PHASE TRANSITION, phase transformation, in a broad sense - the transition of a substance from one phases to another when external conditions change - temperature, pressure, magnetic and electric. fields, etc.; in the narrow sense - an abrupt change in physical. properties with a continuous change in external parameters. The difference between the two interpretations of the term "F. p." seen from the following example. In a narrow sense, the transition of a substance from the gas phase to the plasma one (cf. Plasma) is not a F. p., since ionization gas occurs gradually, but in a broad sense it is F. p. In this article, the term "F. p." considered in a narrow sense.

The value of temperature, pressure or k.-l. another physical The quantities at which a phase transition occurs are called the transition point.

There are F. p. of two kinds. During F. p. of the first kind, such thermodynamic conditions change abruptly. characteristics of a substance, such as density, concentration of components; in a unit of mass, a very definite amount of heat is released or absorbed, which is called. transition heat. With F. p. of the second kind of some kind of physical. a value equal to zero on one side of the transition point gradually increases (from zero) as you move away from the transition point to the other side. In this case, the density and concentrations change continuously, heat is not released or absorbed.

F. p. is a phenomenon widespread in nature. Phonic phenomena of the first kind include: evaporation and condensation, melting and solidification, sublimation and condensation into a solid phase, and certain structural transitions in solids, for example. education martensite in an iron-carbon alloy. AT antiferromagnets with one axis of magnetization of magnetic sublattices A phase transition of the first kind occurs in an external magnetic field directed along the axis. At a certain value of the field, the moments of the magnetic sublattices are rotated perpendicular to the direction of the field (sublattice "overturning" occurs). In pure superconductors, a magnetic field induces a phase transition of the first kind from the superconducting to the normal state. .

At absolute zero temperature and a fixed volume, the phase with the lowest energy value is thermodynamically equilibrium. A phase transition of the first kind in this case occurs at those values ​​of pressure and external fields at which the energies of two different phases are compared. If you fix not the volume of the body V, and the pressure R, then in a thermodynamic state. equilibrium, the minimum is the Gibbs energy F (or G), and at the transition point in phase equilibrium there are phases with the same values ​​of F .

Many substances at low pressures crystallize into loosely packed structures. For example, crystalline hydrogen consists of molecules located at relatively large distances from each other; structure graphite is a series of far-spaced layers of carbon atoms. At sufficiently high pressures, such loose structures correspond to large values ​​of the Gibbs energy. Lower values ​​of Ф under these conditions correspond to equilibrium close-packed phases. Therefore, at high pressures, graphite transforms into diamond, and molecular crystalline. hydrogen must go into atomic (metal). quantum liquids 3 He and 4 He remain liquid at normal pressure down to the lowest temperatures reached (T ~ 0.001 K). The reason for this is the weak interaction of particles and the large amplitude of their oscillations at temp-pax close to abs. zero (the so-called zero oscillations ). However, an increase in pressure (up to 20 atm at T = 0 K) leads to solidification of liquid helium. At non-zero temp-pax and given pressure and temperature, the equilibrium phase is still the phase with the minimum Gibbs energy (the minimum energy, from which the work of the pressure forces and the amount of heat reported to the system are subtracted).

For F. p. of the first kind, the existence of a region of metastable equilibrium near the curve of the F. p. of the first kind is characteristic (for example, a liquid can be heated to a temperature above the boiling point or supercooled below the freezing point). Metastable states exist for quite a long time, for the reason that the formation of a new phase with a lower value of F (thermodynamically more favorable) begins with the appearance of nuclei of this phase. The gain in the Φ value during the formation of a nucleus is proportional to its volume, and the loss is proportional to the surface area (to the value surface energy). The resulting small embryos increase F, and therefore, with an overwhelming probability, they will decrease and disappear. However, nuclei that have reached a certain critical size grow, and the entire substance passes into a new phase. The formation of the embryo is critical. size is a very unlikely process and occurs quite rarely. The probability of formation of nuclei is critical. size increases if the substance contains foreign macroscopic inclusions. sizes (e.g., dust particles in a liquid). close critical point the difference between the equilibrium phases and the surface energy decrease, nuclei of large sizes and bizarre shapes are easily formed, which affects the properties of the substance .

Examples of F. p. II kind - the appearance (below a certain temperature in each case) of a magnetic moment in a magnet during the transition paramagnet - ferromagnet, antiferromagnetic ordering during the transition paramagnet - antiferromagnet, appearance of superconductivity in metals and alloys, occurrence of superfluidity in 4 He and 3 He, ordering of alloys, appearance of spontaneous (spontaneous) polarization of matter during the transition of paraelectric ferroelectric etc.

L. D. Landau(1937) proposed a general interpretation of all PTs of the second kind as points of change in symmetry: above the transition point, the system has a higher symmetry than below the transition point. For example, in a magnet above the transition point of the direction of elementary magnetic moments (spins) particles are randomly distributed. Therefore, the simultaneous rotation of all spins does not change the physical. system properties. Below the transition points, the backs have a preferential orientation. Their simultaneous rotation changes the direction of the magnetic moment of the system. Another example: in a two-component alloy, the atoms of which A and B located at the nodes of a simple cubic crystal lattice, the disordered state is characterized by a chaotic distribution of atoms L and B over the lattice sites, so that a shift of the lattice by one period does not change its properties. Below the transition point, the alloy atoms are ordered: ...ABAB... A shift of such a lattice by a period leads to the replacement of all atoms A by B or vice versa. As a result of the establishment of order in the arrangement of atoms, the symmetry of the lattice decreases.

Symmetry itself appears and disappears abruptly. However, the value characterizing the asymmetry (order parameter) can change continuously. For a phase transition of the second kind, the order parameter is equal to zero above the transition point and at the transition point itself. In a similar way behaves, for example, the magnetic moment of a ferromagnet, electric. polarization of a ferroelectric, density of the superfluid component in liquid 4 He, probability of detecting an atom BUT in the corresponding site of the crystal. two-component alloy gratings, etc.

The absence of jumps in density, concentration, and heat of transition is characteristic of phase II of the second kind. But exactly the same picture is observed in the critical. point on the curve F. p. of the first kind . The similarity is very deep. Close to critical point, the state of matter can be characterized by a quantity that plays the role of an order parameter. For example, in the case of a critical points on the liquid-vapour equilibrium curve are the density deviation from the mean value. When moving along the critical isochore from the side of high temperatures, the gas is homogeneous, and this value is equal to zero. Below critical temperature the substance separates into two phases, in each of which the deviation of the density from the critical one is not equal to zero. Since the phases differ little from each other near the point of phase II phases, it is possible to form large nuclei of one phase in another. (fluctuations), in the same way as near critical. points. Many criticisms are associated with this. phenomena during F. p. of the second kind: an infinite increase in the magnetic susceptibility of ferromagnets and the dielectric constant of ferroelectrics (an analogue is the increase in compressibility near the critical point of liquid-vapor), an infinite increase in heat capacity, anomalous scattering of electromagnetic waves [of light in liquid and vapor , X-ray in solids], neutrons in ferromagnets. Dynamic phenomena also change significantly, which is associated with a very slow absorption of the resulting fluctuations. For example, near the critical point liquid-vapor narrows the Rayleigh line light scattering, near Curie points ferromagnets and Neel points antiferromagnets, spin diffusion slows down etc. Cf. fluctuation size (correlation radius) R increases as we approach the point of the second kind F. p. and becomes infinitely large at this point.

Modern advances in the theory of functional phenomena of the second kind and critical phenomena are based on the similarity hypothesis. It is assumed that if we accept R per unit of length, and cf. the value of the order parameter of the cell with the edge R- per unit of measurement of the order parameter, then the entire pattern of fluctuations will depend neither on the proximity to the transition point, nor on the specific substance. All thermodynamic. quantities are power functions R. The exponents are called critical dimensions (indices). They do not depend on a specific substance and are determined only by the nature of the order parameter. For example, the dimensions at the Curie point of an isotropic material, the order parameter of which is the magnetization vector, differ from the dimensions in the critical. point liquid - vapor or at the Curie point of a uniaxial magnet, where the order parameter is a scalar value.

Near the transition point equation of state has a characteristic form of law corresponding states. For example, near the critical point liquid-vapor ratio (p - p k) / (p f - p g) depends only on (p - p c) / (p f - p g) * K T(here p is the density, p k is the critical density, p f is the density of the liquid, p g is the density of the gas, R - pressure, p to - critical pressure, K T - isothermal compressibility), moreover, the type of dependence with a suitable choice of scale is the same for all liquids .

Great progress has been made in theoretical critical calculation. dimensions and equations of state are in good agreement with experimental data.

The further development of the theory of FPs of the second kind is connected with the application of the methods of quantum field theory, in particular the method of the renormalization group. This method allows, in principle, to find critical indices with any required accuracy.

The division of phase transitions into two kinds is somewhat arbitrary, since there are phase transitions of the first kind with small jumps in heat capacity and other quantities and small heats of transition with highly developed fluctuations. F. p. is a collective phenomenon that occurs at strictly defined values ​​of temperature and other quantities only in a system that has, in the limit, an arbitrarily large number of particles.

Lit .: Landau L. D., Lifshits E. M., Statistical Physics, 2nd ed., M., 1964 (Theoretical Physics, vol. 5); Landau L. D., Akhiezer A. I., Lifshits E. M., Course of general physics. Mechanics and molecular physics, 2nd ed., M., 1969; Bpayt R., Phase transitions, trans. from English, M., 1967;Fisher M., The nature of the critical state, trans. from English, M., 1968; Stanley G., Phase transitions and critical phenomena, trans. from English, M., 1973; Anisimov M. A., Studies of critical phenomena in liquids, "Advances in physical sciences", 1974, v. 114, c. 2; Patashinsky A. 3., Pokrovsky V. L., Fluctuation theory of phase transitions, M., 1975; Quantum field theory and physics of phase transitions, trans. from English, M., 1975 (News of fundamental physics, issue 6); Wilson K., Kogut J., Renormalization group and s-expansion, trans. from English, M., 1975 (News of Fundamental Physics, v. 5).

AT. L. Pokrovsky.

According to the materials of the BSE.

Belousova Julia, Koban Anastasia

The paper describes the phase transitions of matter. Phase balance. Melting, crystallization, evaporation, condensation.

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Research work in physics: Phase transitions of matter

Plan: Object area and object of work Relevance of the study Purpose and objectives of the study Acquaintance with the initial information about phase transitions Types of phase transitions Phase equilibrium Processes in phase transitions Conclusion

Objective area Physics is the science of the universe, which allows us to consider and cognize the process around us in all its subtleties. “The most beautiful thing we can experience is the incomprehensible. It is the source of true art and science.” Albert Einstein.

Object of study For the object of study in this area, we will consider the process of phase transition of matter.

Relevance of the topic This topic is interesting and relevant because in recent years, the widespread use of phase transitions in various fields of science and technology is well known. Phase transitions can be attributed to the most practical ways of applying physical effects. This is due to the fact that phase transitions are: Often used in patents and practical solutions.

Purpose of the work: Acquaintance with the basic ideas of modern science about various types of phase equilibrium and about the physical features of the processes of transitions of matter from one phase to another.

Tasks: Consideration of the concept of phase transition Identification of the types of phase transition and main characteristics Consideration of phase equilibrium Establishment of various processes of phase transition

The concept of phase transition Phase transition, phase transformation, in a broad sense - the transition of a substance from one phase to another when external conditions change - temperature, pressure, magnetic and electric fields, etc. In a narrow sense, it is an abrupt change in physical properties with a continuous change in external parameters.

Types of phase transitions Phase transitions are divided into types I and II. Changes in the state of aggregation of a substance are called phase transitions of the first kind if: 1) The temperature is constant during the entire transition. 2) The volume of the system is changing. 3) The entropy of the system changes. Phase transitions of the second kind - phase transitions in which the first derivatives of thermodynamic potentials with respect to pressure and temperature change continuously, while their second derivatives experience a jump. From this it follows, in particular, that the energy and volume of a substance do not change during a second-order phase transition, but its heat capacity, compressibility, various susceptibilities, etc., change.

Phase transition diagram depicting the first and second order boundaries of the liquid and gaseous phases

Phase equilibrium The condition of phase equilibrium can be obtained from the theorems of thermodynamics. When a system is in equilibrium, the temperatures and pressures of all its phases are the same. If they are kept constant, then the thermodynamic potential of the system can only decrease. At equilibrium, it takes on a minimum value. Let m 1 be the mass of the first, and m 2 be the mass of the second phase.  1 and  2 specific thermodynamic potentials of matter in these phases. The thermodynamic potential of the entire system is represented as Ф = m 1  1 + m 2  2. If  1   2, then any transformation of phase 1 into phase 2 is accompanied by a decrease in Ф. This transformation will occur until the entire phase 1 passes to a more stable phase 2. Then the system will become single-phase, and its thermodynamic potential will reach the minimum value m  2 . On the contrary, if  1   2, then phase 2 will eventually turn into phase 1. Only under the condition  1 (P, T) =  2 (P, T) (1) The phases will be in equilibrium with each other. Thus, the condition for phase equilibrium is the equality of their specific thermodynamic potentials.

Diagram of the phase equilibrium of carbon dioxide:

The meaning of condition (1) is that for any phase transformations, the value of the specific thermodynamic potential remains unchanged. Thus, with all changes in the state of matter, its specific thermodynamic potential always changes continuously

Processes in phase transitions Consider: Evaporation and condensation Melting and crystallization Boiling and overheating of a liquid

Evaporation and condensation The transition of a liquid to a gaseous state is called evaporation, the transition to a gaseous state of a solid is called sublimation. The heat that must be imparted to a unit mass of a substance in order to turn it into vapor at the same temperature as the substance had before evaporation is called the specific heat of evaporation. During condensation, the heat expended during evaporation is given back: the liquid formed during condensation heats up. A vapor that is in equilibrium with its liquid is said to be saturated. The pressure at which equilibrium is observed is called the saturation vapor pressure.

Evaporation of some liquid Evaporation of some types of liquids in the diagram

Melting and crystallization The transition of a crystalline body into a liquid state occurs at a certain temperature for each substance and requires the expenditure of a certain amount of heat, called the heat of fusion. The melting point depends on the pressure. Thus, the transition from the crystalline to the liquid state occurs under quite definite conditions, characterized by pressures and temperatures. The set of these values ​​corresponds to the curve in the diagram (p, T), which is commonly called the melting curve

The reverse melting process of crystallization proceeds as follows. When the liquid is cooled to a temperature at which the solid and liquid phases can be in equilibrium at a given pressure (i.e., to the same temperature at which melting occurred), crystals begin to grow simultaneously around the so-called nuclei or crystallization centers. Growing more and more, individual crystals eventually merge with each other, forming a polycrystalline solid. The crystallization process is accompanied by the release of the same amount of heat that is absorbed during melting.

Melting

Diagram: Melting - Crystallization

Boiling and superheating of a liquid If the liquid in the vessel is heated at constant external pressure from the free surface of the liquid. This process of vaporization is called evaporation. Upon reaching a certain temperature, called the boiling point, the formation of steam begins to occur not only from the free surface, but vapor bubbles grow and rise to the surface, dragging the liquid itself with them. The process of vaporization becomes turbulent. This phenomenon is called boiling. Superheated water can be obtained, for example, in a quartz flask with smooth walls. Thoroughly rinse the flask first with sulfuric, nitric or some other acid, and then with distilled water. Distilled water is poured into the washed flask, from which the air dissolved in it is removed by prolonged boiling. After that, the water in the flask can be heated on a gas burner to a temperature much higher than the boiling point, and yet it will not boil, but only evaporate intensively from the free surface. Only occasionally does a vapor bubble form at the bottom of the flask, which grows rapidly, separates from the bottom and rises to the surface of the liquid, and its dimensions increase greatly when raised. Then the water remains calm for a long time. If a germ of a gaseous form is introduced into such water, for example, a pinch of tea is thrown, then it will boil violently, and its temperature will quickly drop to the boiling point. This effective experience has the character of an explosion.

Boiling Water temperature at nucleate boiling

Conclusion This work made it possible to learn more about the processes occurring when one state of matter passes into another, what characteristics each of the phases and states has. Seeing the processes around us, we can easily tell how it happens, knowing only the basic theory. Therefore, physics helps us to learn most of the laws of natural science that will help us in the future.

2. Phase transitions of the first and second kind………………………..4

3. Ideal gas………………………………………………………….7

4. Real gas………………………………………………………....8

5. Molecular-kinetic theory of critical phenomena….….9

6. Superfluidity………………………………………………………..11

7. Superconductivity………………………………………………..13

7.1 Discovery of superconductivity………………….…...13

7.2 Electron - phonon interaction……………..14

7.3 Superconductors of the first and second kind………...16

7.4 Recipe for making a superconductor…………….17

7.5 Safety precautions………………………………….18

7.6 The Meisner Effect…………………………………………………………………………20

8. Conclusion………………………….……………………….22

9. References…………………………………………….25

1. Introduction.

Phases are called homogeneous different parts of physico-chemical systems. A substance is homogeneous when all the parameters of the state of the substance are the same in all its volumes, the dimensions of which are large compared to the interatomic states. Mixtures of different gases always form one phase if they are in the same concentration throughout the volume.

The same substance, depending on external conditions, can be in one of three states of aggregation - liquid, solid or gaseous. Depending on external conditions, it can be in one phase, or in several phases at once. In the nature around us, we especially often observe phase transitions of water. For example: evaporation, condensation. There are pressure and temperature conditions under which the substance is in equilibrium in different phases. For example, when liquefying a gas in a state of phase equilibrium, the volume can be anything, and the transition temperature is related to the saturation vapor pressure. The temperatures at which transitions from one phase to another occur are called transition temperatures. They depend on pressure, although to varying degrees: the melting point is weaker, the temperature of vaporization and sublimation is stronger. At normal and constant pressure, the transition occurs at a certain temperature, and here melting, boiling and sublimation (or sublimation.) take place. Sublimation is the transition of a substance from a solid to a gaseous state, which can be observed, for example, in the shells of cometary tails. When a comet is far from the sun, almost all of its mass is concentrated in its nucleus, which measures 10-12 kilometers. The nucleus, surrounded by a small shell of gas, is the so-called head of a comet. When approaching the Sun, the nucleus and shells of the comet begin to heat up, the probability of sublimation increases, and desublimation decreases. The gases escaping from the comet's nucleus entrain solid particles with them, the comet's head increases in volume and becomes gaseous and dusty in composition.

2. Phase transitions of the first and second kind.

Phase transitions are of several kinds. Changes in the aggregate states of a substance are called first-order phase transitions if:

1) The temperature is constant during the entire transition.

2) The volume of the system is changing.

3) The entropy of the system changes.

For such a phase transition to occur, it is necessary for a given mass of substance to sheathe a certain amount of heat corresponding to the latent heat of transformation. Indeed, during the transition of the condensed phase to a phase with a lower density, a certain amount of energy must be imparted in the form of heat, which will go to destroy the crystal lattice (during melting) or to remove liquid molecules from each other (during vaporization). During the transformation, latent heat will go to the transformation of cohesive forces, the intensity of thermal motion will not change, as a result, the temperature will remain constant. With such a transition, the degree of disorder, and hence the entropy, increases. If the process goes in the opposite direction, then latent heat is released. Phase transitions of the first kind include: the transformation of a solid into a liquid (melting) and the reverse process (crystallization), liquid - into vapor (evaporation, boiling). One crystalline modification - to another (polymorphic transformations). Phase transitions of the second kind include: the transition of a normal conductor to a superconducting state, helium-1 to superfluid helium-2, a ferromagnet to a paramagnet. Metals such as iron, cobalt, nickel and gadolinium stand out for their ability to be highly magnetized and to maintain a state of magnetization for a long time. They are called ferromagnets. Most metals (alkali and alkaline earth metals and a significant part of transition metals) are weakly magnetized and do not retain this state outside a magnetic field - these are paramagnets. Phase transitions of the second, third, and so on kind are associated with the order of those derivatives of the thermodynamic potential ∂f that experience finite measurements at the transition point. Such a classification of phase transformations is associated with the work of the theoretical physicist Paul Ernest (1880 -1933). So, in the case of a second-order phase transition, the second-order derivatives experience jumps at the transition point: heat capacity at constant pressure Cp \u003d -T (∂f 2 / ∂T 2), compressibility β \u003d - (1 / V 0) (∂ 2 f / ∂p 2), thermal expansion coefficient α=(1/V 0)(∂ 2 f/∂Tp), while the first derivatives remain continuous. This means that there is no release (absorption) of heat and no change in specific volume (φ - thermodynamic potential).

The state of phase equilibrium is characterized by a certain relationship between the phase transformation temperature and pressure. Numerically, this dependence for phase transitions is given by the Clausius-Clapeyron equation: Dp/DT=q/TDV. Research at low temperatures is a very important branch of physics. The fact is that in this way it is possible to get rid of interference associated with chaotic thermal motion and study phenomena in a “pure” form. This is especially important in the study of quantum regularities. Usually, due to chaotic thermal motion, a physical quantity is averaged over a large number of its different values, and quantum jumps are “smeared out”.

Low temperatures (cryogenic temperatures), in physics and cryogenic technology, the temperature range is below 120°K (0°C=273°K); the work of Carnot (he worked on a heat engine) and Clausius laid the foundation for research on the properties of gases and vapors, or technical thermodynamics. In 1850, Clausius noticed that saturated water vapor partially condenses during expansion and becomes superheated during compression. Renu made a special contribution to the development of this scientific discipline. The intrinsic volume of gas molecules at room temperature is approximately one thousandth of the volume occupied by the gas. In addition, molecules are attracted to each other at distances greater than those from which their repulsion begins.

Equal to the specific values ​​of the entropy, taken with the opposite sign, and volume: (4.30) If at points that satisfy the phase equilibrium: , the first derivatives of the chemical potential for different phases experience a discontinuity: , (4.31) they say that the thermodynamic system is experiencing a phase transition of the 1st kind. Phase transitions of the first kind are characterized by the presence of latent heat of the phase transition, ...

Against overlifts, zero and maximum protection. - provide for stopping the vessels at intermediate points of the trunk. light signaling about the operating modes of the lifting unit in the building of the lifting machine, from the operator of the loading device, from the dispatcher. Modern adjustable DC electric drives for automated lifting installations are based on DC motors ...

44.5 cm, c = 12 cm, a = 20 cm, l = 8 cm. The force action of the magnetic system was estimated by a value equal to the product of the field modulus H and its gradient. It was found that the distribution of the field modulus H of the magnetic system under consideration is characterized by a pronounced angular dependence. Therefore, the calculation of the field modulus H was carried out with a step of 1° for points located on two different arcs for all...

The system consists in obtaining its “phase portrait” (Volkenshtein, 1978). It makes it possible to reveal the stationary states of the system and the nature of its dynamics when deviating from them. The method of phase portraits is used in engineering to analyze and predict the behavior of physical systems of varying complexity and in mathematical ecology to analyze population dynamics (Volkenshtein, 1978; Svirezhev...

concept phase in thermodynamics are considered in a broader sense than aggregate states. According to, under phase in thermodynamics, they understand the thermodynamically equilibrium state of a substance, which differs in physical properties from other possible equilibrium states of the same substance. Sometimes a non-equilibrium metastable state of a substance is also called a phase, but metastable. The phases of a substance may differ in the nature of the movement of structural particles and the presence or absence of an ordered structure. Different crystalline phases may differ from each other in the type of crystal structure, electrical conductivity, electrical and magnetic properties, etc. Liquid phases differ from each other in the concentration of components, the presence or absence of superconductivity, etc.

The transition of a substance from one phase to another is called phase transition . Phase transitions include the phenomena of vaporization and melting, condensation and crystallization, etc. In a two-phase system, the phases are in equilibrium at the same temperature. With an increase in volume, some of the liquid turns into vapor, but at the same time, in order to maintain the temperature unchanged, it is necessary to transfer a certain amount of heat from the outside. Thus, to carry out the transition from the liquid phase to the gaseous system, it is necessary to transfer heat without changing the temperature of the system. This heat is used to change the phase state of matter and is called heat of phase transformation or latent heat of transition . With increasing temperature, the latent heat of transition of a fixed mass of matter decreases, and at the critical temperature it is equal to zero. To characterize the phase transition, the specific heat of the phase transition is used. Specific heat of phase transition is the amount of latent heat per unit mass of a substance.

Phase transitions with absorption or release of latent heat of transition are called first-order phase transitions . In this case, the internal energy and density change abruptly. When moving from a more ordered state to a less ordered state, entropy increases. The table lists first-order phase transitions and their main characteristics.

Table. Phase transitions of the first rad and their main characteristics .

phase transition	Transition direction	Latent heat of transition	Change in entropy during a phase transition
vaporization	liquid  steam	L P is the specific heat of vaporization, t- mass of liquid converted to vapor.	Entropy increases
Condensation	Steam  liquid	, where L KOH is the value of the specific heat of condensation, t- mass of vapor converted to liquid	Entropy Decreases ΔS cr< 0
Melting	Solid  liquid	, where L PL is the specific heat of fusion, t- mass of a solid body converted to liquid	Entropy increases ΔS pl > 0
Crystallization	liquid  solid	, where L KR t- the mass of a liquid converted into a solid body - a crystal	Entropy Decreases ΔS cr< 0
Sublimation (or sublimation)	Solid  Steam	, where L With is the specific heat of sublimation, t- mass of solid body converted to steam	Entropy increases
desublimation (Crystallization bypassing the liquid phase)	Steam  Solid (bypassing the liquid phase)	, where L KR is the value of the specific heat of crystallization, t- mass of vapor transferred to a solid body - a crystal	Entropy Decreases ΔS cr< 0

With there is a relationship between the pressure at which the two-phase system is in equilibrium and the temperature during first-order phase transitions. This relationship is described . Consider the derivation of this equation for closed systems. If the number of particles in the system is constant, then the change in internal energy, according to the first law of thermodynamics, is determined by the expression: . The equilibrium between the phases will come under the condition that T 1 \u003d T 2 and P 1 \u003d P 2. Consider an infinitely small reversible Carnot cycle (Fig. 6.8), whose isotherms correspond to the state of a two-phase system at temperatures T and dT. Since the state parameters in this case change infinitely little, the isotherms and adiabats in Fig. 6.8 are shown as straight lines. The pressure in such a cycle changes by dP . The work of the system per cycle is determined by the formula:
. Let us assume that the cycle is implemented for a system whose mass of matter is equal to one. The efficiency of such an elementary Carnot cycle can be determined by the formulas:
or
, where L P is the specific heat of vaporization. Equating the right parts of these equalities, and substituting the expression of work through pressure and volume, we get:
. We correlate the change in pressure with the change in temperature and get:

(6.23)

Equation (6.23) is called Clausius-Clapeyron equation . Analyzing this equation, we can conclude that with increasing temperature, the pressure increases. This follows from the fact that
, which means
.

The Clausius-Clapeyron equation is applicable not only to the liquid-vapor transition. It applies to all transitions of the first kind. In general, it can be written like this:

(6.24)

Using the Clapeyron-Clausius equation, one can represent the state diagram of the system in the P,T coordinates (Fig. 6.9). In this diagram, curve 1 is the sublimation curve. It corresponds to the equilibrium state of two phases: solid and vapor. The points to the left of this curve characterize the single-phase solid state. The points on the right characterize the vapor state. Curve 2 is the melting curve. It corresponds to the equilibrium state of two phases: solid and liquid. The points to the left of this curve characterize the single-phase solid state. The points to the right of it up to curve 3 characterize the liquid state. Curve 3 is the vaporization curve. It corresponds to the equilibrium state of two phases: liquid and vapor. The points lying to the left of this curve characterize the single-phase liquid state. The points on the right characterize the vapor state. Curve 3, in contrast to curves 1 and 2, is bounded on both sides. On the one hand - a triple point Tr, on the other hand - the critical point K (Fig. 6.9). triple point describes the equilibrium state of three phases at once: solid, liquid and vapor.