What phase transitions of the first kind do you know. Phase transitions

The transition of matter from one state to another is a very common occurrence in nature. Boiling water in a kettle, freezing of rivers in winter, melting of metal, liquefaction of gases, demagnetization of ferrites when heated, etc. relate precisely to such phenomena, called phase transitions. Phase transitions are detected by a sharp change in the properties and features (anomalies) of the characteristics of a substance at the time of the phase transition: by the release or absorption of latent heat; jump in volume or jump in heat capacity and coefficient of thermal expansion; change in electrical resistance; the appearance of magnetic, ferroelectric, piezomagnetic properties, changes in the X-ray diffraction pattern, etc. Which of the phases of a substance is stable under certain conditions is determined by one of the thermodynamic potentials. At a given temperature and volume in a thermostat, this is the Helmholtz free energy, at a given temperature and pressure, the Gibbs potential.

Let me remind you that the Helmholtz potential F (free energy) is the difference between the internal energy of a substance E and its entropy S multiplied by the absolute temperature T:

Both energy and entropy in (1) are functions of external conditions (pressure p and temperature T), and the phase that occurs under certain external conditions has the smallest Gibbs potential of all possible phases. In terms of thermodynamics, this is a principle. When external conditions change, it may turn out that the free energy of the other phase has become smaller. The change in external conditions always occurs continuously, and therefore it can be described by some dependence of the volume of the system on temperature. Given this agreement in the values of T and V, we can say that the change in phase stability and the transition of a substance from one phase to another occur at a certain temperature along the thermodynamic path, and the values for both phases are functions of the temperature near this point. Let us consider in more detail how the change occurs sign. Close addiction for one and for the other phase can be approximated by some polynomials that depend on:

The difference between the free energies of two phases takes the form

As long as the difference is small enough, we can restrict ourselves to the first term and state that if , then phase I is stable at low temperatures, and phase II is stable at high temperatures. At the transition point itself, the first derivative of the free energy with respect to temperature naturally undergoes a jump: at , and at . As we know, there is, in fact, the entropy of things. Consequently, during a phase transition, the entropy experiences a jump, determining the latent heat of transition , since . The described transitions are called transitions of the first kind, and they are widely known and studied at school. We all know about the latent heat of vaporization or melting. That's what it is .

Describing the transition in the framework of the above thermodynamic considerations, we did not consider only one, at first glance, unlikely possibility: it may happen that not only free energies are equal, but also their derivatives with respect to temperature, that is, . It follows from (2) that such a temperature, at least from the point of view of the equilibrium properties of the substance, should not be singled out. Indeed, at and in the first approximation with respect to we have

and, at least at this point, no phase transition should occur: the Gibbs potential, which was smaller at , will also be smaller at .

In nature, of course, not everything is so simple. Sometimes there are deep reasons for the two equalities and to hold at the same time. Moreover, phase I becomes absolutely unstable with respect to arbitrarily small fluctuations of the internal degrees of freedom at , and phase II - at . In this case, those transitions occur which, according to the well-known classification of Ehrenfest, are called transitions of the second kind. This name is due to the fact that during second-order transitions, only the second derivative of the Gibbs potential with respect to temperature jumps. As we know, the second derivative of free energy with respect to temperature determines the heat capacity of a substance

Thus, during transitions of the second kind, a jump in the heat capacity of the substance should be observed, but there should be no latent heat. Since at , phase II is absolutely unstable with respect to small fluctuations, and the same applies to phase I at , neither overheating nor overcooling should be observed during second-order transitions, that is, there is no temperature hysteresis of the phase transition point. There are other remarkable features that characterize these transitions.

What are the underlying causes of the thermodynamically necessary conditions for a second-order transition? The fact is that the same substance exists both at and at. The interactions between the elements that make it up do not change abruptly, this is the physical nature of the fact that the thermodynamic potentials for both phases cannot be completely independent. How the relationship between and , and etc. arises can be traced on simple models of phase transitions by calculating the thermodynamic potentials under different external conditions using the methods of statistical mechanics. The easiest way to calculate free energy.

WIKIPEDIA

Phase transition(phase transformation) in thermodynamics - the transition of a substance from one thermodynamic phase to another when external conditions change. From the point of view of the movement of a system along a phase diagram with a change in its intensive parameters (temperature, pressure, etc.), a phase transition occurs when the system crosses the line separating two phases. Since different thermodynamic phases are described by different equations of state, it is always possible to find a quantity that changes abruptly during a phase transition.

Since the division into thermodynamic phases is a smaller classification of states than the division into aggregate states of a substance, not every phase transition is accompanied by a change in the aggregate state. However, any change in the state of aggregation is a phase transition.

The most frequently considered phase transitions are those with a change in temperature, but at a constant pressure (usually equal to 1 atmosphere). That is why the terms “point” (and not line) of a phase transition, melting point, etc. are often used. Of course, a phase transition can occur both with a change in pressure and at constant temperature and pressure, but also with a change in the concentration of components (for example, the appearance of salt crystals in a solution that has reached saturation).

At first-order phase transition the most important primary extensive parameters change abruptly: the specific volume, the amount of stored internal energy, the concentration of components, etc. We emphasize: we mean the abrupt change in these quantities with changes in temperature, pressure, etc., and not an abrupt change in time (for the latter, see the section below Dynamics of phase transitions).

The most common examples phase transitions of the first kind:

melting and crystallization

evaporation and condensation

sublimation and desublimation

At phase transition of the second kind density and internal energy do not change, so such a phase transition may not be visible to the naked eye. The jump is experienced by their derivatives with respect to temperature and pressure: heat capacity, coefficient of thermal expansion, various susceptibilities, etc.

Phase transitions of the second kind occur in those cases when the symmetry of the structure of matter changes (symmetry can completely disappear or decrease). The description of a second-order phase transition as a consequence of a change in symmetry is given by Landau's theory. At present, it is customary to talk not about a change in symmetry, but about the appearance at the transition point order parameter, equal to zero in a less ordered phase and changing from zero (at the transition point) to nonzero values in a more ordered phase.

The most common examples of second-order phase transitions are:

the passage of the system through a critical point

transition paramagnet-ferromagnet or paramagnet-antiferromagnet (order parameter - magnetization)

the transition of metals and alloys to the state of superconductivity (the order parameter is the density of the superconducting condensate)

transition of liquid helium to a superfluid state (pp - density of the superfluid component)

transition of amorphous materials to a glassy state

Modern physics also investigates systems that have phase transitions of the third or higher order.

Recently, the concept of a quantum phase transition has become widespread, i.e. a phase transition controlled not by classical thermal fluctuations, but by quantum ones, which exist even at absolute zero temperatures, where a classical phase transition cannot be realized due to the Nernst theorem.

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Phase transitions, transitions of a substance from one phase to another with a change in the state parameters characterizing the thermodynamic equilibrium. The temperature value, or some other physical quantity, at which phase transitions occur in a one-component system, is called the transition point. During phase transitions of the first kind, the properties expressed by the first derivatives of G with respect to pressure R, t-re T and other parameters, change abruptly with a continuous change in these parameters. In this case, the transition heat is released or absorbed. In a one-component system, the transition temperature T1 related to pressure R 1 Clausius-Clapeyron equation dp 1 /dT 1 ==QIT 1 D V, where Q- heat of transition, D V- volume jump. Phase transitions of the first kind are characterized by hysteresis phenomena (for example, overheating or supercooling of one of the phases), which are necessary for the formation of nuclei of the other phase and for the phase transitions to occur at a finite rate. In the absence of stable nuclei, the superheated (supercooled) phase is in a state of metastable equilibrium. The same phase can exist (albeit metastablely) on both sides of the transition point to (however, crystalline phases cannot be superheated above temperature or sublimation). At point F. p. I kind of Gibbs energy G as a function is continuous, and both phases can coexist for an arbitrarily long time, that is, the so-called phase separation takes place (for example, the coexistence of both it or and for a given total volume of the system).

phase transitions of the first kind are widespread phenomena in nature. These include both from the gas to the liquid phase, melting and solidification, and (desublimation) from the gas to the solid phase, most polymorphic transformations, some structural transitions in solids, for example, the formation of martensite in -. In clean ones, a sufficiently strong magnetic field causes first-order phase transitions from the superconducting to the normal state.

At phase transitions of the second kind, the quantity itself G and first derivatives G on T, p and other parameters of the states change continuously, and the second derivatives (respectively, the coefficient and thermal expansion) with a continuous change in parameters change abruptly or are singular. Heat is neither released nor absorbed, hysteresis phenomena and metastable states are absent. Second-order phase transitions observed with a change in temperature include, for example, transitions from a paramagnetic (disordered) state to a magnetically ordered state (ferro- and ferrimagnetic at the antiferromagnetic point at the Neel point) with the appearance of spontaneous magnetization (respectively, in the entire lattice or in each of magnetic sublattices); transition - with the advent of spontaneous. the appearance of an ordered state in solids (in ordering alloys); the transition of smectic liquid crystals into the nematic phase, accompanied by an anomalous increase in heat capacity, as well as transitions between different smectic phases; l - transition to 4 He, accompanied by the appearance of anomalously high and superfluidity. Transition to the superconducting state in the absence of a magnetic field.

Phase transitions can be associated with a change in pressure. Many substances at low pressures crystallize into loosely packed structures. For example, the structure is a series of layers that are far apart. At sufficiently high pressures, large values of the Gibbs energy correspond to such loose structures, while equilibrium close-packed phases correspond to smaller values. Therefore, at high pressures, graphite transforms into diamond. Quantum 4 He and 3 He remain liquid at normal pressure down to the lowest temperatures reached near absolute zero. The reason for this is the weak interaction and large amplitude of their "zero oscillations" (the high probability of quantum tunneling from one fixed position to another). However, the rise causes the liquid helium to solidify; for example, 4 He at 2.5 MPa forms hexagen, a close-packed lattice.

The general interpretation of second-order phase transitions was proposed by L. D. Landau in 1937. Above the transition point, the system, as a rule, has a higher symmetry than below the transition point, therefore, second-order phase transitions are interpreted as a point of symmetry change. For example, in a ferromagnet above the Curie point, the directions of the spin magnetic moments of the particles are distributed randomly, so the simultaneous rotation of all spins around the same axis by the same angle does not change the physical. system properties. Below the transition points, the spins have a preferential orientation, and their joint rotation in the sense indicated above changes the direction of the magnetic moment of the system. In a two-component alloy, whose atoms A and B are located at the sites of a simple cubic crystal lattice, the disordered state is characterized by a chaotic distribution of A and B over the lattice sites, so that a lattice shift by one period does not change the properties. Below the transition point, the atoms of the alloy are ordered: ...ABAB... A shift of such a lattice by a period leads to the replacement of all A by B and vice versa. Thus, the symmetry of the lattice decreases, since the sublattices formed by atoms A and B become nonequivalent.

Symmetry appears and disappears abruptly; in this case, the violation of symmetry can be characterized by physical. quantity, which during phase transitions of the second kind changes continuously and is called. order parameter. For pure liquids, such a parameter is the density, for solutions - the composition, for ferro- and ferrimagnets - spontaneous magnetization, for ferroelectrics - spontaneous electric polarization, for alloys - the proportion of ordered for smectic liquid crystals - the amplitude of the density wave, etc. In all of the above cases at temperatures above the point of phase transitions of the second kind, the order parameter is equal to zero, below this point its anomalous growth begins, leading to max. value at T = O.

The absence of transition heat, density jumps, and concentrations, which is characteristic of second-order phase transitions, is also observed at the critical point on the curves of first-order phase transitions. The similarity is very deep. The state of matter near the critical point can also be characterized by a quantity that plays the role of an order parameter. For example, in the case of liquid-vapor equilibrium, such a parameter is the deviation of the substance density from the critical value: when moving along the critical isochore from the side of high temperatures, the gas is homogeneous and the density deviation from the critical value is zero, and below the critical temperature, the substance separates into two phases, in each of which the density deviation from the critical value is not equal to zero.

Since the phases differ little from each other near the point of second-order phase transitions, fluctuations of the order parameter are possible, just as near the critical point. Associated with this are critical phenomena at the points of phase transitions of the second kind: an anomalous increase in the magnetic susceptibility of ferromagnets and the dielectric susceptibility of ferroelectrics (an analogue is the growth near the critical point of the liquid-vapor transition); a sharp increase in heat capacity; anomalous scattering of light waves in the liquid - vapor system (the so-called critical opalescence), X-rays in solids, neutrons in ferromagnets. The dynamic processes also change significantly, which is associated with a very slow dissipation of the resulting fluctuations. For example, near the liquid-vapor critical point, the line of Rayleigh scattering of light narrows, near the Curie and Neel points, respectively, in ferromagnets and antiferromagnets, spin diffusion slows down (the propagation of excess magnetization occurring according to the laws of diffusion). The average size of the fluctuation (correlation radius) increases as it approaches the point of second-order phase transitions and becomes anomalously large at this point. This means that any part of the substance at the transition point "feels" the changes that have occurred in other parts. On the contrary, far from the transition point of the second kind, the fluctuations are statistically independent and random changes in the state in a given part of the system do not affect the properties of its other parts.

P, t-re T, and other parameters change abruptly with a continuous change in these parameters. In this case, the transition heat is released or absorbed. In a one-component system, the transition temperature T 1 is related to p 1 Clapeyron - Clausius by the equation dp 1 /dT 1 = QIT 1 DV, where Q is the heat of transition, DV is the volume jump. Phase transitions of the first kind are characterized by hysteresis phenomena (for example, overheating or supercooling of one of the phases), which are necessary for the formation of nuclei of the other phase and the flow of phase transitions at a finite rate. In the absence of stable nuclei, the superheated (supercooled) phase is in a metastable state (see ). The same phase can exist (albeit metastablely) on both sides of the transition point to (however, the crystalline phases cannot be overheated above the temperature or ). At the point phase transitions I kind G as a function is continuous (see the figure in Art.), and both phases can coexist for an arbitrarily long time, i.e., there is a so-called. phase separation (for example, the coexistence of both its or and for a given total volume of the system).

F Atomic transitions of the first kind are widespread phenomena in nature. These include both from the gas to the liquid phase, and solidification, and (desublimation) from the gas to the solid phase, most polymorphic transformations, some structural transitions in, for example, the formation of martensite in -. In pure enough strong magnetic. the field causes phase transitions of the first kind from the superconducting to the normal state.

During phase transitions of the second kind, the value of G itself and the first derivatives of G with respect to T, p, etc. change continuously, and the second derivatives (respectively, coefficient and thermal expansion) change abruptly or are singular with a continuous change in parameters. Heat is neither released nor absorbed, hysteresis phenomena and metastable states are absent. To phase transitions Type II, observed with a change in temperature, include, for example, transitions from a paramagnetic (disordered) state to a magnetically ordered (ferro- and ferrimagnetic in, antiferromagnetic in) with the appearance of spontaneous magnetization (respectively, in the entire lattice or in each of magnetic sublattices); transition - with the advent of spontaneous; the emergence of an ordered state in (in ordering); smectic transition. in the nematic phase, accompanied by abnormal growth, as well as transitions between decomp. smectic phases; l -transition to 4 He, accompanied by the appearance of anomalously high and superfluidity (see); transition to the superconducting state in the absence of a magnet. fields.

Phase transitions may be associated with change. Many substances at small crystallize into loosely packed structures. For example, the structure is a series of layers that are far apart from each other. At sufficiently high values, large values correspond to such loose structures, and equilibrium close-packed phases correspond to smaller values. Therefore, at large it goes to . Quantum 4 He and 3 He under normal conditions remain liquid up to the lowest of the reached t-p near abs. zero. The reason for this is in the weak interaction. and large amplitude of their "zero oscillations" (high probability of quantum tunneling from one fixed position to another). However, the rise causes the liquid to solidify; for example, 4 He at 2.5 MPa forms hexagen, a close-packed lattice.

General interpretation phase transitions Type II was proposed by L. D. Landau in 1937. Above the transition point, the system, as a rule, has a higher transition point than below the transition point, therefore a phase transition of the second kind is interpreted as a change point. For example, in the higher direction of the spin magn. moments of particles are distributed randomly, so the simultaneous rotation of all around the same axis at the same angle does not change the physical. St. in the system. Below transition points have advantages. orientation, and their joint rotation in the above sense changes the direction of the magnetic. moment of the system. In a two-component, to-rogo A and B are located at the nodes of a simple cubic. crystalline lattice, disordered state is characterized by chaotic. distribution of A and B over the lattice nodes, so that the lattice shift by one period does not change the r.v. Below the transition points are arranged in order: ...ABAB... A shift of such a lattice by a period leads to the replacement of all A by B and vice versa. T. arr., the lattice decreases, since the sublattices formed by A and B become non-equivalent.

Appears and disappears abruptly; at the same time, the violation can be characterized by physical. value, to-heaven during phase transitions of the second kind changes continuously and is called. order parameter. For pure, such a parameter is density, for solutions - composition, for ferro-and - spontaneous magnetization, for ferroelectrics - spontaneous electric. , for - the proportion of ordered for smectic. - the amplitude of the density wave, etc. In all of the above cases, at t-rah above the point of phase transitions of the second kind, the order parameter is zero, below this point, its anomalous growth begins, leading to max. value at T = O.

The absence of the heat of transition, density jumps, and , which is characteristic of second-order phase transitions, is also observed in critical. point on the curves of phase transitions of the first kind (see ). The similarity is very deep. State in-va about critical. points can also be characterized by a quantity that plays the role of an order parameter. For example, in the case of - such a parameter is the deviation of the density in-va from the critical. values: when moving along a critical the isochore from the side of high tr is homogeneous and the density deviation from the critical. value is zero, and below the critical. t-ry in-in is stratified 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 the phase transition of the second kind, the existence of fluctuations of the order parameter is possible, in the same way as near the critical. points. Critical is associated with this. phenomena at the points of phase transitions of the second kind: anomalous growth of magn. susceptibility and dielectric. susceptibility (analogue is growth near the critical transition point - ); a sharp increase ; anomalous scattering of light waves in the system

Phase transitions

PHASE TRANSITIONS (phase transformations), transitions of a substance from one phase to another, occurring when temperature, pressure or under the influence of any other external factors (for example, magnetic or electric fields). Phase transitions, accompanied by a jump-like change in the density and entropy of matter, are called phase transitions of the 1st kind; These include evaporation melting, condensation, crystallization. In the course of such phase transitions, heat phase transitions. Phase transitions of the 2nd kind density and the entropy of matter change continuously at the transition point, the athermal capacity, compressibility, and other similar quantities experience a jump. As a rule, this changes and, accordingly, symmetry phase (for example, magnetic during phase transitions from a paramagnetic to a ferromagnetic state at the Curie point).

Phasetransitionsfirstkind phase transitions, for which the first derivatives change abruptly thermodynamic potentials on intense parameters system (temperature or pressure). Transitions of the first kind are realized both during the transition of the system from one state of aggregation to another, and within one state of aggregation (in contrast to phase transitions second kind that occur within a single state of aggregation).

Examples of first-order phase transitions

during the transition of the system from one state of aggregation to another: crystallization(liquid phase transition to solid), melting(transition of the solid phase into the liquid), condensation(transition of the gaseous phase into a solid or liquid), sublimation(transition of a solid phase into a gaseous one), eutectic, peritectic imonotectic transformations.

within one state of aggregation: eutectic, peritectic and polymorphic transformations, decomposition of supersaturated solid solutions, decomposition (stratification) of liquid solutions, ordering of solid solutions.

Sometimes, first-order phase transitions are also referred to as martensitic transformations(conditionally, since at the entrance of the martensitic transformation, a transition to a stable, but non-equilibrium state is realized - metastable state).

Phasetransitionssecondkind-phase transitions, for which the first derivatives thermodynamic potentials in pressure and temperature change continuously, while their second derivatives experience a jump. It follows, in particular, that energy and the volume of a substance do not change during a second-order phase transition, but its heat capacity, compressibility, various susceptibilities, etc.

FP (Wiki)

Classification of phase transitions

At first-order phase transition the most important, primary extensive parameters change abruptly: the specific volume, the amount of stored internal energy, the concentration of components, etc. We emphasize: we mean the abrupt change in these quantities with changes in temperature, pressure, etc., and not an abrupt change in time (for the latter, see the section below Dynamics of phase transitions).

The most common examples phase transitions of the first kind:

melting and crystallization

evaporation and condensation

sublimation and desublimation

The most common examples of second-order phase transitions are:

passage of the system through a critical point

paramagnet-ferromagnet or paramagnet-antiferromagnet transition (order parameter - magnetization)

transition of metals and alloys to the state of superconductivity (the order parameter is the density of the superconducting condensate)

transition of liquid helium to the superfluid state (pp - density of the superfluid component)

transition of amorphous materials to a glassy state

The existence of phase transitions of more than the second order has not yet been experimentally confirmed.

Recently, the concept of a quantum phase transition has become widespread, that is, a phase transition controlled not by classical thermal fluctuations, but by quantum ones, which exist even at absolute zero temperatures, where a classical phase transition cannot be realized due to the Nernst theorem.

Dynamics of phase transitions

As mentioned above, a jump in the properties of a substance means a jump with a change in temperature and pressure. In reality, when acting on the system, we do not change these quantities, but its volume and its total internal energy. This change always occurs at some finite rate, which means that in order to "cover" the entire gap in density or specific internal energy, we need some finite time. During this time, the phase transition does not occur immediately in the entire volume of the substance, but gradually. In this case, in the case of a first-order phase transition, a certain amount of energy is released (or taken away), which is called heat of phase transition. In order for the phase transition not to stop, it is necessary to continuously remove (or supply) this heat, or compensate for it by performing work on the system.

As a result, during this time, the point on the phase diagram describing the system "freezes" (that is, the pressure and temperature remain constant) until the process is completed.

Concepts of phase and phase transition. Phase transitions of the first and second kind

Phases- these are various homogeneous 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 elementary 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. Phases are stable states of a certain state of aggregation. The concept of a phase is broader than the concept of an aggregate state.

Depending on external conditions, the system can be in equilibrium either in one phase or in several phases at once. Their equilibrium existence is called phase balance.

Evaporation and condensation - frequently observed phase transitions of water in the natural environment. When water passes into steam, evaporation first occurs - the transition of the surface layer of the liquid into steam, while only the fastest molecules pass into steam: they must overcome the attraction of surrounding molecules, therefore their average kinetic energy and, accordingly, the temperature of the liquid decrease. Observed in everyday life and the reverse process - condensation. Both of these processes depend on external conditions. In some cases, a dynamic equilibrium is established between them, when the number of molecules leaving the liquid becomes equal to the number of molecules returning to it. Molecules in a liquid are bound by attractive forces that hold them within the liquid. If molecules with velocities that exceed the average are near the surface, they can leave it. Then the average speed of the remaining molecules will decrease and the temperature of the liquid will decrease. For evaporation at a constant temperature, a certain amount of heat must be imparted to the liquid: Q= rt, where r is the specific heat of vaporization, which decreases with increasing temperature. At room temperature, for one molecule of water, the heat of vaporization is 10 -20 J, while the average energy of thermal motion is 6.06 10 -21 J. This means that

molecules with an energy that is 10 times the energy of thermal motion. When passing through the liquid surface, the potential energy of a fast molecule increases, while the kinetic energy decreases. Therefore, the average kinetic energies of vapor and liquid molecules at thermal equilibrium are equal.

Saturated steam - it is a vapor in dynamic equilibrium, corresponding to a given temperature, with its liquid. Experience shows that it does not obey the Boyle-Mariotte law, since its pressure does not depend on volume. Saturated vapor pressure is the highest pressure that steam can have at a given temperature. The processes of evaporation and condensation of water cause complex interactions between the atmosphere and the hydrosphere, which are important for the formation of weather and climate. There is a continuous exchange of matter (water cycle) and energy between the atmosphere and the hydrosphere.

Studies have shown that about 7,000 km 3 of water evaporates per day from the surface of the World Ocean, which makes up 94% of the earth's hydrosphere, and about the same amount falls in the form of precipitation. Water vapor, carried away by the convection movement of air, rises up and enters the cold layers of the troposphere. As it rises, the vapor becomes more and more saturated, then condenses to form raindrops. In the process of steam condensation in the troposphere, about 1.6-10 22 J of heat is released per day, which is tens of thousands of times greater than the energy generated by mankind over the same time.

Boiling- the process of transition of a liquid into vapor as a result of the emergence of bubbles filled with vapor. Boiling occurs throughout the volume. The rupture of bubbles at the surface of a boiling liquid indicates that the vapor pressure in them exceeds the pressure above the surface of the liquid. At a temperature of 100 °C, the saturated vapor pressure is equal to the air pressure above the surface of the liquid (this is how this point on the scale was chosen). At an altitude of 5 km, the air pressure is half as much and water boils there at 82 ° C, and at the border of the troposphere (17 km) - at approximately 65 ° C. Therefore, the boiling point of a liquid corresponds to the temperature at which its saturated vapor pressure is equal to the external pressure. The weak gravitational field of the Moon (gravitational acceleration near its surface is only 1.7 m/s 2) is not able to hold the atmosphere, and in the absence of atmospheric pressure, the liquid instantly boils away, so the lunar "seas" are waterless and are formed by solidified lava. For the same reason, the Martian "channels" are also waterless.

A substance can be in equilibrium and in different phases. So, 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 phase equilibrium curve can be obtained by projecting onto a plane (p, t) areas of transition to the liquid state. Analytically, the equilibrium curve of two phases is determined from the solution of the Clausius-Clapeyron differential equation. Similarly, it is possible to obtain melting and sublimation curves, which are connected at one point of the plane (R, D), at the triple point (see Fig. 7.1), where in certain proportions they are in equal

all three phases. The triple point of water corresponds to a pressure of 569.24 Pa and a temperature of -0.0075 °C; carbon dioxide - 5.18 10 5 Pa and 56.6 ° C, respectively. Therefore, at atmospheric pressure R, equal to 101.3 kPa, carbon dioxide can be in a solid or gaseous state. At the critical temperature, the physical properties of liquid and vapor become the same. At temperatures above the critical point, the substance can only be in the gaseous state. For water - T= 374.2 °С, R= 22.12 MPa; for chlorine - 144 ° C and 7.71 MPa, respectively.

Transition temperatures are the temperatures at which transitions from one phase to another occur. They depend on pressure, although to varying degrees: the melting point is weaker, the temperatures of vaporization and sublimation are stronger. At normal and constant pressures, the transition occurs at a certain temperature, and here melting, boiling and sublimation (or sublimation) points take place.

The transition of matter from a solid state directly to a gaseous state 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 has a size of 10-12 km. The nucleus is surrounded by a small shell of gas - this is the comet's head. When approaching the Sun, the core and shell of the comet begin to heat up, the probability of sublimation increases, and desublimation (the reverse process) decreases. The gases escaping from the comet's nucleus carry away solid particles, the comet's head increases in volume and becomes gas and dust in composition. The pressure of the cometary nucleus is very low, so the liquid phase does not occur. Along with the head, the comet's tail also grows, which stretches away from the Sun. In some comets it reaches hundreds of millions of kilometers at perihelion, but the densities in the cometary matter are negligible. With each approach to the Sun, comets lose most of their mass, more and more volatile substances sublimate in the nucleus, and gradually it crumbles into meteor bodies that form meteor showers. Over the 5 billion years of the existence of the solar system, many comets ended their existence this way.

In the spring of 1986, automatic Soviet stations "Vega-1" and "Vega-2" were sent into space to study Halley's comet, which passed at a distance of 9000 and 8200 km from it, respectively, and the NASA station "Giotto" - at a distance of only 600 km from the comet's nucleus. The nucleus was 14 x 7.5 km in size, dark in color and about 400 K in temperature. When the space stations passed through the comet's head, about 40,000 kg of icy matter sublimated in 1 s.

In late autumn, when a sharp cold snap sets in after wet weather, one can observe on the branches of trees and on wires

Hoarfrost is desublimated ice crystals. A similar phenomenon is used when storing ice cream, when carbon dioxide is cooled, as the molecules passing into steam carry away energy. On Mars, the phenomena of sublimation and desublimation of carbon dioxide in the polar caps play the same role as evaporation - condensation in the atmosphere and hydrosphere of the Earth.

The heat capacity tends to zero at ultralow temperatures, as Nernst established. From this, Planck showed that near absolute zero, all processes proceed without a change in entropy. Einstein's theory of the heat capacity of solids at low temperatures made it possible to formulate Nernst's result as the third law of thermodynamics. The unusual properties of substances observed at low temperatures - superfluidity and superconductivity - have been explained in modern theory as macroscopic quantum effects.

Phase transitions are of several kinds. During a phase transition, the temperature does not change, but the volume of the system does.

Phase transitions of the first kind changes in the aggregate states of a substance are called if: the temperature is constant during the entire transition; the volume of the system changes; the entropy of the system changes. For such a phase transition to occur, it is necessary to impart a certain amount of heat to a given mass of substance, corresponding to the latent heat of transformation.

Indeed, during the transition from a more 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 is expended to overcome cohesive forces, the intensity of thermal motion does not change, as a result, the temperature remains 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 second kind associated with a change in the symmetry of the system: above the transition point, the system, as a rule, has a higher symmetry, as L.D. Landau showed in 1937. For example, in a magnet, the spin moments above the transition point are randomly oriented, and the simultaneous rotation of all spins around the same axis through the same angle does not change the properties of the system. Below the transition points, the spins have some preferential orientation, and their simultaneous rotation changes the direction of the magnetic moment of the system. Landau introduced the ordering factor and expanded the thermodynamic potential at the transition point in powers of this coefficient, on the basis of which he built a classification of all possible types of transitions.

Dov, as well as the theory of the phenomena of superfluidity and superconductivity. On this basis, Landau and Lifshitz considered many important problems - the transition of a ferroelectric to a paraelectric, a ferromagnet to a paramagnet, sound absorption at the transition point, the transition of metals and alloys to the superconducting state, etc.

The calculation of the thermodynamic properties of a system based on statistical mechanics involves the choice of a specific model of the system, and the more complex the system, the simpler the model should be. E. Ising proposed a model of a ferromagnet (1925) and solved the problem of a one-dimensional chain, taking into account the interaction with the nearest neighbors for any fields and temperatures. In the mathematical description of such systems of particles with intense interaction, a simplified model is chosen, when only pair-type interaction occurs (such a two-dimensional model is called the Ising lattice). But phase transitions were not always calculated, probably due to some unaccounted phenomena common to systems of many particles, and the nature of the particles themselves (liquid particles or magnets) does not matter. L. Onsager gave an exact solution for the two-dimensional Ising model (1944). He placed dipoles at the lattice nodes, which can orient themselves in only two ways, and each such dipole can only interact with its neighbor. It turned out that at the transition point, the heat capacity goes to infinity according to the logarithmic law symmetrically on both sides of the transition point. Later it turned out that this conclusion is very important for all second-order phase transitions. Onsager's work showed that the method of statistical mechanics makes it possible to obtain new results for phase transformations.

Phase transitions of the second, third, etc. genera are related to the order of those derivatives of the thermodynamic potential Ф, which experience finite changes at the transition point. Such a classification of phase transformations is associated with the work of the theoretical physicist P. Ehrenfest. In the case of a second-order phase transition, the second-order derivatives experience jumps at the transition point: heat capacity at constant pressure C p =, compressibility , coefficient

thermal expansion coefficient, while per-

all derivatives remain continuous. This means that there is no release (absorption) of heat and no change in specific volume.

Quantum field theory began to be used for calculations of particle systems only in the 70s. 20th century The system was considered as a lattice with a variable step, which made it possible to change the accuracy of calculations and approach the description of a real system and use a computer. The American theoretical physicist C. Wilson, having applied a new method of calculations, received a qualitative leap in the understanding of second-order phase transitions associated with the rearrangement of the symmetry of the system. In fact, he connected quantum mechanics with statistical, and his work received fundamental

mental meaning. They are applicable in combustion processes, and in electronics, and in the description of cosmic phenomena and nuclear interactions. Wilson investigated a wide class of critical phenomena and created a general theory of second-order phase transitions.

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Concepts of phase and phase transition. Phase transitions of the first and second kind

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