Absolute temperature as a measure of the average kinetic energy of thermal motion of particles of a substance. Average kinetic energy of thermal motion of gas molecules

« Physics - 10th grade"

Absolute temperature.

Instead of temperature Θ, expressed in energy units, we introduce temperature, expressed in degrees familiar to us.

Θ = kT, (9.12)

where k is the proportionality coefficient.

>The temperature determined by equality (9.12) is called absolute.

This name, as we will now see, has sufficient grounds. Taking into account definition (9.12), we obtain

This formula introduces a temperature scale (in degrees), independent of the substance used to measure temperature.

The temperature determined by formula (9.13) obviously cannot be negative, since all the quantities on the left side of this formula are obviously positive. Consequently, the lowest possible value of temperature T is the value T = 0 if the pressure p or volume V is equal to zero.

The limiting temperature at which pressure ideal gas vanishes at a fixed volume or at which the volume of an ideal gas tends to zero at a constant pressure is called absolute zero temperature.

This is the most low temperature in nature, that “greatest or last degree of cold”, the existence of which Lomonosov predicted.

The English scientist W. Thomson (Lord Kelvin) (1824-1907) introduced the absolute temperature scale. Zero temperature on an absolute scale (also called Kelvin scale) corresponds to absolute zero, and each temperature unit on this scale is equal to a degree on the Celsius scale.

The SI unit of absolute temperature is called kelvin(denoted by the letter K).

Boltzmann's constant.

Let us determine the coefficient k in formula (9.13) so that a change in temperature by one kelvin (1 K) is equal to a change in temperature by one degree Celsius (1 °C).

We know the values of Θ at 0 °C and 100 °C (see formulas (9.9) and (9.11)). Let us denote the absolute temperature at 0 °C by T 1, and at 100 °C by T 2. Then according to formula (9.12)

Θ 100 - Θ 0 = k(T 2 -T 1),

Θ 100 - Θ 0 = k 100 K = (5.14 - 3.76) 10 -21 J.

Coefficient

k = 1.38 10 -23 J/K (9.14)

called Boltzmann constant in honor of L. Boltzmann, one of the founders of molecular kinetic theory gases

Boltzmann's constant relates the temperature Θ in energy units to the temperature T in kelvins.

This is one of the most important constants in molecular kinetic theory.

Knowing Boltzmann's constant, you can find the value of absolute zero on the Celsius scale. To do this, we first find the absolute temperature value corresponding to 0 °C. Since at 0 °C kT 1 = 3.76 10 -21 J, then

One kelvin and one degree Celsius are the same. Therefore, any value of absolute temperature T will be 273 degrees higher than the corresponding temperature t Celsius:

T (K) = (f + 273) (°C). (9.15)

The change in absolute temperature ΔT is equal to the change in temperature on the Celsius scale Δt: ΔT(K) = Δt (°C).

Figure 9.5 shows the absolute scale and the Celsius scale for comparison. Absolute zero corresponds to temperature t = -273 °C.

In the USA the Fahrenheit scale is used. The freezing point of water on this scale is 32 °F, and the boiling point is 212 °E. Temperature is converted from the Fahrenheit scale to the Celsius scale using the formula t(°C) = 5/9 (t(°F) - 32).

Note the most important fact: Absolute zero temperature is unattainable!

Temperature is a measure of average kinetic energy molecules.

The most important corollary follows from the basic equation of molecular kinetic theory (9.8) and the definition of temperature (9.13):
absolute temperature is a measure of the average kinetic energy of molecular motion.

Let's prove it.

From equations (9.7) and (9.13) it follows that This implies the relationship between the average kinetic energy forward motion molecules and temperature:

The average kinetic energy of the chaotic translational motion of gas molecules is proportional to the absolute temperature.

The higher the temperature, the faster the molecules move. Thus, the previously put forward guess about the connection between temperature and the average speed of molecules received reliable justification. The relationship (9.16) between temperature and the average kinetic energy of translational motion of molecules has been established for ideal gases.

However, it turns out to be true for any substances in which the movement of atoms or molecules obeys the laws of Newtonian mechanics. This is true for liquids and also for solids, where atoms can only oscillate around equilibrium positions at the nodes of the crystal lattice.

As the temperature approaches absolute zero, the energy of thermal motion of molecules approaches zero, i.e., the translational thermal motion of molecules stops.

Dependence of gas pressure on the concentration of its molecules and temperature. Considering that from formula (9.13) we obtain an expression showing the dependence of gas pressure on the concentration of molecules and temperature:

From formula (9.17) it follows that at the same pressures and temperatures, the concentration of molecules in all gases is the same.

This follows Avogadro's law, known to you from your chemistry course.

Avogadro's Law:

Equal volumes of gases at the same temperatures and pressures contain the same number of molecules.

Temperature.

The basic equation of the molecular kinetic theory for an ideal gas establishes a connection between an easily measured macroscopic parameter - pressure - and such microscopic gas parameters as average kinetic energy and molecular concentration.

But by measuring only the gas pressure, we cannot find out either the average kinetic energy of the molecules individually or their concentration. Consequently, to find the microscopic parameters of a gas, measurements of some other physical quantity related to

average kinetic energy of molecules. Such a quantity in physics is temperature.

From everyday experience, everyone knows that there are hot and cold bodies. When two bodies come into contact, one of which we perceive as hot and the other as cold, changes in the physical parameters of both the first and second bodies occur. For example, solids and liquids usually expand when heated. Some time after establishing contact between the bodies, changes in the macroscopic parameters of the bodies stop. This state of bodies is called thermal equilibrium. A physical parameter that is the same in all parts of a system of bodies in a state of thermal equilibrium is called body temperature. If, when two bodies come into contact, none of their physical parameters, for example volume, pressure, change, then there is no heat transfer between the bodies and the temperature of the bodies is the same.

Thermometers.

In everyday practice, the most common method of measuring temperature is using a liquid thermometer.

The liquid thermometer uses the property of liquids to expand when heated. Mercury, alcohol, and glycerin are usually used as working fluids. To measure body temperature, the thermometer is brought into contact with that body; Heat transfer will take place between the body and the thermometer until thermal equilibrium is established. The mass of the thermometer should be significantly less than body weight, since otherwise the measurement process can significantly change body temperature.

Changes in the volume of liquid in the thermometer stop when heat exchange between the body and the thermometer stops. In this case, the temperature of the liquid in the thermometer is equal to body temperature.

By marking on the thermometer tube the position of the end of the liquid column when placing the thermometer in melting ice, and then in boiling water at normal pressure and dividing the segment between these marks by 100 equal parts, obtain a temperature scale in Celsius. The temperature of melting ice is assumed to be equal (Fig. 83), boiling water - (Fig. 84). The change in the length of the liquid column in the thermometer by one hundredth of the length between the 0 marks corresponds to a change in temperature by

A significant disadvantage of the method of measuring temperature using liquid thermometers is that the temperature scale is associated with specific physical properties a certain substance used as a working fluid in a thermometer - mercury, glycerin, alcohol. The change in volume of different liquids under the same heating turns out to be somewhat different. Therefore, mercury and glycerin thermometers, whose readings are the same at 0 and 100 °C, give different readings at other temperatures.

Gases are in a state of thermal equilibrium.

In order to find a more perfect way to determine temperature, it is necessary to find a value that would be the same for any bodies in a state of thermal equilibrium.

Experimental studies of the properties of gases have shown that for any gases in a state of thermal equilibrium, the ratio of the product of the gas pressure and its volume to the number of molecules is the same:

This experimental fact allows us to accept the value 0 as a natural measure of temperature.

Since, taking into account the basic equation of molecular kinetic theory (24.2), we obtain

Consequently, the average kinetic energy of the molecules of any gases that are in thermal equilibrium is the same. The value 0 is equal to two-thirds of the average kinetic energy of the random thermal motion of gas molecules and is expressed in joules.

In physics, temperature is usually expressed in degrees, assuming that the temperature T in degrees and the value 0 are related by the equation

where is a proportionality coefficient depending on the choice of temperature unit.

From here we get

The last equation shows that it is possible to choose a temperature scale that does not depend on the nature of the gas used as the working fluid.

In practice, temperature measurement based on the use of equation (25.4) is carried out using a gas thermometer (Fig. 85). Its structure is as follows: there is gas in a vessel of constant volume, the amount of gas remains unchanged. At constant values of the volume V and the number of molecules, the gas pressure measured by a manometer can serve as a measure of the temperature of the gas, and therefore of any body with which the gas is in thermal equilibrium.

Absolute temperature scale.

The temperature measurement scale in accordance with equation (25.4) is called the absolute scale. It was proposed by the English physicist W. Kelvia (Thomson) (1824-1907), which is why the scale is also called the Kelvin scale.

Before the introduction of the absolute temperature scale, the Celsius temperature scale became widespread in practice. Therefore, the unit of temperature on the absolute scale, called the kelvin, is chosen to be equal to one degree on the Celsius scale:

Absolute zero temperature.

On the left side of equation (25.4) all quantities can only have positive values or be equal to zero. Therefore, the absolute temperature T can only be positive or equal to zero. The temperature at which the pressure of an ideal gas at constant volume should be equal to zero is called absolute zero temperature.

Boltzmann's constant.

The value of the constant k in equation (25.4) can be found from known values pressure and volume of a gas with a known number of molecules at two temperatures

As is known, 1 mole of any gas contains approximately molecules and at normal pressure Pa occupies a volume

Experiments have shown that when any gas is applied at a constant volume from 0 to 100 ° C, its pressure increases from up to Pa. Substituting these values into equation (25.6), we get

The coefficient is called Boltzmann's constant, in honor of the Austrian physicist Ludwig Boltzmann (1844-1906), one of the creators of molecular kinetic theory.

It represents the energy that is determined by the speed of movement of various points belonging to this system. In this case, one should distinguish between the energy that characterizes translational motion and rotational motion. Moreover, the average kinetic energy is the average difference between the total energy of the entire system and its rest energy, that is, in essence, its value is the average value of potential energy.

Its physical value is determined by the formula 3 / 2 kT, which indicates: T - temperature, k - Boltzmann constant. This value can serve as a kind of criterion for comparison (standard) for the energies contained in various types thermal movement. For example, the average kinetic energy for gas molecules when studying translational motion is equal to 17 (- 10) nJ at a gas temperature of 500 C. As a rule, electrons have the greatest energy during translational motion, but the energy of neutral atoms and ions is much less.

This value, if we consider any solution, gas or liquid at a given temperature, has a constant value. This statement is also true for colloidal solutions.

The situation is somewhat different with solids. In these substances, the average kinetic energy of any particle is too small to overcome the forces of molecular attraction, and therefore it can only move around a certain point, which conditionally fixes a certain equilibrium position of the particle over a long period of time. This property allows the solid to be quite stable in shape and volume.

If we consider the conditions: translational motion and an ideal gas, then here the average kinetic energy is not a quantity dependent on molecular weight, and therefore is defined as a value directly proportional to the absolute temperature.

We have given all these judgments with the aim of showing that they are valid for all types states of aggregation substances - in any of them, temperature acts as the main characteristic, reflecting the dynamics and intensity of the thermal movement of elements. And this is the essence of molecular kinetic theory and the content of the concept of thermal equilibrium.

As is known, if two physical bodies come into interaction with each other, then a heat exchange process occurs between them. If the body is a closed system, that is, it does not interact with any bodies, then its heat exchange process will last as long as it takes to equalize the temperatures of this body and environment. This state is called thermodynamic equilibrium. This conclusion has been repeatedly confirmed by experimental results. To determine the average kinetic energy, one should refer to the characteristics of the temperature of a given body and its heat transfer properties.

It is also important to take into account that microprocesses inside bodies do not end when the body enters thermodynamic equilibrium. In this state, molecules move inside bodies, change their speeds, impacts and collisions. Therefore, only one of our several statements is true - the volume of the body, the pressure (if we are talking about gas), may differ, but the temperature will still remain constant. This once again confirms the statement that the average kinetic energy of thermal motion in isolated systems is determined solely by the temperature indicator.

This pattern was established during experiments by J. Charles in 1787. While conducting experiments, he noticed that when bodies (gases) are heated by the same amount, their pressure changes in accordance with the direct proportional law. This observation made it possible to create many useful instruments and things, in particular a gas thermometer.

In this lesson we will analyze a physical quantity that is already familiar to us from the eighth grade course - temperature. We will supplement its definition as a measure of thermal equilibrium and a measure of average kinetic energy. We will describe the disadvantages of some and the advantages of other methods of measuring temperatures, introduce the concept of an absolute temperature scale and, finally, derive the dependence of the kinetic energy of gas molecules and gas pressure on temperature.

There are two reasons for this:

Various thermometers use various substances as an indicator, therefore thermometers react differently to the same temperature change depending on the properties of a particular substance;
Arbitrariness in choosing the starting point for the temperature scale.

Therefore, such thermometers are not suitable for any accurate temperature measurements. And since the eighteenth century, more accurate thermometers have been used, which are gas thermometers (see Fig. 2)

Rice. 2. Gas thermometer ()

The reason for this is the fact that gases expand the same when the temperature changes by the same amount. The following applies to gas thermometers:

That is, to measure temperature, either the change in pressure is recorded at a constant volume, or the volume at a constant pressure.

Gas thermometers often use rarefied hydrogen, which, as we remember, fits the ideal gas model very well.

In addition to the imperfection of household thermometers, there is also the imperfection of many scales that are used in everyday life. In particular, the Celsius scale, as the most familiar to us. As with thermometers, these scales select a random starting level (for the Celsius scale, this is the melting point of ice). Therefore, to work with physical quantities another, absolute scale is needed.

This scale was introduced in 1848 by the English physicist William Thompson (Lord Kelvin) (Fig. 3). Knowing that as temperatures increase, the thermal speed of movement of molecules and atoms also increases, it is not difficult to establish that as temperatures decrease, the speed will fall and at a certain temperature will sooner or later become zero, as will the pressure (based on the basic MKT equation). This temperature was chosen as the starting point. It is obvious that the temperature cannot reach a value less than this value, which is why it is called “absolute zero temperature”. For convenience, 1 degree on the Kelvin scale was given in accordance with 1 degree on the Celsius scale.

So, we get the following:

Temperature designation - ;

Unit of measurement - K, "kelvin"

Translation to the Kelvin scale:

Therefore, absolute zero temperature is the temperature

Rice. 3. William Thompson ()

Now, to determine temperature as a measure of the average kinetic energy of molecules, it makes sense to generalize the reasoning that we gave in defining the absolute temperature scale:

So, as we see, temperature is indeed a measure of the average kinetic energy of translational motion. The specific formulaic relationship was derived by the Austrian physicist Ludwig Boltzmann (Fig. 4):

Here is the so-called Boltzmann coefficient. This is a constant numerically equal to:

As we see, the dimension of this coefficient is , that is, it is a kind of conversion factor from the temperature scale to the energy scale, because we now understand that, in fact, we had to measure temperature in energy units.

Now let's look at how the pressure of an ideal gas depends on temperature. To do this, we write the basic MKT equation in the following form:

and substitute into this formula the expression for the relationship between the average kinetic energy and temperature. We get:

Rice. 4. Ludwig Boltzmann ()

In the next lesson we will formulate the equation of state of an ideal gas.

Bibliography

Myakishev G.Ya., Sinyakov A.Z. Molecular physics. Thermodynamics. - M.: Bustard, 2010.
Gendenshtein L.E., Dick Yu.I. Physics 10th grade. - M.: Ilexa, 2005.
Kasyanov V.A. Physics 10th grade. - M.: Bustard, 2010.

Great Encyclopedia of Oil and Gas ().
youtube.com().
E-science.ru ().

Homework

Page 66: No. 478-481. Physics. Problem book. 10-11 grades. Rymkevich A.P. - M.: Bustard, 2013. ()
How is the Celsius temperature scale determined?
Indicate the temperature range on the Kelvin scale for your city in summer and winter.
Air consists mainly of nitrogen and oxygen. The kinetic energy of which gas molecules is greater?
*How does the expansion of gases differ from the expansion of liquids and solids?

Equation of state of an ideal gas in the form pV= n RT or p = nkT can also be justified by methods of the kinetic theory of gases. Based on the kinetic approach, a relatively simple expression is derived for the pressure of an ideal gas in a vessel, which is obtained as a result of averaging the momentum of molecules transferred to the wall of the vessel during numerous collisions of molecules with the wall. The amount of pressure obtained in this case is determined as

Where would v 2 s – average value of the squared speed of molecules, m– the mass of the molecule.

The average kinetic energy of gas molecules (per one molecule) is determined by the expression

The kinetic energy of the translational motion of atoms and molecules, averaged over a huge number of randomly moving particles, is a measure of what is called temperature. If the temperature T is measured in degrees Kelvin (K), then its relationship with Ek is given by the relation

This ratio allows, in particular, to give a more distinct physical meaning Boltzmann constant

Internal energy of an ideal gas.

In the ideal gas theory, the potential energy of interaction between molecules is considered equal to zero. Therefore, the internal energy of an ideal gas is determined by the kinetic energy of motion of all its molecules. The average energy of motion of one molecule is equal to

Since one kilomole contains molecules, the internal energy of one kilomole of gas will be

Considering that, we get

For any gas mass m, i.e. for any number of kilomoles internal energy

From this expression it follows that internal energy is a unique function of state and, therefore, when the system performs any process, as a result of which the system returns to its original state, the total change in internal energy is zero. Mathematically, this is written as the identity

Maxwell distribution

Maxwell distribution -probability distribution, found in physics And chemistry. It lies at the base kinetic theory of gases, which explains many fundamental properties of gases, including pressure And diffusion. The Maxwell distribution is also applicable to electronic transfer processes and other phenomena. Maxwell's distribution applies to many properties of individual molecules in a gas. It is usually thought of as the distribution of energies of molecules in a gas, but it can also be applied to the distribution of velocities, momenta, and modulus of molecules. It can also be expressed as discrete distribution over many discrete energy levels, or as a continuous distribution along some continuum of energy.

The Maxwell distribution can and should be obtained using statistical mechanics(see origin statistical sums). As an energy distribution, it corresponds to the most probable energy distribution, in a collision-dominated system consisting of a large number of non-interacting particles, in which quantum effects are negligible. Since the interaction between molecules in a gas is usually quite small, the Maxwell distribution gives a fairly good approximation of the situation existing in a gas.

In many other cases, however, the dominance condition is not even approximately satisfied elastic collisions over all other processes. This is true, for example, in physics ionosphere and space plasma, where the processes of recombination and collisional excitation (that is, radiative processes) have great importance, especially for electrons. The assumption of the applicability of the Maxwell distribution would in this case not only give quantitatively incorrect results, but would even prevent a correct understanding of the physics of processes at a qualitative level. Also, in the case where quantum de Broglie wavelength gas particles is not small compared to the distance between particles, deviations from the Maxwell distribution due to quantum effects will be observed.

The Maxwell energy distribution can be expressed as a discrete energy distribution:

where is the number of molecules having energy at the temperature of the system, is the total number of molecules in the system and - Boltzmann constant. (Note that sometimes the above equation is written with a factor indicating the degree of degeneracy of the energy levels. In this case, the sum will be over all energies, not all states of the system.) Since speed is related to energy, equation (1) can be used to derive the relationship between temperature and the speeds of molecules in a gas. The denominator in equation (1) is known as the canonical statistical sum.

Boltzmann distribution.

Boltzmann distribution- probability distribution of various energy states ideal thermodynamic system (ideal gas of atoms or molecules) in conditions thermodynamic equilibrium; open L. Boltzmann V 1868 -1871 .

According to Boltzmann distribution the average number of particles with total energy is

where is the multiplicity of the state of a particle with energy - the number of possible states of a particle with energy. The constant is found from the condition that the sum over all possible values is equal to the given total number of particles in the system (normalization condition):

In the case when the motion of particles obeys classical mechanics, the energy can be considered to consist of

The phenomenon of transference. Diffusion

transference phenomenathermal conductivity(energy transfer), diffusion(mass transfer) and internal friction(momentum transfer). Let us limit ourselves to one-dimensional transfer phenomena. We will choose the reference system so that the x axis is directed sideways in the direction of the

Diffusion . When spontaneous penetration and mixing of particles of two contacting gases, liquids and even solids occurs; diffusion is the exchange of masses of particles of these bodies, and the phenomenon arises and continues as long as there is a density gradient. During the formation of molecular kinetic theory, contradictions arose regarding the phenomenon of diffusion. Since molecules move through space at enormous speeds, diffusion must occur very quickly. If you open the lid of a vessel with an odorous substance in a room, the smell spreads quite slowly. But there is no contradiction here. At atmospheric pressure molecules have a short free path and, in collisions with other molecules, mostly “stand” in place. The phenomenon of diffusion for a chemically homogeneous gas obeys Fick's law: (3) where j m - mass flux density- value determined by the mass of a substance diffusing per unit time through a unit area perpendicular to the x-axis, D - diffusion (diffusion coefficient), dρ/dx is the density gradient, which is equal to the rate of change in density per unit length x in the direction of the normal to this area. The minus sign indicates that mass transfer occurs in the direction of decreasing density (therefore the signs of j m and dρ/dx are opposite). Diffusion D is numerically equal to the mass flux density with a density gradient equal to unity. According to the kinetic theory of gases, (4)

Transference phenomenon. Thermal conductivity

In thermodynamically nonequilibrium systems, special irreversible processes occur, called transference phenomena, as a result of which spatial transfer of mass, momentum, and energy occurs. Transfer phenomena include thermal conductivity(energy transfer), diffusion(mass transfer) and internal friction(momentum transfer). Let us limit ourselves to one-dimensional transfer phenomena. We will choose the reference system so that the x axis is directed towards the direction of translation. Thermal conductivity . If in the first region of the gas the average kinetic energy of molecules is greater than in the second, then due to constant collisions of molecules over time, a process of equalization of the average kinetic energies of molecules occurs, i.e., equalization of temperatures. The transfer of energy in the form of heat is subject to Fourier's law: (1) where j E - heat flux density- a quantity that is determined by the energy transferred in the form of heat per unit time through a unit area perpendicular to the x-axis, λ - thermal conductivity, - temperature gradient equal to the rate of temperature change per unit length x in the direction of the normal to this area. The minus sign indicates that during thermal conduction, energy moves in the direction of decreasing temperature (therefore the signs of j E and are opposite). Thermal conductivity λ is equal to the heat flux density at a temperature gradient equal to unity. It can be shown that (2) where c V - specific heat gas at constant volume (the amount of heat required to heat 1 kg of gas by 1 K at constant volume), ρ - gas density,<ν > - average speed thermal movement of molecules,<l> - average free path.

The phenomenon of transference. Viscosity

Internal friction (viscosity ). The essence of the mechanism for the occurrence of internal friction between parallel layers of gas (liquid) that move at different speeds is that due to chaotic thermal motion, molecules are exchanged between the layers, as a result of which the momentum of the layer that moves faster decreases slower - increases, which leads to braking of the layer that moves faster, and acceleration of the layer that moves slower. As is known, the force of internal friction between two layers of gas (liquid) obeys Newton's law: (5) where η is dynamic viscosity (viscosity), d ν /dx is the velocity gradient, which shows the rate of change in velocity in the x direction perpendicular to the direction of movement of the layers, S is the area on which the force F acts. According to Newton’s second law, the interaction of two layers can be considered as a process in which per unit time from one layer an impulse is transmitted to the other, whose modulus is equal to acting force. Then expression (5) can be written as (6) where j p - momentum flux density- the quantity that is determined by the total impulse transferred per unit time in the positive direction of the x axis through a unit area perpendicular to the x axis, d ν /dx - speed gradient. The minus sign indicates that the momentum is transferred in the direction of decreasing speed (therefore the signs j p and d ν /dx are opposite). Dynamic viscosityη is numerically equal to the momentum flux density with a velocity gradient equal to unity; it is calculated using formula (7) From a comparison of formulas (1), (3) and (6), which describe transfer phenomena, it follows that the patterns of all transfer phenomena are similar to each other. These laws were known long before they were substantiated and derived from the molecular kinetic theory, which made it possible to establish that the external similarity of their mathematical expressions is a consequence of the commonality of the underlying phenomena of thermal conductivity, diffusion and internal friction of the molecular mechanism of mixing molecules in the process their chaotic movement and collisions with each other. The considered laws of Fourier, Fick and Newton do not reveal the molecular kinetic essence of the coefficients λ, D and η. Expressions for the transfer coefficients are obtained from kinetic theory. They are written without conclusion, since a strict and formal consideration of transfer phenomena is quite cumbersome, and a qualitative one does not make sense. Formulas (2), (4) and (7) give the relationship between the transfer coefficients and the characteristics of the thermal motion of molecules. From these formulas follow simple relationships between λ, D and η: and

Real gases. Van der Waals equation. Isotherms of real gas.

Real gas -gas, which is not described Clapeyron - Mendeleev equation of state for an ideal gas.

The relationships between its parameters show that molecules in a real gas interact with each other and occupy a certain volume. The state of a real gas is often described in practice by the generalized Mendeleev-Clapeyron equation:

where p is pressure; V - volume; T - temperature; Z r = Z r (p,T) - compressibility factor gas; m - mass; M - molar mass; R- gas constant.

Van der Waals gas equation of state -the equation, connecting the main thermodynamic quantities in the gas model van der Waals.

Although the model ideal gas describes behavior well real gases at low pressures and high temperatures, in other conditions its correspondence with experience much worse. In particular, this is manifested in the fact that real gases can be translated into liquid and even in solid state, but the ideal ones cannot.

To more accurately describe the behavior of real gases at low temperatures, a van der Waals gas model was created that takes into account the forces of intermolecular interaction. In this model internal energy becomes a function not only temperature, but also volume.

The van der Waals equation is one of the well-known approximate equations of state, which has a compact form and takes into account the basic characteristics of a gas with intermolecular interaction .

Since the entire process occurs at a constant temperature T, a curve that depicts the dependence of pressure p on volume V, called isotherm . At volume V 1 begins condensation gas, and with a volume of V 2 it ends. If V > V 1 then the substance will be in a gaseous state, and if V< V 2 - в жидком.

Solid. Dulong and Petit's law. Thermal expansion of solids. Melting.

Solid - this is one of four states of matter, different from other states of aggregation ( liquids, gases, plasma) stability of form and character thermal movement atoms, committing small fluctuations near equilibrium positions .

Distinguish crystalline And amorphous solids. Chapter physicists, which studies the composition and internal structure of solids, is called solid state physics. The way a solid body changes shape under impacts and movement is studied in a separate discipline - mechanics of solid (deformable) body. The third science deals with the movement of an absolutely rigid body - rigid body kinematics.

Technical devices created by man use various properties of a solid body. In the past, solids were used as a structural material and the use was based on directly tangible mechanical properties such as hardness, weight, plastic, elasticity, fragility. IN modern world The use of a solid is based on physical properties that are often only discovered through laboratory testing.

Law Dulong - Petit (Law of constant heat capacity) - empirical law, Whereby molar heat capacity solids at room temperature close to 3R :

Where R - universal gas constant.

The law is derived under the assumption that the crystal lattice of a body consists of atoms, each of which performs harmonic vibrations in three directions, determined by the structure of the lattice, and vibrations in different directions are absolutely independent of each other. It turns out that each atom represents three oscillator with energy E, defined by the following formula:

The formula follows from the equipartition theorem energy by degrees of freedom. Since each oscillator has one degree of freedom, then its average kinetic energy is equal to , and since the oscillations occur harmoniously, then the average potential energy equal to the average kinetic, and the total energy - according to their sum. The number of oscillators in one mole of a substance is , their total energy is numerically equal to the heat capacity of the body - hence the Dulong-Petit law.

Let us present a table of experimental values of the heat capacity of the series chemical elements for normal temperatures:

Thermal expansion -change in the linear dimensions and shape of the body when it changes temperature. Quantitatively, the thermal expansion of liquids and gases at constant pressure is characterized by isobaric expansion coefficient(volumetric coefficient of thermal expansion). To characterize the thermal expansion of solids, the coefficient of linear thermal expansion is additionally introduced.

Chapter physicists one who studies this property is called dilatometry .

Thermal expansion of bodies is taken into account when designing all installations, instruments and machines operating under variable temperature conditions.

The basic Law thermal expansion states that a body with a linear size in the corresponding dimension, with an increase in its temperature, expands by an amount equal to:

where is the so-called coefficient of linear thermal expansion. Similar formulas are available for calculating changes in area and volume of a body. In the simplest case presented, when the coefficient of thermal expansion does not depend on either the temperature or the direction of expansion, the substance will expand uniformly in all directions in strict accordance with the above formula.

Melting is the process of the body transitioning from crystalline solid to liquid state, that is, the transition of a substance from one state of aggregation to another. Melting occurs with absorption specific heat of fusion and is phase transition of the first kind, which is accompanied spasmodic change heat capacity at a specific temperature point of transformation for each substance - melting temperature.

Melting ability refers to physical properties substances

At normal pressure, maximum melting point among metals has tungsten(3422 °C), among simple substances - carbon(according to various sources 3500 - 4500 °C ) and among arbitrary substances - tantalum hafnium carbide Ta 4 HfC 5 (4216 °C). We can assume that the lowest melting point is helium: at normal pressure it remains liquid at arbitrarily low temperatures.

Many substances at normal pressure do not have a liquid phase. When heated, they sublimation immediately go into a gaseous state.

Liquids. Surface melting. Wetting.

Liquid - a substance found in a liquid state of aggregation, occupying an intermediate position between solid and gaseous states . The main property of a liquid, which distinguishes it from substances in other states of aggregation, is the ability to change its shape indefinitely under the influence of tangential mechanical stresses, even arbitrarily small, while practically maintaining its volume.

Surface phenomena , physical and chemical phenomena that are caused by the special (compared to bulk) properties of surface layers liquids and solids. The most general and important property of these layers is the excess free energy F = s S, where s is the surface (interfacial) tension, for solids - the specific free surface energy. S-interface area. Surface phenomena occur most pronouncedly in heterogeneous systems with a highly developed phase interface, i.e. dispersed systems. The study of patterns of surface phenomena is integral part colloid chemistry and is extremely important for all its practical applications.

Spontaneous surface phenomena occur due to a decrease in surface energy systems. They can be caused by a decrease in the total surface of the system or a decrease in surface tension at the interface. Surface phenomena associated with a decrease in the total surface include: 1) capillary phenomena. in particular, the acquisition of spherical drops (in fogs) and gas bubbles (in a liquid medium). a form in which the surface of the drop (bubble) is minimal. 2) Coalescence- merging of droplets into emulsions(or gas bubbles in foams)with them directly. contact. 3) Sintering small solid particles in powders at sufficiently high temperatures. 4) Collective recrystallization - enlargement of grains of polycrystalline material with increasing temperature. 5) Isothermal distillation- increasing the volume of large droplets by reducing small ones. Moreover, due to increased pressure vapors liquids with a higher surface curvature occurs evaporation small drops and their subsequent condensation on larger drops. For a liquid located on a solid substrate, the surface surface plays a significant role in the transfer of matter from small droplets to large ones. diffusion. Isothermal distillation solid particles can occur through the liquid phase due to the increased solubility of smaller particles.

Under certain conditions, spontaneous surface phenomena can occur in the system, accompanied by an increase in the total interphase surface area. Thus, spontaneous dispersion and formation of stable lyophilic colloidal systems(for example, critical emulsions) occurs under conditions where the increase in surface energy caused by grinding particles, is compensated by their involvement in thermal motion and a corresponding increase entropy(cm. Microemulsions). With the homogeneous formation of nuclei of a new phase during vapor condensation, boiling. crystallization from solutions and melts the increase in the energy of the system due to the formation of a new surface is compensated by a decrease in the chemical. potential of the substance at phase transition. The critical sizes of nuclei, above which the release of a new phase occurs spontaneously, depend on surface tension, as well as on the amount of overheating (supercooling, supersaturation). The relationship between these parameters is determined by the Gibbs equation (see. The emergence of a new phase).

Wetting -physical interaction liquids with surface solid or other liquid. There are two types of wetting:

Immersion(the entire surface of the solid is in contact with the liquid)

Contact(comprises three phases- solid, liquid, gaseous)

Wetting depends on the relationship between adhesive forces molecules liquids with molecules (or atoms) wetted body ( adhesion) and the forces of mutual adhesion of liquid molecules ( cohesion).

If a liquid comes into contact with a solid, there are two possibilities:

Liquid molecules are attracted to each other more strongly than to solid molecules. As a result of the attractive force between the molecules of the liquid, it is collected into a droplet. This is how he behaves mercury on glass, water on paraffin or “greasy” surface. In this case they say that the liquid does not wet surface;

Liquid molecules are attracted to each other less than to solid molecules. As a result, the liquid tends to press against the surface and spreads over it. This is how mercury behaves zinc plate, water on clean glass or wood. In this case they say that the liquid wets surface.

The degree of wetting is characterized by the contact angle. The contact angle (or contact angle) is the angle formed by the tangent planes to the interfacial surfaces limiting the wetting liquid, and the apex of the angle lies on the line of separation of the three phases. Measured by the sessile drop method . In the case of powders, reliable methods give high degree reproducibility, has not yet been developed (as of 2008). A gravimetric method for determining the degree of wetting has been proposed, but it has not yet been standardized.

Measuring the degree of wetting is very important in many industries (paints, pharmaceuticals, cosmetics, etc.). For example, special coatings are applied to car windshields, which must be resistant to various types of pollution. The composition and physical properties of glass and contact lens coatings can be optimized based on contact angle measurements. .

For example, a popular method of increasing oil production by injecting water into a reservoir is based on the fact that water fills the pores and squeezes out oil. In the case of small pores and clean water this is far from true, so we have to add special Surfactant. Wettability assessment rocks when adding solutions of different compositions, it can be measured using various instruments.