A gas is called ideal if it can be neglected. Ideal gas, definition and properties

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 and molecular structure material world. The molecular kinetic theory of the structure of matter (MKT) is based on three main principles:

• all substances are made up of tiny particles(molecules, atoms, elementary particles) between which there are gaps;
• particles are in continuous thermal motion;
• there are interaction forces between particles of matter (attraction and repulsion); the nature of these forces is electromagnetic.

Means, 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 are positive and negative charges almost identical. 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:

1. there is a lot of distance between molecules more sizes molecules;
2. gas molecules are very small and are elastic balls;
3. the forces of attraction tend to zero;
4. interactions between gas molecules occur only during collisions, and collisions are considered absolutely elastic;
5. the molecules of this gas move randomly;
6. 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:

1. open – for measuring small pressures above atmospheric
2. 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, open end which is soldered to tube B, through which gas flows, and the closed one 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 total number molecules, V – volume of gas

Then we get or

Since at a constant gas mass N remains unchanged, then Nk – constant number, 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 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 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 movement of the piston FΔh = A is the work of moving the piston performed by this force against external forces when gas expands.

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.

Satisfying the following conditions:

1) the intrinsic 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 each other and with the walls of the vessel are absolutely elastic.

2. What parameters characterize the state of the gas? Give a molecular kinetic interpretation of the parameters p, T.

The state of a given gas mass m is characterized by the following parameters: pressure p, volume V, temperature T.

3. Write down the formula connecting temperatures on the Kelvin scale and on the Celsius scale? What is the physical meaning of absolute zero?

The relationship between thermodynamic temperature T and temperature on the centigrade Celsius scale is T = t + 273.15. At absolute zero, the energy of molecules is zero.

4. Write down the equation of state of an ideal gas.

The equation of state of an ideal gas (sometimes the Clapeyron equation or the Clapeyron-Mendeleev equation) is a formula that establishes the relationship between pressure, molar volume and absolute temperature of an ideal gas. The equation has the form: , where p is pressure, Vμ is molar volume, T is absolute temperature, R is the universal gas constant.

5. Which process is called isothermal? Write down and formulate the Boyle-Mariotte law and draw a graph of pressure versus volume.

D For a given mass of gas at a constant temperature, the product of the gas pressure and its volume is a constant value, at . A process occurring at a constant temperature is called isothermal.

6. What process is called isochoric? Write down and formulate Charles's law. Draw a graph of pressure versus temperature.

D The pressure of a given mass of gas at constant volume changes linearly with temperature, at .

A process occurring at constant volume is called isochoric.

7. What process is called isobaric? Write down and formulate Gay-Lussac's law. Draw a graph of volume versus temperature.

ABOUT The volume of a given mass of gas at constant pressure changes linearly with temperature: , at . A process occurring at constant pressure is called isobaric.

8. What process is called adiabatic? Write down Poisson's equation and represent it graphically. (see Appendix No. 2)

A diabatic process is a process that occurs without heat exchange with environment, hence .

Work during adiabatic expansion is carried out due to the loss of internal energy.

Poisson's equation, where is the adiabatic exponent.

9. Write down and formulate the first law of thermodynamics. Give the concept of internal energy, work, amount of heat.

The amount of heat received by the system goes to change its internal energy and perform work against external forces.

The change in the internal energy of a system during its transition from one state to another is equal to the sum of the work of external forces and the amount of heat transferred to the system and does not depend on the method in which this transition is carried out.

10. Write down the expression for the work of gas expansion. How to represent it graphically on a pV diagram.

11. Apply the first law of thermodynamics to all processes considered in this laboratory work and analyze the consequences arising from it.
12. Define specific and molar heat capacities and write down the relationship between them.

The specific heat capacity of a substance is a value equal to the amount of heat required to heat 1 kg of a substance by 1 K.

C=cM.
13. Derive Mayer's equation. Which heat capacity C P or C V is greater and why?

Relationship between molar and heat capacities (Mayer's equations).

Relationship between specific heat capacities

Degrees of freedom are the number in mechanics, the number of possible movements independent of each other mechanical system. The number of degrees of freedom depends on the number of material particles forming the system, and the number and nature of mechanical connections imposed on the system. For a free particle the number of degrees of freedom is 3, for a free particle solid- 6, for a body having a fixed axis of rotation, the number of degrees of freedom is 1, etc. For any holonomic system (system with geometric connections), the number of degrees of freedom is equal to the number s of mutually independent coordinates that determine the position of the system, and is given by the equality 5 = 3n - k, where n

16. Draw and explain on the pV diagram sequentially all the processes occurring with the gas.

17. What is the reason for the change in air temperature in the cylinder when air is pumped into the cylinder and when it is released from the cylinder?

18. Derive a calculation formula to determine the ratio of heat capacities γ.

With this example, we can look in detail at how mathematical models are transformed into physical models.

First of all, an ideal gas is mathematical gas model. And with mathematical point of view, the idea is very simple: the atoms (or molecules) of this very gas “do not see” each other. That is, each particle perceives the vessel as completely empty. Such particles can pass through each other. From this it follows, for example, that all particles can gather at one spatial point.

On the other hand, an ideal gas is physical term. This means that we need to understand what physics is responsible for this mathematical model.

a) So, firstly, in order for atoms to “not see” each other, there must be no potential forces interactions, that is, forces depending on the distance between particles. In terms of energy, this requirement sounds like this: “the potential energy of particle interaction is zero.” Such a strict equality to zero is still mathematics, in physics we can soften this condition by saying “potential energy of particle interaction much less...". What? Energy can only be compared with energy, and kinetic energy makes the greatest contribution to a system of moving particles. And here is our first condition:

1) The potential energy of interaction of gas particles is much less than their kinetic energy.

b) In the mathematical model, molecules are represented as mathematical points, that is, without size. IN real world We cannot demand this. How can we formulate this condition physically? Why do we need dimensionless molecules? So that they don't collide with each other. We cannot prohibit the collision of particles of non-zero size without introducing repulsive forces into the system. But we excluded the repulsive forces with the first point. Then we will have to allow collisions in the system, but with the imposition of 3 conditions: rarely, quickly and without loss of energy. And here are 3 more points:

2) The average free path of particles (that is, the distance traveled between two successive collisions) is much larger than their size.

3) The collision time is negligible.

4) All centennials occur without loss of energy.

We will extend points 3) and 4) to collisions with the walls of the vessel. If all four requirements are met, then we can consider our gas ideal.

c) Another interesting detail. Our collisions do introduce something into the system. Namely, changes in speeds. Moreover, the module and direction. So whatever the distribution of velocities is at the very beginning, after many collisions they will already be distributed according to Maxwell. Therefore, strictly speaking, we need to demand that the distribution of speeds be like this initially. Then our collisions will not affect the original physics of the system:

5) Particles in the system have random velocities distributed according to Maxwell's law.

Implicitly, we have already required the applicability of Newton’s law in the system (for the law of conservation of momentum, for example):

6) Newton’s laws apply in the system.

The science of physics plays a significant role in the study of the surrounding world. Therefore, its concepts and laws begin to be taught at school. The properties of a substance are measured in different aspects. If we consider its state of aggregation, then there is a special technique. An ideal gas is a physical concept that allows us to evaluate the properties and characteristics of the material that makes up our entire world.

General definition

An ideal gas is a model in which interactions between molecules are neglected. The process of interaction of particles of any substance with each other is quite complex.

When they fly close to each other and are at a very short distance, they strongly repel each other. But at great distances, relatively small forces of attraction act between molecules. If the average distance at which they are from each other is large, this position of the substance is called a rarefied gas. The interaction of such particles manifests itself as rare collisions of molecules. This only happens when they fly close to each other. In an ideal gas, the interaction of molecules is not taken into account at all. In an ideal gas the number of molecules is very large. Therefore, calculations occur only using a statistical method. Moreover, it should be noted that the particles of the substance in this case are distributed evenly in space. This is the most common state of an ideal gas.

When can a gas be considered ideal?

There are several factors due to which a gas is called ideal. The first sign is the behavior of molecules as absolutely elastic bodies; there are no attractive forces between them. In this case, the gas will be very discharged. The distance between the smallest components of the substance will be much larger than their sizes. In this case, thermal equilibrium will be achieved instantly throughout the entire volume. To achieve the position of an ideal gas in laboratory conditions, the real type is rarefied accordingly. Some substances in a gaseous state, even at room temperature and normal atmospheric pressure, practically do not differ from the ideal state.

Limits of application of the model

Natural gas is considered depending on the tasks assigned. If a researcher is tasked with determining the relationship between temperature, volume and pressure, then the ideal state of matter can be considered in which the gas has high accuracy up to pressures measured in several tens of atmospheres. But in the case of studying phase transitions, for example, evaporation and condensation, the process of achieving equilibrium in a gas, the model under consideration cannot be used even at very low pressure. Gas pressure on the wall of the test tube occurs when molecules randomly hit the glass. When such shocks are frequent, the human body can perceive these changes as a continuous impact.

Ideal gas equation

Based on the main principles of molecular kinetic theory, the main equation of an ideal gas was derived.

The work of an ideal gas has the following expression: p = 1 / 3 m 0 nv 2, where p is the ideal gas pressure, m 0 - molecular mass, v 2 - average particle concentration, square of molecular speed. If we define the average kinetic movement particles of matter, as Ek = m 0 n/ 2, then the equation will have the following form: p = 2 / 3 nEk. Gas molecules, hitting the walls of the vessel, interact with them as elastic bodies according to the laws of mechanics. The impulse from such impacts is transmitted to the walls of the vessel.

Temperature

By calculating only the gas pressure on the walls of a vessel, it is impossible to determine the average kinetic energy of its particles.

Moreover, this cannot be done either for an individual molecule or for their concentration. Therefore, to measure gas parameters, it is necessary to determine one more quantity. It is temperature, which is also related to the kinetic energy of molecules. This indicator is scalar physical quantity. Temperature describes thermodynamic equilibrium. In this state, there is no change in parameters at the micro level. Temperature is measured as the deviation from zero. It characterizes saturation chaotic movement smallest particles gas It is measured by the average value of their kinetic energy. This indicator is determined using thermometers in degrees of various marks. There is a thermodynamic absolute scale (Kelvin) and its empirical varieties. They differ in their starting points.

Equation of position of an ideal gas taking into account temperature

Physicist Boltzmann states that the average kinetic energy of a particle is proportional to absolute indicator temperature. Ek = 3 / 2 kT, where k = 1.38∙10-23, T is temperature. The work of an ideal gas will be equal to: P = NkT/V, where N is the number of molecules, V is the volume of the vessel. If we add the concentration n = N/V to this indicator, then the above formula will look like this: p = nkT. These two equations have various shapes records, but they relate pressure, volume and temperature for an ideal gas. These calculations can be applied to both pure gases and their mixtures. In the latter version, n should be understood as the entire number of molecules of substances, their total concentration or the total number of moles in the substance.

Three gas laws

The ideal gas and its particular laws were discovered experimentally and only then confirmed theoretically.

The first particular law states that an ideal gas at constant mass and temperature will have pressure inversely proportional to its volume. A process in which the temperature is constant is called isothermal. If the pressure is constant during the study, then the volume is proportional to the absolute temperature. This law bears the name of Gay-Lussac. An isochoric process occurs at a constant volume. In this case, the pressure will be proportional to the absolute temperature. Its name is Charles's law. These are three particular laws of behavior of an ideal gas. They were confirmed only after mastering knowledge about molecules.

Absolute measurement scale

In the absolute scale of measurement, the unit is usually called Kelvin. It was chosen based on the popular Celsius scale. One Kelvin corresponds to one degree Celsius. But in the absolute scale, zero is taken to be the value at which the pressure of an ideal gas at constant volume will be zero.

This is a generally accepted system. This temperature value is called absolute zero. Having made the appropriate calculations, you can get the answer that the value of this indicator will be -273 degrees Celsius. This confirms that there is a relationship between the absolute and Celsius scales. It can be expressed in the following equation: T = t + 237. It should be noted that it is impossible to achieve absolute zero. Any cooling process is based on the evaporation of molecules from the surface of a substance. Approaching absolute zero, the translational motion of particles slows down so much that evaporation stops almost completely. But from a purely theoretical point of view, if it were possible to actually reach the point of absolute zero, then the speed of movement of the molecules would decrease so much that it could be called absent altogether. The thermal movement of molecules would cease.

By studying the concept of an ideal gas, you can understand the principle of operation of any substance. By expanding knowledge in this area, one can understand the properties and behavior of any gaseous substance.