; R=8.31), we obtain new expressions for determining .

(17) .

An experimental determination of the velocities of movement of silver vapor molecules was first carried out in 1920 by Stern.

Rice. 5. Stern's experiment.

Air was pumped out of the glass cylinder E (Fig. 5). A second cylinder D was placed inside this cylinder, having a common axis O with it. Along the generatrix of the cylinder D there was a cut in the form of a narrow slot C. A silver-plated platinum wire was stretched along the axis, through which current could be passed. At the same time, the wire was heated, and the silver from its surface turned into steam. Silver vapor molecules scattered in different directions, some of them passed through slot C of cylinder D, and on the inner surface of cylinder E a silver deposit appeared in the form of a narrow strip. On fig. 5 the position of the silver strip is marked with the letter A.

When the whole system was brought into very rapid motion in such a way that the wire was the axis of rotation, then the strip A on the cylinder E turned out to be displaced to the side, i.e. for example, not at point A, but at point B. This happened because while the silver molecules flew the path CA, point A of cylinder E had time to turn by a distance AB and the silver molecules fell not at point A, but at point B.

Let us denote the shift of the silver strip AB = d; the radius of the cylinder E through R, the radius of the cylinder D through r, and the number of revolutions of the entire system per second through n.

In one revolution of the system, point A on the surface of cylinder E will travel a path equal to the circumference 2πR, and in 1 second it will travel a path. The time t during which point A has moved a distance AB = d will be equal to:. During the time t, the silver vapor molecules flew a distance CA = R - r . Their speed v can be found as the distance traveled divided by the time:or, replacing t, we get:.

The silver coating on the cylinder wall D turned out to be blurry, which confirmed the presence of different velocities of the molecules. From experience, it was possible to determine the most probable speed v ver which corresponded to the greatest thickness of the silver plaque.

The most probable speed can be calculated using the formula given by Maxwell:(eighteen). According to Maxwell's calculations, the arithmetic mean velocity of molecules is: (19).

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

From the basic equation of the molecular kinetic theory (formula (14) follows Avogadro's law: equal volumes of dissimilar gases under the same conditions (the same temperature and the same pressure) contain the same number of molecules:(for one gas),(for other gas).

If V 1 = V 2 ; T 1 = T 2; r 1 \u003d r 2, then n 01 \u003d n 02.

Recall that the unit of the amount of a substance in the SI system is the mole (gram-molecule) mass m one mole of a substance is called the molar mass of that substance. The number of molecules contained in one mole of different substances is the same and is called the Avogadro number (N A = 6.0210 23 1/mol).

We write the equation of state for an ideal gas for one mole:, where Vm - the volume of one mole of gas;, where Vm - the volume of one mole of gas; (universal gas constant).

Finally we have: (26).

Equation (26) is called the Clapeyron equation (for one mole of gas). Under normal conditions (p = 1.01310 5 Pa and T = 273.15 0 K) the molar volume of any gas V m = 22.410 -3 . From formula (26) we determine; .

From equation (26) for a mole of gas, one can go to the Mendeleev-Clapeyron equation for any gas mass m.

Attitude gives the number of moles of the gas. We multiply the left and right parts of inequality (26) by.

We have where is the volume of the gas.

Let's finally write: (27 ) . Equation (27) is the Mendeleev-Clapeyron equation. The gas density can be introduced into this equation and .

In formula (27), we replace V and obtain or .

7. Experienced gas laws. Pressure of a mixture of ideal gases (Dalton's law).

Empirically, long before the advent of molecular-kinetic theory, a number of laws were discovered that describe equilibrium isoprocesses in an ideal gas. An isoprocess is an equilibrium process in which one of the state parameters does not change (is constant). There are isothermal (T = const), isobaric (p = const), isochoric (V = const) isoprocesses. An isothermal process is described by the Boyle-Mariotte law: "if during the process the mass and temperature of an ideal gas do not change, then the product of the gas pressure and its volume is a constant PV = const (29). The graphic representation of the equation of state is called a state diagram. In the case of isoprocesses, state diagrams are depicted as two-dimensional (flat) curves and are called isotherms, isobars, and isochores, respectively.

Isotherms corresponding to two different temperatures are shown in Figs. 6.

Rice. 6. Isotherms corresponding to two different temperatures.

The isobaric process is described by the Gay-Lussac law: "if during the process the pressure and mass of an ideal gas do not change, then the ratio of the gas volume to its absolute temperature is a constant:(30).

Isobars corresponding to two different pressures are shown in Fig.7.

Rice. 7. Isobars corresponding to two different pressures.

The equation of the isobaric process can be written differently:31), where V 0 - gas volume at 0 0 C; V t - volume of gas at t 0 C; t is the gas temperature in degrees Celsius;α - coefficient of volumetric expansion. From formula (31) it follows that. The experiments of the French physicist Gay-Lussac (1802) showed that the coefficients of volumetric expansion of all types of gases are the same and, i.e. when heated by 1 0 C gas increases its volume by a fraction of the volume it occupied at 0 0 C. In fig. 8 shows a graph of the dependence of the volume of gas V t temperature t 0C.

Rice. eight. Graph of gas volume V t temperature t 0C.

The isochoric process is described by Charles's law: "if during the process the volume and mass of an ideal gas do not change, then the ratio of the gas pressure to its absolute temperature is a constant:

(32).

Isochores corresponding to two different volumes are shown in fig. 9.

Rice. 9. Isochores corresponding to two different volumes.

The isochoric process equation can be written differently:(33), where - gas pressure at FROM; - gas pressure at t; t is the gas temperature in degrees Celsius;- temperature coefficient of pressure. From formula (33) it follows that. For all gases and . If the gas is heated toC (at V=const), then the gas pressure will increase bypart of the pressure that he had whenC. Figure 10 shows a graph of gas pressure versus temperature t.

Rice. ten. Graph of gas pressure versus temperature t.

If we continue line AB until it intersects the x-axis (point), then the value of this abscissa is determined from formula (33), ifequate to zero.

;

Therefore, at a temperaturethe gas pressure would have to go to zero, however, with such cooling, the gas will not retain its gaseous state, but will turn into a liquid and even into a solid. Temperatureis called absolute zero.

In the case of a mechanical mixture of gases that do not enter into chemical reactions, the pressure of the mixture is also determined by the formula, where (mixture concentrationis equal to the sum of the concentrations of the components of the mixture in total n - components).

Dalton's law states: Mixture pressureis equal to the sum of the partial pressures of the gases forming the mixture.. Pressure called partial. Partial pressure is the pressure that a given gas would create if it alone occupied the vessel in which the mixture is located (in the same amount in which it is contained in the mixture).

BIBLIOGRAPHY

1. Brychkov Yu.A., Marichev O.I., Prudnikov A.P. Tables of indefinite integrals: A Handbook. - M.: Nauka, 1986.

2. Kogan M.N. Dynamics of rarefied gas. M., Fizmatlit, 1999.

3. A. K. Kikoin, Molecular Physics. M., Fizmatlit, 1976.

4. Sivukhin D.V. General course of physics, v. 2. Thermodynamics and molecular physics. M., Fizmatlit, 1989.

5. Kiryanov A.P., Korshunov S.M. Thermodynamics and molecular physics. Student aid. Ed. prof. HELL. Gladun. - M., "Enlightenment", 1977.

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