As is known, many substances in nature can be in three states of aggregation: solid, liquid And gaseous.
The doctrine of the properties of matter in various states of aggregation is based on ideas about the atomic-molecular structure of the material world. The molecular kinetic theory of the structure of matter (MKT) is based on three main principles:
- all substances consist of tiny particles (molecules, atoms, elementary particles), between which there are spaces;
- particles are in continuous thermal motion;
- there are interaction forces between particles of matter (attraction and repulsion); the nature of these forces is electromagnetic.
This means that the state of aggregation of a substance depends on the relative position of the molecules, the distance between them, the forces of interaction between them and the nature of their movement.
The interaction between particles of a substance is most pronounced in the solid state. The distance between molecules is approximately equal to their own sizes. This leads to a fairly strong interaction, which practically makes it impossible for the particles to move: they oscillate around a certain equilibrium position. They retain their shape and volume.
The properties of liquids are also explained by their structure. Particles of matter in liquids interact less intensely than in solids, and therefore can change their location abruptly - liquids do not retain their shape - they are fluid. Liquids retain volume.
A gas is a collection of molecules moving randomly in all directions independently of each other. Gases do not have their own shape, occupy the entire volume provided to them and are easily compressed.
There is another state of matter - plasma. Plasma is a partially or fully ionized gas in which the densities of positive and negative charges are almost equal. When heated strongly enough, any substance evaporates, turning into a gas. If you increase the temperature further, the process of thermal ionization will sharply intensify, i.e., gas molecules will begin to disintegrate into their constituent atoms, which then turn into ions.
Ideal gas model. Relationship between pressure and average kinetic energy.
To clarify the laws that govern the behavior of a substance in the gaseous state, an idealized model of real gases is considered - an ideal gas. This is a gas whose molecules are considered as material points that do not interact with each other at a distance, but interact with each other and with the walls of the container during collisions.
Ideal gas – It is a gas in which the interaction between its molecules is negligible. (Ek>>Er)
An ideal gas is a model invented by scientists to understand the gases that we actually observe in nature. It cannot describe any gas. Not applicable when the gas is highly compressed, when the gas turns into a liquid state. Real gases behave like ideal gases when the average distance between molecules is many times larger than their sizes, i.e. at sufficiently large vacuums.
Properties of an ideal gas:
- the distance between molecules is much greater than the size of the molecules;
- gas molecules are very small and are elastic balls;
- the forces of attraction tend to zero;
- interactions between gas molecules occur only during collisions, and collisions are considered absolutely elastic;
- the molecules of this gas move randomly;
- movement of molecules according to Newton's laws.
The state of a certain mass of gaseous substance is characterized by physical quantities dependent on each other, called state parameters. These include volumeV, pressurepand temperatureT.
Gas volume denoted by V. Volume gas always coincides with the volume of the container it occupies. SI unit of volume m 3.
Pressure– physical quantity equal to the ratio of forceF, acting on a surface element perpendicular to it, to the areaSthis element.
p = F/ S SI unit of pressure pascal[Pa]
Until now, non-systemic units of pressure are used:
technical atmosphere 1 at = 9.81-104 Pa;
physical atmosphere 1 atm = 1.013-105 Pa;
millimeters of mercury 1 mmHg Art. = 133 Pa;
1 atm = = 760 mm Hg. Art. = 1013 hPa.
How does gas pressure arise? Each gas molecule, hitting the wall of the vessel in which it is located, acts on the wall with a certain force for a short period of time. As a result of random impacts on the wall, the force exerted by all molecules per unit area of the wall changes rapidly with time relative to a certain (average) value.
Gas pressureoccurs as a result of random impacts of molecules on the walls of the vessel containing the gas.
Using the ideal gas model, we can calculate gas pressure on the wall of the vessel.
During the interaction of a molecule with the wall of a vessel, forces arise between them that obey Newton’s third law. As a result, the projection υ x the molecular speed perpendicular to the wall changes its sign to the opposite, and the projection υ y the speed parallel to the wall remains unchanged.
Devices that measure pressure are called pressure gauges. Pressure gauges record the time-average pressure force per unit area of its sensitive element (membrane) or other pressure receiver.
Liquid pressure gauges:
- open – for measuring small pressures above atmospheric
- closed - for measuring small pressures below atmospheric, i.e. small vacuum
Metal pressure gauge– for measuring high pressures.
Its main part is a curved tube A, the open end of which is soldered to tube B, through which gas flows, and the closed end is connected to the arrow. Gas enters through the tap and tube B into tube A and unbends it. The free end of the tube, moving, sets the transmission mechanism and the pointer in motion. The scale is graduated in pressure units.
Basic equation of the molecular kinetic theory of an ideal gas.
Basic MKT equation: the pressure of an ideal gas is proportional to the product of the mass of the molecule, the concentration of the molecules and the mean square of the speed of the molecules
p= 1/3m 0· n·v 2
m 0 - mass of one gas molecule;
n = N/V – number of molecules per unit volume, or concentration of molecules;
v 2 - root mean square speed of movement of molecules.
Since the average kinetic energy of translational motion of molecules is E = m 0 *v 2 /2, then multiplying the basic MKT equation by 2, we obtain p = 2/3 n (m 0 v 2)/2 = 2/3 E n
p = 2/3 E n
Gas pressure is equal to 2/3 of the average kinetic energy of translational motion of the molecules contained in a unit volume of gas.
Since m 0 n = m 0 N/V = m/V = ρ, where ρ is the gas density, we have p= 1/3· ρ·v 2
United gas law.
Macroscopic quantities that unambiguously characterize the state of a gas are calledthermodynamic parameters of gas.
The most important thermodynamic parameters of a gas are itsvolumeV, pressure p and temperature T.
Any change in the state of a gas is calledthermodynamic process.
In any thermodynamic process, the gas parameters that determine its state change.
The relationship between the values of certain parameters at the beginning and end of the process is calledgas law.
The gas law expressing the relationship between all three gas parameters is calledunited gas law.
p = nkT
Ratio p = nkT relating the pressure of a gas to its temperature and concentration of molecules was obtained for a model of an ideal gas, the molecules of which interact with each other and with the walls of the vessel only during elastic collisions. This relationship can be written in another form, establishing a connection between the macroscopic parameters of a gas - volume V, pressure p, temperature T and the amount of substance ν. To do this you need to use the equalities
where n is the concentration of molecules, N is the total number of molecules, V is the volume of gas
Then we get or
Since at a constant gas mass N remains unchanged, then Nk is a constant number, which means
At a constant mass of a gas, the product of volume and pressure divided by the absolute temperature of the gas is the same value for all states of this mass of gas.
The equation establishing the relationship between pressure, volume and temperature of a gas was obtained in the middle of the 19th century by the French physicist B. Clapeyron and is often called Clayperon equation.
The Clayperon equation can be written in another form.
p = nkT,
considering that
Here N– number of molecules in the vessel, ν – amount of substance, N A is Avogadro’s constant, m– mass of gas in the vessel, M– molar mass of gas. As a result we get:
Product of Avogadro's constant N A byBoltzmann constantk is called universal (molar) gas constant and is designated by the letter R.
Its numerical value in SI R= 8.31 J/mol K
Ratio
called ideal gas equation of state.
In the form we received, it was first written down by D.I. Mendeleev. Therefore, the equation of state of the gas is called Clapeyron–Mendeleev equation.`
For one mole of any gas this relationship takes the form: pV=RT
Let's install physical meaning of the molar gas constant. Let us assume that in a certain cylinder under the piston at temperature E there is 1 mole of gas, the volume of which is V. If the gas is heated isobarically (at constant pressure) by 1 K, then the piston will rise to a height Δh, and the volume of the gas will increase by ΔV.
Let's write the equation pV=RT for heated gas: p (V + ΔV) = R (T + 1)
and subtract from this equality the equation pV=RT, corresponding to the state of the gas before heating. We get pΔV = R
ΔV = SΔh, where S is the area of the base of the cylinder. Let's substitute into the resulting equation:
pS = F – pressure force.
We obtain FΔh = R, and the product of the force and the displacement of the piston FΔh = A is the work of moving the piston performed by this force against external forces during gas expansion.
Thus, R = A.
The universal (molar) gas constant is numerically equal to the work done by 1 mole of gas when it is heated isobarically by 1 K.
An ideal gas is a theoretical model of a gas in which the sizes and interactions of gas particles are neglected and only their elastic collisions are taken into account.
The ideal gas model was proposed in 1847 by J. Herapat. Based on this model, gas laws were theoretically derived (Boyle-Mariotte law, Gay-Lussac law, Charles law, Avogadro law), which had previously been established experimentally. The ideal gas model was the basis for the molecular kinetic theory of gases.
The basic laws of an ideal gas are equation of state And Avogadro's law in which for the first time the macro characteristics of a gas (pressure, temperature, mass) were related to the mass of the molecule (the Mendeleev-Clapeyron equation, or the equation of state of an ideal gas)
In the simplest model of a gas, molecules are considered to be very small, solid balls with mass. The movement of individual molecules obeys Newton's laws of mechanics. Of course, not all processes in rarefied gases can be explained using such a model, but gas pressure can be calculated using it.
2. Basic equation of MKT
§ Ideal gas. To explain the properties of matter in the gaseous state, the ideal gas model is used. The ideal gas model assumes the following: molecules have a negligibly small volume compared to the volume of the vessel, there are no attractive forces between molecules, and when molecules collide with each other and with the walls of the vessel, repulsive forces act.
§ Ideal gas pressure. One of the first and important successes of molecular kinetic theory was the qualitative and quantitative explanation of the phenomenon of gas pressure on the walls of a vessel.
§ A qualitative explanation of gas pressure is that molecules of an ideal gas, when colliding with the walls of a vessel, interact with them according to the laws of mechanics as elastic bodies. When a molecule collides with the wall of a vessel, the projection of the velocity vector onto the axis OH, perpendicular to the wall, changes its sign to the opposite, but remains constant in magnitude
§ During a collision, the molecule acts on the wall with a force equal, according to Newton’s third law, to the force in magnitude and directed oppositely.
§ There are a lot of gas molecules, and their impacts on the wall follow one after another with a very high frequency. The average value of the geometric sum of forces acting on the part of individual molecules during their collisions with the wall of the vessel is the gas pressure force. Gas pressure is equal to the ratio of the modulus of pressure force to the wall area S:
§ Based on the use of the basic principles of molecular kinetic theory, an equation was obtained that made it possible to calculate the gas pressure if the mass is known m 0 gas molecules, the average value of the squared speed of molecules and concentration n molecules:
§ The equation is called the basic equation of molecular kinetic theory.
Denoting the average value of the kinetic energy of the translational motion of molecules of an ideal gas:
3. Gas pressure
Pressure is the force per unit area.
The pressure of a gas is the result of its molecules hitting the walls of the container.
Gas pressure. Mendeleev - Clayperon equation
Gas pressure. Clayperon equation.
Unified gas law (at m-const).
Ticket No. 25
Pure solids in the usual state are crystals with almost complete ordering of structural units: atoms, ions or molecules. A small group of amorphous solids is known - glass, resins, plastics, etc., the components of which (macromolecules or macroions) are almost completely unordered. Amorphous solids can be considered as supercooled liquids with very high viscosity. They do not have an ordered crystal lattice, do not have specific melting points, but melt over a wide temperature range. They are isotropic; this means that the physical properties of such substances are constant in all directions.
Unlike amorphous bodies and liquids, in crystals there is, as schematically shown in the figure, long-range order in the arrangement of atoms of a solid body. The atoms in this case are located at the nodes of a regular spatial grid (crystal lattice). For any direction in space A, B, C, D, E, ..., passing through the centers of atoms, the distance between the centers of two neighboring atoms remains unchanged along the entire line, but differs for different lines. In accordance with this, the physical properties (elastic, mechanical, thermal, electrical, magnetic, optical, etc., will, generally speaking, be different in different directions. The unequal properties of a crystal in different directions are called anisotropy.
Ticket No. 26
An external mechanical effect on a body causes a displacement of atoms from equilibrium positions and leads to a change in the shape and volume of the body, i.e., to its deformation. The simplest types of deformation are tension and compression. Cables of cranes, cable cars, towing cables, and strings of musical instruments experience tension. The walls and foundations of buildings are subject to compression. Bends are experienced by floor beams in buildings and bridges. Bending deformation is reduced to compression and tension deformations, which vary in different parts of the body.
Strain and stress. Compressive and tensile deformation can be characterized by absolute elongation Δl, equal to the difference in sample lengths before stretching l 0 and after it l :
Absolute elongation in tension is positive, and in compression it is negative.
The ratio of absolute elongation to the length of the sample is called relative elongation :
When a body deforms, elastic forces arise. A physical quantity equal to the ratio of the modulus of elastic force to the cross-sectional area of a body is called mechanical stress :
The SI unit of mechanical stress is pascal(Pa). .
The simplest types of deformation of the body as a whole:
§ tension-compression,
§ torsion.
In most practical cases, the observed deformation is a combination of several simultaneous simple deformations. Ultimately, however, any deformation can be reduced to two simplest ones: tension (or compression) and shear.
Ticket No. 27
Melting is the process of transition of a substance from a solid crystalline state to a liquid. Melting occurs at a constant temperature with heat absorption. The constancy of the temperature is explained by the fact that during melting, all the heat supplied goes to disorder the regular spatial arrangement of atoms (molecules) in the crystal lattice. In this case, the average distance between atoms and, consequently, the interaction forces changes slightly. Melting point for a given crystal? its important characteristic, but it is not a constant value, but significantly depends on the external pressure at which melting occurs. For most crystals (except water and some alloys), the melting temperature increases with increasing external pressure, since moving atoms away from each other at higher pressure requires greater energy of thermal motion, i.e., a higher temperature.
Specific heat of fusion- the amount of heat that must be imparted to one unit of mass of a crystalline substance in an equilibrium isobaric-isothermal process in order to transfer it from a solid (crystalline) state to a liquid (the same amount of heat is released during crystallization of the substance).
The heat of fusion is a special case of the heat of a first-order phase transition.
A distinction is made between specific heat of fusion (J/kg) and molar heat (J/mol).
The specific heat of fusion is denoted by the letter (Greek letter lambda) Formula for calculating the specific heat of fusion: , where is the specific heat of fusion, is the amount of heat received by the substance during melting (or released during crystallization), is the mass of the melting (crystallizing) substance.
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Thermodynamics- a branch of physics that studies the relationships and transformations of heat and other forms of energy. Chemical thermodynamics, which studies physical and chemical transformations associated with the release or absorption of heat, as well as thermal engineering, have become separate disciplines.
In thermodynamics, we deal not with individual molecules, but with macroscopic bodies consisting of a huge number of particles. These bodies are called thermodynamic systems. In thermodynamics, thermal phenomena are described by macroscopic quantities - pressure, temperature, volume, ..., which are not applicable to individual molecules and atoms.
In theoretical physics, along with phenomenological thermodynamics, which studies the phenomenology of thermal processes, there is statistical thermodynamics, which was created for the mechanical substantiation of thermodynamics and was one of the first branches of statistical physics
.The internal energy of a body (denoted as E or U) is the sum of the energies of molecular interactions and thermal motions of the molecule. Internal energy is a unique function of the state of the system. This means that whenever a system finds itself in a given state, its internal energy takes on the value inherent in this state, regardless of the previous history of the system. Consequently, the change in internal energy during the transition from one state to another will always be equal to the difference between its values in the final and initial states, regardless of the path along which the transition took place.
The internal energy of a body cannot be measured directly. You can only determine the change in internal energy:
§ - brought to the body heat, measured in joules
§ - Job performed by a body against external forces, measured in joules
This formula is a mathematical expression first law of thermodynamics
For quasi-static processes the following relation holds:
§ - temperature, measured in kelvins
§ - entropy, measured in joules/kelvin
§ - pressure, measured in pascals
§ - chemical potential
§ - number of particles in the system
Molecules can be considered as systems of material points (atoms) performing both translational and rotational motions. When studying the movement of a body, it is necessary to know its position relative to the selected coordinate system. For this purpose, the concept of degrees of freedom of a body is introduced. The number of independent coordinates that completely determine the position of the body in space is called the number of degrees of freedom of the body.
When a point moves along a straight line, to estimate its position, you need to know one coordinate, i.e. a point has one degree of freedom. If the point of motion is on a plane, its position is characterized by two coordinates; in this case, the point has two degrees of freedom. The position of a point in space is determined by 3 coordinates. The number of degrees of freedom is usually denoted by the letter i. Molecules that consist of an ordinary atom are considered material points and have three degrees of freedom (argon, helium).
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| Work in thermodynamics. | |
| In thermodynamics, the movement of a body as a whole is not considered and we are talking about the movement of parts of a macroscopic body relative to each other. When work is done, the volume of the body changes, but its speed remains zero. But speed body molecules change! Therefore, body temperature changes. The reason is that when colliding with a moving piston (gas compression), the kinetic energy of the molecules changes - the piston gives up part of its mechanical energy. When colliding with a retreating piston (expansion), the velocities of the molecules decrease and the gas cools. When doing work in thermodynamics, the state of macroscopic bodies changes: their volume and temperature. | |
| - the force acting on the gas from the piston. A is the work of external forces to compress the gas. - the force acting on the piston from the gas side. A" is the work of gas by expansion. = - - according to Newton's 3rd law. Therefore: A = - A" = pS, where p is the pressure, S is the area of the piston. If the gas expands: Dh=h 2 - h 1 - piston movement. V 1 = Sh 1 ; V 2 =Sh 2. |  |
Physical meaning of the molar gas constant. Let an ideal gas undergo an isobaric transition from the 1st state to the 2nd state. The pressure in both states is the same, let us denote it p. For any state, the Clapeyron-Mendeleev equation is valid, so we can write:
p 1 V 1 = RT 1 And p 2 V 2 = RT 2.
Let's find the work done by the gas:
A = p V = p(V 2 – V 1) = pV 2 – pV 1.
Let us substitute the relations obtained above, then:
A = RT 2 – RT 1 = R(T 2 – T 1).
The change in temperature is in parentheses, so we finally get:
If there is one mole of gas and the temperature change is 1 K, then the work is equal to the molar gas constant.
The molar gas constant is numerically equal to the work done by one mole of an ideal gas when it is heated isobarically by 1 K.
Ticket No. 30
1.Heat transfer physical transfer process thermal energy from a hotter body to a colder one either directly (by contact) or through a separating (body or environment) partition made of any material. When physical bodies of one system are at different temperature, then it happens thermal energy transfer, or heat transfer from one body to another before the onset thermodynamic equilibrium. Spontaneous heat transfer Always occurs from a hotter body to a colder one, which is a consequence second law of thermodynamics
2. In total, there are three simple (elementary) types of heat transfer:
§ Thermal conductivity
§ Convection
§ Thermal radiation
There are also various types of complex heat transfer, which are a combination of elementary types. The main ones:
§ heat transfer (convective heat exchange between liquid or gas flows and the surface of a solid);
§ heat transfer (heat exchange from hot liquid to cold liquid through the wall separating them);
§ convective-radiative heat transfer (combined heat transfer by radiation and convection);
§ thermomagnetic convection
Ticket No. 35
Heat engines.
Heat engines convert part of the internal energy of the system into mechanical energy and, due to it, perform mechanical work.
For a heat engine to operate, three bodies must be present: a heater, a working fluid and a refrigerator (Fig. 5.1).
The heat engine operates cyclically. Having received a certain amount of heat from the heater Q 1, the working fluid, expanding, does mechanical work A, then returns to its original state - it compresses, while the unspent part of the heat Q 2 it gives to the refrigerator.
Rice. 5.1.
Work per cycle is equal to:
A = Q 1 – Q 2,
and efficiency heat engine is calculated by the formula:
The efficiency of the first steam engines was did not exceed 10–15%. Efficiency modern steam turbines used in power plants are close to 25%, while for gas turbines it reaches 50%. Internal combustion engines are efficient. 40–45%, and for turbojet engines it is 60–70%.
It is impossible to create a heat engine that would convert all the heat received from the heater into mechanical work.
This is an alternative formulation second law of thermodynamics.
An ideal gas is a model of a rarefied gas in which interactions between molecules are neglected. The forces of interaction between molecules are quite complex. At very short distances, when molecules come close to each other, large forces act between them.the magnitude of the repulsive force. At large or intermediate distances between molecules, relatively weak attractive forces act. If the distances between molecules are on average large, which is observed in a fairly rarefied gas, then the interaction manifests itself in the form of relatively rare collisions of molecules with each other when they fly close. In an ideal gas, the interaction of molecules is completely neglected.
The theory was created by the German physicist R. Clausis in 1957 for a model of a real gas called an ideal gas. Main features of the model:
- · the distances between molecules are large compared to their sizes;
- · there is no interaction between molecules at a distance;
- · When molecules collide, large repulsive forces act;
- · the collision time is much less than the time of free movement between collisions;
- · movements obey Newton's law;
- · molecules - elastic balls;
- · Withinteraction forces occur during a collision.
The limits of applicability of the ideal gas model depend on the problem under consideration. If it is necessary to establish a relationship between pressure, volume and temperature, then the gas can be considered ideal with good accuracy up to pressures of several tens of atmospheres. If a phase transition such as evaporation or condensation is being studied or the process of establishing equilibrium in a gas is being considered, then the ideal gas model cannot be used even at pressures of several millimeters of mercury.
The gas pressure on the wall of a vessel is a consequence of chaotic impacts of molecules on the wall; due to their high frequency, the effect of these impacts is perceived by our senses or instruments as a continuous force acting on the wall of the vessel and creating pressure.
Let one molecule be in a vessel shaped like a rectangular parallelepiped (Fig. 1). Let us consider, for example, the impacts of this molecule on the right wall of the vessel, perpendicular to the X axis. We consider the impacts of the molecule on the walls to be absolutely elastic, then the angle of reflection of the molecule from the wall is equal to the angle of incidence, and the magnitude of the velocity does not change as a result of the impact. In our case, upon impact, the projection of the molecule's velocity onto the axis U does not change, and the projection of the velocity onto the axis X changes sign. Thus, the projection of the impulse changes upon impact by an amount equal to , the sign “-” means that the projection of the final velocity is negative, and the projection of the initial velocity is positive.
Let us determine the number of impacts of a molecule on a given wall in 1 second. The magnitude of the velocity projection does not change when hitting any wall, i.e. we can say that the movement of a molecule along the axis X uniform. In 1 second, it flies a distance equal to the projection of speed. From the impact to the next impact on the same wall, the molecule flies along the X axis a distance equal to twice the length of the vessel 2
L. Therefore, the number of impacts of the molecule on the selected wall is equal to . According to Newton's 2nd law, the average force is equal to the change in momentum of the body per unit time. If, with each impact on the wall, the particle changes momentum by an amount , and the number of impacts per unit time is equal to , then the average force acting on the molecule from the wall (equal in magnitude to the force acting on the wall from the molecule) is equal to , and the average pressure of the molecule equal to the wall 
, Where V– volume of the vessel.
If all molecules had the same speed, then the total pressure would be obtained simply by multiplying this value by the number of particles N, i.e. . But since gas molecules have different speeds, this formula will contain the average value of the square of the speed, then the formula will take the form: .
The square of the velocity module is equal to the sum of the squares of its projections, this also occurs for their average values: 
. Due to the chaotic nature of thermal motion, the average values of all squares of velocity projections are the same, because there is no preferential movement of molecules in any direction. Therefore, and then the formula for gas pressure will take the form: . If we introduce the kinetic energy of the molecule, we obtain where is the average kinetic energy of the molecule.
According to Boltzmann, the average kinetic energy of a molecule is proportional to the absolute temperature, and then the pressure of an ideal gas is equal to or
If you enter the particle concentration , the formula will be rewritten as follows:
The number of particles can be represented as the product of the number of moles and the number of particles in a mole, equal to Avogadro's number, and the product . Then (1) will be written as:
Let's consider particular gas laws. At constant temperature and mass, it follows from (4) that, i.e. at a constant temperature and mass of a gas, its pressure is inversely proportional to its volume. This law is called Boyle and Mariotte's law, and the process in which the temperature is constant is called isothermal.
For an isobaric process occurring at constant pressure, it follows from (4) that , i.e. volume is proportional to absolute temperature. This law is called Gay-Lussac's law.
For an isochoric process occurring at a constant volume, it follows from (4) that , i.e. pressure is proportional to absolute temperature. This law is called Charles's law.
These three gas laws are thus special cases of the ideal gas equation of state. Historically, they were first discovered experimentally, and only much later obtained theoretically, based on molecular concepts.
Ideal gas(ideal gas) – a gas whose interaction forces between molecules can be neglected. Or: a gas whose equilibrium state is described by the Clapeyron equation and in which there are no intermolecular interaction forces, and the volume of the molecules is zero.
Ideal gas- a mathematical model of a gas, in which, within the framework of molecular kinetic theory, it is assumed that: 1) the potential energy of interaction of the particles that make up the gas can be neglected in comparison with their kinetic energy; 2) the total volume of gas particles is negligible; 3) there are no forces of attraction or repulsion between the particles, the collisions of the particles with each other and with the walls of the vessel are absolutely elastic; 4) the interaction time between particles is negligible compared to the average time between collisions. In the extended model of an ideal gas, the particles of which it consists are in the form of elastic spheres or ellipsoids, which makes it possible to take 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. In thermodynamics, an ideal gas is one that obeys the Clapeyron-Mendeleev thermal equation of state.
The model is widely used to solve gas thermodynamics and aerogasdynamics problems. For example, air at atmospheric pressure and room temperature is described with great accuracy by this model. In the case of extreme temperatures or pressures, a more accurate model, such as a van der Waals gas model, which takes into account the attraction between molecules, is required.
There are classical ideal gas (its properties are derived from the laws of classical mechanics and described by Boltzmann statistics) and quantum ideal gas (properties are determined by the laws of quantum mechanics and described by Fermi-Dirac or Bose-Einstein statistics).
The existence of atmospheric pressure was demonstrated by a number of experiments in the 17th century. One of the first proofs of the hypothesis was the Magdeburg hemispheres, designed by the German engineer Guericke. Air was pumped out of the sphere formed by the hemispheres, after which it was difficult to separate them due to external air pressure. Another experiment as part of the study of the nature of atmospheric pressure was carried out by Robert Boyle. It consisted in the fact that if you solder a curved glass tube from the short end, and constantly add mercury to the long elbow, it would not rise to the top of the short elbow, since the air in the tube, compressing, would balance the pressure of the mercury on it. By 1662, these experiments led to the formulation of the Boyle-Mariotte law.
In 1802, Gay-Lussac first published in the open press the law of volumes (called Gay-Lussac's law in Russian-language literature), but Gay-Lussac himself believed that the discovery was made by Jacques Charles in an unpublished work dating back to 1787. Independently of them, the law was discovered in 1801 by the English physicist John Dalton. In addition, the law was described qualitatively by the Frenchman Guillaume Amonton at the end of the 17th century. Subsequently, he refined his experiments and found that when the temperature changes from 0 to 100 °C, the volume of air increases linearly by 0.375. Having carried out similar experiments with other gases, Gay-Lussac found that this number is the same for all gases, despite the generally accepted opinion that different gases expand in different ways when heated.
In 1834, from a combination of these laws, Clapeyron was able to create the ideal gas equation. The same law, already using molecular kinetic theory, was formulated by August Kroenig in 1856 and Rudolf Clausius in 1857.
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, and the internal energy is the sum of the energies of the gas particles.
According to an equivalent formulation, an ideal gas is a gas that simultaneously obeys the Boyle-Mariotte and Gay-Lussac law, that is:
,where is pressure and is absolute temperature. The properties of an ideal gas are described by the Clapeyron-Mendeleev equation:
, where is the universal gas constant, is the mass, is the molar mass,
,where is the particle concentration and is Boltzmann’s constant.
Details Category: Molecular kinetic theory Published 05.11.2014 07:28 Views: 12962Gas is one of four states of aggregation in which a substance can exist.
The particles that make up the gas are very mobile. They move almost freely and chaotically, periodically colliding with each other like billiard balls. Such a collision is called elastic collision . During a collision, they dramatically change the nature of their movement.
Since in gaseous substances the distance between molecules, atoms and ions is much greater than their sizes, these particles interact very weakly with each other, and their potential interaction energy is very small compared to the kinetic energy.
The connections between molecules in a real gas are complex. Therefore, it is also quite difficult to describe the dependence of its temperature, pressure, volume on the properties of the molecules themselves, their quantity, and the speed of their movement. But the task is greatly simplified if, instead of real gas, we consider its mathematical model - ideal gas .
It is assumed that in the ideal gas model there are no attractive or repulsive forces between molecules. They all move independently of each other. And the laws of classical Newtonian mechanics can be applied to each of them. And they interact with each other only during elastic collisions. The time of the collision itself is very short compared to the time between collisions.
Classical ideal gas
Let's try to imagine the molecules of an ideal gas as small balls located in a huge cube at a great distance from each other. Because of this distance, they cannot interact with each other. Therefore, their potential energy is zero. But these balls move at great speed. This means they have kinetic energy. When they collide with each other and with the walls of the cube, they behave like balls, that is, they bounce elastically. At the same time, they change the direction of their movement, but do not change their speed. This is roughly what the motion of molecules in an ideal gas looks like.
- The potential energy of interaction between molecules of an ideal gas is so small that it is neglected compared to kinetic energy.
- Molecules in an ideal gas are also so small that they can be considered material points. And this means that they total volume is also negligible compared to the volume of the vessel in which the gas is located. And this volume is also neglected.
- The average time between collisions of molecules is much greater than the time of their interaction during a collision. Therefore, the interaction time is also neglected.
Gas always takes the shape of the container in which it is located. Moving particles collide with each other and with the walls of the container. During an impact, each molecule exerts some force on the wall for a very short period of time. This is how it arises pressure . The total gas pressure is the sum of the pressures of all molecules.
Ideal gas equation of state
The state of an ideal gas is characterized by three parameters: pressure, volume And temperature. The relationship between them is described by the equation:
Where R - pressure,
V M - molar volume,
R - universal gas constant,
T - absolute temperature (degrees Kelvin).
Because V M = V / n , Where V - volume, n - the amount of substance, and n= m/M , That
Where m - gas mass, M - molar mass. This equation is called Mendeleev-Clayperon equation .
At constant mass the equation becomes:
This equation is called united gas law .
Using the Mendeleev-Cliperon law, one of the gas parameters can be determined if the other two are known.
Isoprocesses
Using the equation of the unified gas law, it is possible to study processes in which the mass of a gas and one of the most important parameters - pressure, temperature or volume - remain constant. In physics such processes are called isoprocesses .
From The unified gas law leads to other important gas laws: Boyle-Mariotte law, Gay-Lussac's law, Charles's law, or Gay-Lussac's second law.
Isothermal process
A process in which pressure or volume changes but temperature remains constant is called isothermal process .
In an isothermal process T = const, m = const .
The behavior of a gas in an isothermal process is described by Boyle-Mariotte law . This law was discovered experimentally English physicist Robert Boyle in 1662 and French physicist Edme Mariotte in 1679. Moreover, they did this independently of each other. The Boyle-Marriott law is formulated as follows: In an ideal gas at a constant temperature, the product of the gas pressure and its volume is also constant.
The Boyle-Marriott equation can be derived from the unified gas law. Substituting into the formula T = const , we get
p · V = const
That's what it is Boyle-Mariotte law . From the formula it is clear that the pressure of a gas at constant temperature is inversely proportional to its volume. The higher the pressure, the lower the volume, and vice versa.
How to explain this phenomenon? Why does the pressure of a gas decrease as the volume of a gas increases?
Since the temperature of the gas does not change, the frequency of collisions of molecules with the walls of the vessel does not change. If the volume increases, the concentration of molecules becomes less. Consequently, per unit area there will be fewer molecules that collide with the walls per unit time. The pressure drops. As the volume decreases, the number of collisions, on the contrary, increases. Accordingly, the pressure increases.
Graphically, an isothermal process is displayed on a curve plane, which is called isotherm . She has a shape hyperboles.
Each temperature value has its own isotherm. The higher the temperature, the higher the corresponding isotherm is located.
Isobaric process
The processes of changing the temperature and volume of a gas at constant pressure are called isobaric . For this process m = const, P = const.
The dependence of the volume of a gas on its temperature at constant pressure was also established experimentally French chemist and physicist Joseph Louis Gay-Lussac, who published it in 1802. That is why it is called Gay-Lussac's law : " Etc and constant pressure, the ratio of the volume of a constant mass of gas to its absolute temperature is a constant value."
At P = const the equation of the unified gas law turns into Gay-Lussac equation .
An example of an isobaric process is a gas located inside a cylinder in which a piston moves. As the temperature rises, the frequency of molecules hitting the walls increases. The pressure increases and the piston rises. As a result, the volume occupied by the gas in the cylinder increases.
Graphically, an isobaric process is represented by a straight line, which is called isobar .
The higher the pressure in the gas, the lower the corresponding isobar is located on the graph.
Isochoric process
Isochoric, or isochoric, is the process of changing the pressure and temperature of an ideal gas at constant volume.
For an isochoric process m = const, V = const.
It is very simple to imagine such a process. It occurs in a vessel of a fixed volume. For example, in a cylinder, the piston in which does not move, but is rigidly fixed.
The isochoric process is described Charles's law : « For a given mass of gas at constant volume, its pressure is proportional to temperature" The French inventor and scientist Jacques Alexandre César Charles established this relationship through experiments in 1787. In 1802, it was clarified by Gay-Lussac. Therefore this law is sometimes called Gay-Lussac's second law.
At V = const from the equation of the unified gas law we get the equation Charles's law or Gay-Lussac's second law .
At constant volume, the pressure of a gas increases if its temperature increases. .
On graphs, an isochoric process is represented by a line called isochore .
The larger the volume occupied by the gas, the lower the isochore corresponding to this volume is located.
In reality, no gas parameter can be maintained unchanged. This can only be done in laboratory conditions.
Of course, an ideal gas does not exist in nature. But in real rarefied gases at very low temperatures and pressures no higher than 200 atmospheres, the distance between the molecules is much greater than their sizes. Therefore, their properties approach those of an ideal gas.