The ideal gas is the number of which. Macroscopic characteristics of the perfect gas

Definition: The perfect gas is called gas, when considering the properties of which the following conditions are followed:
a) the collision of the molecules of such gas occurs as the impact of elastic balls, the dimensions of which are negligible;
b) from the collision to collision molecules are moving uniformly and straightforwardly;
c) neglect the interaction for molecules.

Real gases at room temperature and normal pressure behave like perfect gases. Ideal gases can be considered such gases as helium, hydrogen, whose properties already conventional conditions They correspond to the laws of the perfect gas.

The state of some mass of the ideal gas will be determined by the values \u200b\u200bof three parameters: P, V, T. These values \u200b\u200bcharacterizing the state of the gas are called status parameters. These parameters are naturally linked to each other, so that the change in one of them entails the change in the other. This connection can analytically be specified as a function:

The relationship of the bond between the parameters of any body is called status equation. Consequently, this ratio is the equation for the state of the perfect gas.

Consider some of the status parameters characterizing the state of the gas:

1) Pressure (P). In the gas, the pressure occurs as a result of the chaotic movement of molecules, as a result of which the molecules face each other and with the walls of the vessel. As a result of the blow of molecules about the wall of the vessel from the side of molecules on the wall, there will be some average power df.. Suppose that the surface area ds., then. Hence:

Definition (mechanistic): Pressure - this is a physical value, numerically equal power, acting on a unit of surface area, normal to it.

If the force is evenly distributed over the surface, then. In the system, the pressure is measured in 1P \u003d 1N / m 2.

2) Temperature (T).

Definition (preliminary): Temperature Body is a thermodynamic value that characterizes the condition of the thermodynamic equilibrium of the macroscopic system.

The temperature is the same for all parts of the isolated system in terms of thermodynamic equilibrium. Those. If the contacting bodies are in a state of thermal equilibrium, i.e. Do not exchange energy by heat transfer, the same temperature is attributed to these bodies. If, when establishing thermal contact between bodies, one of them transmits energy to another by means of heat transfer, a large temperature is attributed to the first body than the second.

Any of the properties of the body (temperature feature), temperature -weight can be used to quantify the temperature (measurement) of temperature.

for example: If you select the volume as a temperature feature and assume that with a temperature volume varies linearly, then selecting the temperature of the ice melting temperature, and for 100 ° - the boiling point of water, we obtain the temperature scale called the Celsius scale. According to which the state in which the thermodynamic body has volume V, should be attributed to the temperature:

For the unequivocal determination of the temperature scale, it is necessary to agree, except the method of graduation, also on the choice of the thermometric body (that is, the body that is selected for the measurement) and the temperature feature.

Known two temperature scale:

1) t. - Empirical or practical temperature scale (° C). (On the choice of the thermometric body and the temperature feature for this scale, let's say later).

2) T. - thermodynamic or absolute scale (° K). This scale does not depend on the properties of the thermodynamic body (but about it speech will go later).

Temperature T, counted by absolute scalerelated to temperature T on a practical scale by the ratio

T. = t. + 273,15.

The unit of absolute temperature is called Kelvin. The temperature on a practical scale is measured in degrees. Celsius (° C). Grad values. Kelvin and Grad. Celsius are the same. Temperature equal to 0 ° K is called absolute zero., it corresponds to T \u003d -273,15 ° C

In this example, we can consider in detail how mathematical models are transformed into physical models.

Primarily, perfect Gas. - this is mathematical Gas model. And S. mathematical Point of view, the idea is very simple: 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 come together in one spatial point.

On the other hand, the perfect gas is physical term. So, we need to understand what physics is responsible for such a mathematical model.

a) So, first, so that the atoms "have not seen" each other need to be between them the potential interaction forces, that is, the forces depending on the distance between the particles. In terms of energy, this requirement sounds like this: "The potential energy of the interaction of particles is zero." Such a strict equality zero, it's still mathematics, in physics we can soften this condition by saying "the potential energy of particle interaction much less ... ". What? Energy can be compared only with energy, and the system of moving particles gives the greatest contribution to kinetic energy. And here is our first condition:

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

b) In the mathematical model, the molecule is represented by mathematical dots, that is, without size. IN real world We cannot require such a require. How do we formulate this condition physically? Why do we need dimensionless molecules? So that they do not come across each other. We cannot prohibit the collision of non-zero particles without entering the repulsive force system. But repulsion strength we excluded the first item. Then we will have to solve 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 length of the free mileage of the particles (that is, the distance passed between two consecutive collisions) a lot of their size.

3) the collision time is negligible.

4) All centenings occur without energy loss.

Paragraphs 3) and 4) We will spread to collision with the walls of the vessel. If all four requirements are fulfilled, then we can consider our gas perfect.

c) another interesting detail. Something our collisions in the system are made. Namely, speed changes. Moreover, the module and directions. So whatever the speed distribution was at the very beginning, after a set of collisions, they will already be distributed over Maxwell. Therefore, strictly speaking, we need to require that the speed distribution is already in the initially. Then our clashes will not affect the initial physics of the system:

5) particles in the system have random velocities distributed by the law of Maxwell.

In an implicit form, we have already demanded the applicability of Newton's law in the system (for the law of preserving the impulse, for example):

6) Newton's laws operate in the system.

What errors occur during measurements in laboratory work number 4 "Definition of specific heat of crystallization (melting) and changes in entropy during tin crystallization"? Explain their reasons.

In our laboratory work number 4, such errors arise as composition of tin, room temperature, as well as on the result, long heating of tin can affect. Causes: The composition of tin can contain any impurities, as a result of which it may affect the measurement result. Also, the error can be called room temperature, because every time making this laboratory workwe use different temperatures ambient in the laboratory.

What gas is ideal? Record the equation of the state of the perfect gas and explain it.

Perfect gasthis is gas, whose molecules are considered as material Points The interactions among themselves according to the laws of the impact of elastic balls. Those. The models of the ideal gas neglect their own volume of molecules and the interaction forces between them. Formula: or PV \u003d. This formula gives the relationship between macroparameters of the substance. f (p, v, t) \u003d 0 General view of the status equation.

The process of the system of the system from one state to another.

The equation that establishes the link between pressure, the volume and temperature of the gas was obtained in the middle of the XIX century by the French physicist B. Klapairon, in the form (PV \u003d RT), it was first recorded by D. I. Mendeleev. Therefore, the equation of the state of the gas is called the Klapairone-Mendeleev equation.

Gas can participate in various thermal processes in which all parameters that describe its state (P, V and T) may vary. If the process proceeds quite slowly, then at any time the system is close to its equilibrium state. Such processes are called quasistobatic. In the usual time scale, these processes can leak and not very slowly. For example, gas cuts and compression in sound wave, Hundreds of times in a second, can be viewed as a quasistatic process. Quasistatic processes can be depicted on a state diagram (for example, in the coordinates P, V) in the form of a certain trajectory, each point of which is an equilibrium state.

In the case of a constant mass of the gas, the equation can be written as: The last equation is called combined Gas Law. It turns out the laws of Boil - Mariotta, Charles and Gay Loursak.

29. Word the first beginning of the thermodynamics in general, the form and for each isoprocess. Instruct the graphics of isoproces in coordinates ( pV) , ( pt) , ( Vt) .

The first top of the thermodynamics is the application of the law, the preservation and conversion of energy to the phenomena studied by thermodynamics. The first top of thermodynamics - One of the three major laws of thermodynamics is the law of conservation of energy for thermodynamic systems.

The first top of the thermodynamics was formulated in the middle of the XIX century as a result of the works of the German scientist Yu. R. Mayer, English physics J. P. Joule and German physics of Gelmholts. The first top of the thermodynamics is often formulated as the impossibility of the existence of the perpetual engine of the first kind, which would perform work, without drawing energy from a source.

Energy is a total quantitative measure of all processes and types of interaction in nature, subject to the conservation law. Energy has a certain value in any state of the system, so du Yavl-Xia status function. State Function This function, which in the specified state of the system has a completely definite value that does not depend on how way or method the system is given to this state. It is characterized by a complete differential. F-I process- Functions, the value of which is determined by the type of process, as a result of which the system has changed its state. The process functions include work, heat.

The first top of the thermodynamics:

1) with the isobaric process(P \u003d const) - Zacon Gay Lussa. At p \u003d const diagram of this process (isobar) in the coordinates P, V, a straight, parallel axis V is depicted. With the isobaric process, the operation of the gas when expanding the volume from to equal to is determined by the rectangle area.

2) with an isothermal process - the process of changing the state of the thermodynamic system at a constant temperature (T \u003d const) PV \u003d const-equation of the Boyle Mariotta. At t \u003d const - du \u003d 0; The diagram of this process (isotherm) in the coordinates P, V is a hyperbole located on the diagram, the higher the higher the temperature at which the process took place.

3) with a isochorine process (V \u003d const) -Processions of changes in the state of the thermodynamic system at a constant volume (V \u003d const). For perfect gases, the isochoric process is described by the Challa's law: for this mass of gas at a constant volume, the pressure is directly proportional to the temperature:

With v \u003d const-

As you know, many substances in nature can be in three aggregate states: solid, liquidand gaseous.

The doctrine of the properties of the substance in various aggregate states is based on the ideas about the atomic molecular structure material world. The molecular-kinetic theory of the structure of the substance (MKT) is three main provisions:

• all substances consist of the smallest particles (molecules, atoms, elementary particles), between which there are gaps;
• particles are in continuous thermal motion;
• between the particles of the substance exist interaction (attraction and repulsion); The nature of these forces is electromagnetic.

It means that the aggregate state of the substance depends on mutual location molecules, distances between them, the interaction forces between them and the nature of their movement.

The interaction of the substance particles in the hard state is the interaction of particles of matter. The distance between molecules is approximately equal to their own sizes. This leads to a sufficiently strong interaction that practically deprives particles of the ability to move: they fluctuate about some equilibrium position. They retain the form and volume.

The properties of liquids are also explained by their structure. Particles of substance in liquids interact less intensively than in solid bodiesAnd therefore, they can jump from changing their location - liquids do not retain their form - they are fluid. Liquids retain volume.

Gas is a collection of molecules, randomly moving in all directions independently of each other. Gases do not have their own form, occupy the entire volume provided to them and easily compress.

There is another state of substance - plasma. Plasma - partially or completely ionized gas, in which the density of positive and negative charges is almost the same. With sufficiently strong heating, any substance evaporates, turning into gas. If you increase the temperature and further, the process of thermal ionization is sharply intensified, i.e. the gas molecules will begin to decay into the components of their atoms, which are then converted into ions.

Model of perfect gas. Communication between pressure and medium kinetic energy.

To clarify the patterns that the behavior of the substance in the gaseous state is subject to the behavior of the substance, the idealized model of real gases is considered - the perfect gas. This is such a gas whose molecules are considered as material points that do not interact with each other at a distance, but interacting with each other and with the walls of the vessel with collisions.

Perfect Gas. – this gas, the interaction between the molecules of which is negligible. (EK \u003e\u003e EP)

The perfect gas is a model invented by scientists for the knowledge of gases, which we are observing in nature real. It can describe not any gas. Not applicable when gas is strongly compressed when gas goes into a liquid state. Real gases behave as ideal when the average distance between molecules is many times more than their size, i.e. With sufficiently large perceptions.

Properties of the perfect gas:

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

State of some mass gaseous substance characterize dependent on each other physical quantities called status parameters. These include volumeV.Pressurep. and temperatureT..

Gas volumedenotes V.. Volume Gas always coincides with the volume of the vessel that it takes. Unit of volume in si m 3..

Pressure– physical value equal to the ratio of powerF.acting on the surface element perpendicular to it, to the squareS. of this element.

P. = F./ S. Pressure unit in si pascal[Pa]

To date, generate pressure units are used:

Technical atmosphere1 AT \u003d 9.81-104 PA;

Physical atmosphere 1 atm \u003d 1,013-105 pa;

millimeters of mercury pillar1 mm Hg. Art. \u003d 133 Pa;

1 atm \u003d \u003d 760 mm Hg. Art. \u003d 1013 GPa.

How does gas pressure occur? Each gas molecule, hitting the wall of the vessel in which it is, for a small period of time acts on the wall with a certain force. As a result of disorderly blows about the wall, the power of all molecules per unit area of \u200b\u200bthe wall quickly changes with a relatively certain (medium) value.

Gas pressurearises as a result of disorderly blows of molecules about the wall of the vessel in which gas is located.

Using the perfect gas model, you can calculate gas pressure on the wall of the vessel.

In the process of the interaction of the molecule with the wall of the vessel between them, there are forces submitted by the third law of Newton. As a result, the projection υ X. The speed of the molecule, perpendicular to the wall, changes its sign to the opposite, and the projection υ Y. Speed, parallel wall, remains unchanged.

Instruments measuring pressure are called pressure gauges. Pressure gauges fix the average pressure force per unit area of \u200b\u200bits sensing element (membrane) or another pressure receiver.

Liquid manometers:

1. outdoor - for measuring small pressures above atmospheric
2. closed - for measuring small pressures below atmospheric, i.e. Small Vacuum

Metal pressure gauge - to measure high pressures.

Its main part is the curved tube A, the open end of which is soldered to the tube in, through which gas comes, and the closed is connected to the arrow. Gas enters the crane and tube to the tube A and extension it. The free end of the tube, moving, drives the transmitting mechanism and arrow. Scale graded in pressure units.

The main equation of the molecular-kinetic theory of perfect gas.

Basic Equation MKT.: the pressure of the perfect gas is proportional to the product of the mass of the molecule, the concentration of molecules and the average square of the movement of the molecules

p. \u003d 1/3 ·m. 0· n · V. 2

m 0 - Mass of one gas molecule;

n \u003d N / V is the number of molecules per unit volume, or concentration of molecules;

v 2 - the average quadratic speed of molecules.

Since the average kinetic energy of the translational motion of the molecules E \u003d M 0 * V 2/2, then the main equation of MKT for 2, we obtain p \u003d 2/3 · n · (m 0 · v 2) / 2 \u003d 2/3 · e · N.

p \u003d 2/3 · E · n

Gas pressure is 2/3 of the average kinetic energy of the translational movement of molecules, which are contained in a single volume of gas.

Since m 0 · n \u003d m 0 · n / v \u003d m / v \u003d ρ, where ρ is the gas density, then we have p. \u003d 1/3 · ρ ·v. 2

Joint gas law.

Macroscopic values \u200b\u200bunambiguously characterizing the state of the gas are calledthermodynamic gas parameters.

The most important thermodynamic parameters of gas are itsvolumeV., pressure P and temperature T.

Any change in the state of the gas is calledthermodynamic process.

In any thermodynamic process, gas parameters that determine its condition are changed.

The ratio between the values \u200b\u200bof certain parameters at the beginning and end of the process is calledgas law.

Gas lawexpressing the relationship between all three gas parameters is calledjoint gas law.

p. = nKT.

Ratio p. = nKT. the binding gas pressure with its temperature and the concentration of molecules was obtained for the model of perfect gas, the molecules of which interact with each other and with the walls of the vessel only during elastic collisions. This ratio can be recorded in a different form establishing a link between macroscopic gas parameters - V.Pressure p.Temperature T. and the amount of substance ν. To do this, use equality

where n is the concentration of molecules, n is the total number of molecules, V - the volume of gas

Then we get or

Since at a constant mass of gas N remains unchanged, then Nk is a constant number, which means

With a constant mass of gas, the product of the pressure on the pressure divided into absolute gas temperature is the same value for all states of this mass of the gas.

The equation that establishes the relationship between pressure, the volume and temperature of the gas was obtained in the middle of the XIX century by French physicist B. Klapairon and often called it klaperon equation.

Cleperon equation can be written in another form.

p. = nkt

considering that

Here N. - the number of molecules in the vessel, ν is the amount of substance, N. A - constant Avogadro, m. - Mass of gas in the vessel, M. - Molar mass of gas. As a result, we get:

The work of constant avogadro N and onpermanent Boltzmanna K called universal (molar) gas constant And denotes the letter R..

Her numerical value in S. R. \u003d 8.31 J / mol · K

Ratio

called the equalization of the state of the ideal gas.

In the form we obtained, it was first recorded by D. I. Mendeleev. Therefore, the equation of state state is called klapaireron-Mendeleev equation.`

For one praying of any gas, this ratio takes the form: pV \u003d RT.

Installation physical meaning of molar gas constant. Suppose that in some cylinder under the piston at temperatures E there is 1 mol of gas, the volume of which V. If heated the gas isobaro (at constant pressure) by 1 k, then the piston will rise to the height ΔH, and the volume of gas will increase by ΔV.

We write equation pV\u003d Rt.for heated gas: P (V + ΔV) \u003d R (t + 1)

and the PV \u003d RT equation corresponding to the state of the gas before heating from this equality is subtracted. We obtain PΔV \u003d R

ΔV \u003d SΔH, where S is the base area of \u200b\u200bthe cylinder. Substitute to the resulting equation:

pS \u003d F - pressure force.

We obtain fΔh \u003d r, and the product of force on the movement of the piston FΔh \u003d A is the work on the movement of the piston made by this force against external power When expanding gas.

In this way, R. = A..

Universal (molar) gas constant is numerically equal to the work that 1 mol of gas performs during the isobar heating of it on 1 K.