Topics Unified State Exam codifier : change in the aggregate states of matter, melting and crystallization, evaporation and condensation, boiling of liquid, change in energy in phase transitions.
Ice, water and water vapor - examples of three states of aggregation substances: solid, liquid and gaseous. What exact state of aggregation a given substance is in depends on its temperature and other external conditions, in which it is located.
When external conditions change (for example, if the internal energy of a body increases or decreases as a result of heating or cooling), phase transitions can occur - changes in the aggregate states of the body's substance. We will be interested in the following phase transitions.
Melting(solid-liquid) and crystallization(liquid-solid).
Vaporization(liquid vapor) and condensation(steam liquid).
Melting and crystallization
Most solids are crystalline, i.e. have crystal lattice- a strictly defined, periodically repeated arrangement of its particles in space.
Particles (atoms or molecules) of a crystalline solid undergo thermal vibrations near fixed equilibrium positions - nodes crystal lattice.
For example, crystal lattice nodes table salt- these are the vertices of cubic cells of the “three-dimensional checkered paper"(see Fig. 1, in which the balls larger size represent chlorine atoms (image from en.wikipedia.org.)); If you let the water from the salt solution evaporate, the remaining salt will be a pile of small cubes.
Rice. 1. Crystal lattice
Melting called the transformation of a crystalline solid into a liquid. Any body can be melted - to do this you need to heat it to melting point, which depends only on the substance of the body, but not on its shape or size. The melting point of a given substance can be determined from tables.
On the contrary, if you cool a liquid, sooner or later it will turn into a solid state. The transformation of a liquid into a crystalline solid is called crystallization or hardening. Thus, melting and crystallization are mutually inverse processes.
The temperature at which liquid crystallizes is called crystallization temperature. It turns out that the crystallization temperature is equal to the melting temperature: at a given temperature, both processes can occur. So, when ice melts, water crystallizes; What exactly occurs in each specific case - depends on external conditions (for example, whether heat is supplied to the substance or removed from it).
How do melting and crystallization occur? What is their mechanism? To understand the essence of these processes, let us consider graphs of the dependence of body temperature on time during its heating and cooling - the so-called melting and crystallization graphs.
Melting graph
Let's start with the melting graph (Fig. 2). Let in starting moment time (point on the graph), the body is crystalline and has a certain temperature.
Rice. 2. Melting graph
Then heat begins to be supplied to the body (say, the body is placed in a melting furnace), and the body temperature rises to a value - the melting temperature of the given substance. This is a section of the graph.
At the site the body receives the amount of heat
where is the specific heat capacity of the solid substance, and is the mass of the body.
When the melting temperature is reached (at point ) the situation changes qualitatively. Despite the fact that heat continues to be supplied, body temperature remains unchanged. Happening at the site melting body - its gradual transition from solid to liquid. Inside the plot we have a mixture solid and liquid, and the closer to the point, the less solid remains and the more liquid appears. Finally, at a point there was nothing left of the original solid body: it completely turned into a liquid.
The area corresponds to further heating of the liquid (or, as they say, melt). In this area, the liquid absorbs an amount of heat
where is the specific heat capacity of the liquid.
But what we are most interested in now is the phase transition area. Why doesn't the temperature of the mixture change in this area? The heat is coming!
Let's go back to the beginning of the heating process. An increase in the temperature of a solid body in an area is the result of an increase in the intensity of vibrations of its particles at the nodes of the crystal lattice: the supplied heat goes to increase kinetic energy of the particles of the body (in fact, some part of the supplied heat is spent on doing work to increase the average distances between particles - as we know, bodies expand when heated. However, this part is so small that it can be ignored.).
The crystal lattice becomes looser more and more, and at the melting temperature the range of vibrations reaches the limiting value at which the attractive forces between the particles are still able to ensure their ordered arrangement relative to each other. The solid body begins to “crack at the seams”, and further heating destroys the crystal lattice - this is how melting begins in the area.
From this moment, all the heat supplied is used to perform work on breaking the bonds that hold the particles in the nodes of the crystal lattice, i.e. to increase potential particle energy. The kinetic energy of the particles remains the same, so the body temperature does not change. At the point crystal structure disappears completely, there is nothing left to destroy, and the supplied heat again goes to increase the kinetic energy of the particles - to heat the melt.
Specific heat of fusion
So, to transform a solid into a liquid, it is not enough to bring it to the melting point. It is necessary to additionally (already at the melting temperature) provide the body with a certain amount of heat for the complete destruction of the crystal lattice (i.e. to pass through the section).
This amount of heat goes to increase the potential energy of particle interaction. Consequently, the internal energy of the melt at a point is greater than the internal energy of a solid body at a point by an amount.
Experience shows that the value is directly proportional to body weight:
The proportionality coefficient does not depend on the shape and size of the body and is a characteristic of the substance. It's called specific heat of fusion of a substance. The specific heat of fusion of a given substance can be found in the tables.
The specific heat of fusion is numerically equal to the amount of heat required to transform one kilogram of a given crystalline substance brought to the melting point into liquid.
So, specific heat melting of ice is equal to kJ/kg, lead - kJ/kg. We see that it takes almost twice as much energy to destroy the ice crystal lattice! Ice is a substance with a high specific heat of fusion and therefore does not melt immediately in the spring (nature took its own measures: if ice had the same specific heat of fusion as lead, the entire mass of ice and snow would melt with the first thaw, flooding everything around).
Crystallization graph
Now let's move on to consider crystallization- a process reverse to melting. We start from the point of the previous drawing. Let us assume that at the point the heating of the melt has stopped (the stove has been turned off and the melt has been exposed to air). Further changes in the melt temperature are shown in Fig. (3) .
Rice. 3. Crystallization graph
The liquid cools (section) until its temperature reaches the crystallization temperature, which coincides with the melting point.
From this moment on, the temperature of the melt stops changing, although heat still escapes from it into the environment. Happening at the site crystallization melt - its gradual transition to a solid state. Inside the area we again have a mixture of solid and liquid phases, and the closer to the point, the more solid becomes and the less liquid becomes. Finally, at the point there is no liquid left at all - it has completely crystallized.
The next section corresponds to the further cooling of the solid body resulting from crystallization.
We are again interested in the phase transition area: why does the temperature remain unchanged despite the loss of heat?
Let's return to the point again. After the heat supply is stopped, the temperature of the melt decreases, as its particles gradually lose kinetic energy as a result of collisions with environmental molecules and the emission of electromagnetic waves.
When the temperature of the melt drops to the crystallization temperature (point), its particles will slow down so much that the forces of attraction will be able to “unfold” them properly and give them a strictly defined mutual orientation in space. This will create conditions for the emergence of a crystal lattice, and it will actually begin to form due to the further release of energy from the melt into the surrounding space.
At the same time, a counter process of energy release will begin: when the particles take their places at the nodes of the crystal lattice, they potential energy decreases sharply, due to which their kinetic energy increases - the crystallizing liquid is a source of heat (you can often see birds sitting near an ice hole. They warm themselves there!). The heat released during crystallization exactly compensates for the loss of heat to the environment, and therefore the temperature in the area does not change.
At the point, the melt disappears, and along with the completion of crystallization, this internal “generator” of heat also disappears. Due to the ongoing dissipation of energy in external environment the temperature decrease will resume, but the formed solid body (section ) will only cool down.
As experience shows, during crystallization in the area, exactly the same the amount of heat that was absorbed during melting in the area.
Vaporization and condensation
Vaporization is the transition of a liquid into a gaseous state (in steam). There are two ways of vaporization: evaporation and boiling.
Evaporation called vaporization, which occurs at any temperature with free surface liquids. As you remember from the sheet “Saturated Steam”, the cause of evaporation is the departure from the liquid of the fastest molecules that are able to overcome the forces of intermolecular attraction. These molecules form vapor above the surface of the liquid.
Various liquids evaporate from at different speeds: how more power attraction of molecules to each other - the smaller number molecules per unit time will be able to overcome them and fly out, and the lower the rate of evaporation. Ether, acetone, and alcohol evaporate quickly (they are sometimes called volatile liquids), water evaporates more slowly, and oil and mercury evaporate much more slowly than water.
The rate of evaporation increases with increasing temperature (in hot weather, laundry will dry faster), since the average kinetic energy of liquid molecules increases, and thus the number of fast molecules capable of leaving its limits increases.
The rate of evaporation depends on the surface area of the liquid: than larger area, the more molecules gain access to the surface, and evaporation occurs faster (which is why when hanging laundry, it is carefully straightened out).
Simultaneously with evaporation, the reverse process is also observed: the vapor molecules, making random movements above the surface of the liquid, partially return back to the liquid. The transformation of vapor into liquid is called condensation.
Condensation slows down the evaporation of a liquid. So, laundry will dry faster in dry air than in humid air. It will dry faster in the wind: the steam is carried away by the wind, and evaporation occurs more intensely
In some situations, the condensation rate may be equal speed evaporation. Then both processes compensate each other and dynamic equilibrium occurs: the liquid does not evaporate from a tightly sealed bottle for years, and in this case there is saturated steam.
We constantly observe the condensation of water vapor in the atmosphere in the form of clouds, rain and dew that falls in the morning; It is evaporation and condensation that ensure the water cycle in nature, supporting life on Earth.
Since evaporation is the departure of the fastest molecules from the liquid, during the evaporation process the average kinetic energy of liquid molecules decreases, i.e. the liquid cools down. You are well familiar with the feeling of coolness and sometimes even chilliness (especially in the wind) when you come out of the water: water, evaporating over the entire surface of the body, carries away heat, while the wind accelerates the evaporation process (it’s now clear why we blow on hot tea. By the way, It’s even better to draw air into yourself, since dry ambient air then comes to the surface of the tea, and not moist air from our lungs ;-)).
The same coolness can be felt if you run a piece of cotton wool soaked in a volatile solvent (say, acetone or nail polish remover) over your hand. In forty-degree heat, thanks to the increased evaporation of moisture through the pores of our body, we maintain our temperature at a normal level; Without this thermoregulatory mechanism, in such heat we would simply die.
On the contrary, during the process of condensation, the liquid heats up: when the vapor molecules return to the liquid, they are accelerated by attractive forces from nearby liquid molecules, as a result of which the average kinetic energy of the liquid molecules increases (compare this phenomenon with the release of energy during crystallization of a melt!).
Boiling
Boiling- this is the vaporization that occurs throughout the entire volume liquids.
Boiling is possible because a certain amount of air is always dissolved in a liquid, which gets there as a result of diffusion. When the liquid is heated, this air expands, the air bubbles gradually increase in size and become visible naked eye(in a pan of water they deposit on the bottom and walls). Inside the air bubbles there is saturated steam, the pressure of which, as you remember, increases rapidly with increasing temperature.
The larger the bubbles become, the greater the Archimedean force acts on them, and at a certain moment the bubbles begin to separate and float up. Rising upward, the bubbles enter less heated layers of the liquid; the vapor in them condenses, and the bubbles shrink again. The collapse of the bubbles causes the familiar noise that precedes the boiling of the kettle. Finally, over time, the entire liquid warms up evenly, the bubbles reach the surface and burst, throwing out air and steam - the noise is replaced by gurgling, the liquid boils.
The bubbles thus serve as “conductors” of vapor from inside the liquid to its surface. During boiling, along with normal evaporation, the liquid is converted into steam throughout the entire volume - evaporation into air bubbles, followed by the release of steam outside. This is why boiling liquid evaporates very quickly: a kettle, from which the water would evaporate for many days, will boil away in half an hour.
Unlike evaporation, which occurs at any temperature, a liquid begins to boil only when it reaches boiling point- exactly the temperature at which air bubbles are able to float and reach the surface. At boiling point pressure saturated steam becomes equal to the external pressure on the liquid(in particular, atmospheric pressure). Accordingly, the greater the external pressure, the higher the temperature at which boiling will begin.
Under normal conditions atmospheric pressure(atm or Pa) the boiling point of water is . That's why the pressure of saturated water vapor at temperature is Pa. This fact must be known to solve problems - it is often considered known by default.
At the top of Elbrus, the atmospheric pressure is atm, and water there will boil at a temperature of . And under pressure atm, water will begin to boil only at .
The boiling point (at normal atmospheric pressure) is a strictly defined value for a given liquid (boiling points given in the tables of textbooks and reference books are the boiling points of chemically pure liquids. The presence of impurities in a liquid can change the boiling point. For example, tap water contains dissolved chlorine and some salts, so its boiling point at normal atmospheric pressure may differ slightly from ). So, alcohol boils at , ether - at , mercury - at . Please note: the more volatile a liquid is, the lower its boiling point. In the table of boiling points we also see that oxygen boils at. This means that at normal temperatures oxygen is a gas!
We know that if the kettle is removed from the heat, the boiling will immediately stop - the boiling process requires a continuous supply of heat. At the same time, the temperature of the water in the kettle stops changing after boiling, remaining equal all the time. Where does the supplied heat go?
The situation is similar to the melting process: heat is used to increase the potential energy of the molecules. IN in this case- to perform work to remove molecules at such distances that the forces of attraction will be unable to keep the molecules close to each other, and the liquid will turn into a gaseous state.
Boiling graph
Let's consider a graphical representation of the process of heating a liquid - the so-called boiling chart(Fig. 4).
Rice. 4. Boiling graph
The region precedes the onset of boiling. In the area, the liquid boils, its mass decreases. At this point the liquid boils away completely.
To pass the section, i.e. In order for a liquid brought to the boiling point to completely turn into steam, a certain amount of heat must be supplied to it. Experience shows that this amount of heat is directly proportional to the mass of the liquid:
The proportionality factor is called specific heat of vaporization liquids (at boiling point). The specific heat of vaporization is numerically equal to the amount of heat that must be supplied to 1 kg of liquid taken at the boiling point in order to completely convert it into steam.
So, at the specific heat of vaporization of water is equal to kJ/kg. It is interesting to compare it with the specific heat of melting of ice (kJ/kg) - the specific heat of vaporization is almost seven times greater! This is not surprising: after all, to melt ice, you only need to destroy the ordered arrangement of water molecules at the nodes of the crystal lattice; at the same time, the distances between the molecules remain approximately the same. But to turn water into steam you need to do something great job by breaking all bonds between molecules and removing molecules to significant distances from each other.
Condensation graph
The process of steam condensation and subsequent cooling of the liquid looks on the graph symmetrically to the process of heating and boiling. Here's the relevant one condensation graph for the case of one hundred degree water vapor, which is most often encountered in problems (Fig. 5).
Rice. 5. Condensation graph
At the point we have water vapor at . There is condensation in the area; inside this area there is a mixture of steam and water at . At the point there is no more steam, there is only water at . The area is the cooling of this water.
Experience shows that during the condensation of a vapor of a mass (i.e., when passing through a section), exactly the same amount of heat is released that was spent on converting a liquid mass into vapor at a given temperature.
Let's compare the following amounts of heat for fun:
Which is released when water vapor condenses;
, which is released when the resulting 100-degree water cools to a temperature of, say, .
J;
J.
These numbers clearly show that a steam burn is much worse than a boiling water burn. When boiling water comes into contact with the skin, “only” is released (the boiling water cools down). But in case of a burn, steam will first be released by an order of magnitude more heat (steam condenses), one hundred degree water is formed, after which the same value will be added when this water cools.
Phase is a collection of parts of a system that are identical in all physical, chemical properties and structural composition. For example, there are solid, liquid and gaseous phases (called states of aggregation).
Phase transition (phase transformation), V in a broad sense– transition of a substance from one phase to another when external conditions change ( T, R, magnetic and electric fields, etc.); in the narrow sense – an abrupt change in physical properties with a continuous change in external parameters. We will further consider phase transitions in the narrow sense.
There are first-order and second-order phase transitions. First order phase transition is a widespread phenomenon in nature. These include: evaporation and condensation, melting and solidification, sublimation or sublimation (transition of a substance from crystalline state directly, without melting, into gaseous, for example, dry ice) and condensation into the solid phase, etc. Phase transitions Type I are accompanied by the release or absorption of heat (the heat of phase transition q), while the density, concentration of components, molar volume, etc. change abruptly.
A second-order phase transition is not accompanied by the release or absorption of heat, the density changes continuously, but, for example, the molar heat capacity, specific electrical conductivity, viscosity, etc. Examples of second-order phase transitions include the transition magnetic substance from the ferromagnetic state ( m>> 1) in paramagnetic ( m" 1) when heated to a certain temperature, called the Curie point; transition of some metals and alloys at low temperatures from normal condition into superconducting, etc.
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Heat capacity
Specific heat substance - a value equal to the amount of heat required to heat 1 kg of substance by 1 K:
Isochoric process
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Evaporation And condensation - frequently observed phase transitions of water in surrounding nature. When water transforms into steam, evaporation first occurs - the transition of the surface layer of 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. The reverse process is also observed in everyday life - 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 together by attractive forces that keep them inside the liquid. If molecules with speeds that exceed the average are near the surface, they can leave it. Then average speed the remaining molecules will decrease and the temperature of the liquid will decrease. To evaporate at a constant temperature, you need to impart a certain amount of heat 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, whereas average energy thermal movement is equal to 6.06 10 -21 J. This means that they turn into steam
molecules with an energy that is 10 times greater than the energy of thermal motion. When passing through the surface of a liquid, the potential energy of a fast molecule increases, and the kinetic energy decreases. Therefore, the average kinetic energies of vapor and liquid molecules at thermal equilibrium are equal.
Saturated steam - it is steam in dynamic equilibrium, corresponding to a given temperature, with its liquid. Experience shows that it does not obey the Boyle-Marriott 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 determine 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 from the surface of the World Ocean, which makes up 94% of the earth's hydrosphere, about 7,000 km 3 of water evaporates per day and approximately the same amount falls in the form of precipitation. Water vapor, carried away by the convection movement of air, rises and enters the cold layers of the troposphere. As the vapor rises, it becomes increasingly saturated, then condenses to form raindrops. During 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 humanity during the same time.
Boiling- the process of transition of liquid into vapor as a result of the floating of bubbles filled with vapor. Boiling occurs throughout the entire 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 pressure saturated vapors 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 boundary of the troposphere (17 km) - at approximately 65 °C. Therefore, the boiling point of a liquid corresponds to the temperature at which the pressure of its saturated vapor is equal to the external pressure. Weak gravitational field of the Moon (acceleration free fall at its surface is only 1.7 m/s 2) is not able to retain the atmosphere, and in the absence of atmospheric pressure the liquid instantly boils away, so the lunar “seas” are waterless and formed by solidified lava. For the same reason, the Martian “canals” are also waterless.
A substance can be in equilibrium and in different phases. Thus, when a gas is liquefied in a state of phase equilibrium, the volume can be anything, and the transition temperature is related to the saturated vapor pressure. The phase equilibrium curve can be obtained by projection onto a plane (p, T) areas of transition to the liquid state. Analytically, the equilibrium curve of the two phases is determined from the solution differential equation Clausius-Clapeyron. Similarly, one can obtain melting and sublimation curves that connect at one point in the plane (p, D), at the triple point (see Fig. 7.1), where at certain proportions are in equal
weight all three phases. Triple point 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 p, equal to 101.3 kPa, carbon dioxide can be in solid or gaseous state. At critical temperature physical properties liquids and vapor become identical. At temperatures higher critical substance can only be in a gaseous state. For water - T= 374.2 °C, 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 vaporization and sublimation temperatures are stronger. At normal and constant pressures, the transition occurs at a certain temperature, and here the melting, boiling and sublimation (or sublimation) points take place.
The transition of a substance from a solid state directly to a gaseous state can be observed, for example, in shells comet tails. When a comet is far from the Sun, almost all of its mass is concentrated in its nucleus, which measures 10-12 km. The nucleus is surrounded by a small shell of gas - this is the head of the comet. When approaching the Sun, the comet's core and shell begin to heat up, the probability of sublimation increases, and desublimation (the reverse process) decreases. Gases escaping from the comet's nucleus carry along solid particles, the comet's head increases in volume and becomes gas-dust in composition. The pressure around the cometary nucleus is very low, so the liquid phase does not appear. Together with the head, the comet's tail also grows, which extends 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 core, and gradually it disintegrates into meteor bodies that form meteor showers. Over 5 billion years of existence solar system This is how many comets ended their existence.
In the spring of 1986, automatic Soviet stations"Vega-1" and "Vega-2", which passed at a distance of 9000 and 8200 km from it, respectively, and NASA's Giotto station - at a distance of only 600 km from the comet's nucleus. The core had dimensions of 14 x 7.5 km, a dark color and a temperature of about 400 K. When space stations passed through the comet's head, sublimating about 40,000 kg of icy substance in 1 s.
Late autumn, when a sharp cold snap occurs after wet weather, you can see on the branches of trees and on wires
Frost is desublimated ice crystals. A similar phenomenon is used when storing ice cream, when carbon dioxide is cooled, since the molecules turning into steam carry away energy. On Mars, the phenomena of sublimation and desublimation of carbon dioxide in polar caps play the same role as evaporation - condensation in the atmosphere and hydrosphere of the Earth.
Heat capacity tends to zero at ultra-low temperatures, as Nernst established. From here Planck showed that near absolute zero all processes proceed without changing entropy. Einstein's theory of 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 - were explained in modern theory as macroscopic quantum effects.
Phase transitions come in several types. During a phase transition, the temperature does not change, but the volume of the system changes.
First-order phase transitions 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.
In fact, during the transition from a more condensed phase to a phase with a lower density, it is necessary to impart a certain amount of energy in the form of heat, which will go towards destruction crystal lattice(during melting) or the removal of liquid molecules from each other (during vaporization). During the transformation, latent heat is spent on overcoming adhesive forces, the intensity of thermal movement does not change, and as a result the temperature remains constant. With such a transition, the degree of disorder, and therefore entropy, increases. If the process goes in the opposite direction, then latent heat is released.
Phase transitions of the second order are associated with a change in the symmetry of the system: above the transition point, the system, as a rule, has 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 by the same angle does not change the properties of the system. Below the transition point, the backs have a certain preferential orientation, and their simultaneous rotation changes direction magnetic moment systems. Landau introduced the ordering coefficient and expanded the thermodynamic potential at the transition point into powers of this coefficient, on the basis of which he constructed a classification of all possible types transition
Dov, as well as the theory of the phenomena of superfluidity and superconductivity. On this basis, Landau and Lifshitz considered many important tasks- transition of ferroelectric to paraelectric, ferromagnetic to paramagnetic, absorption of sound at the transition point, transition of metals and alloys to the superconducting state, etc.
Calculation of the thermodynamic properties of a system based on statistical mechanics involves the choice of a specific model of the system, and how more complex 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 nearest neighbors for any fields and temperatures. At mathematical description For 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 could not always be 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 lattice nodes that can be oriented only in 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 allows one to obtain new results for phase transformations.
Phase transitions of the second, third, etc. kinds are associated with the order of those derivatives of the thermodynamic potential Ф that experience finite changes at the transition point. This 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
ent thermal expansion, whereas per-
the derivatives remain continuous. This means no release (absorption) of heat and no change in specific volume.
Quantum theory fields began to be used for calculations of particle systems only in the 70s. XX century The system was considered as a lattice with a varying pitch, which made it possible to change the accuracy of calculations and get closer to the description of the real system and use a computer. American theoretical physicist K. Wilson, using new technique calculations, received a qualitative leap in the understanding of second-order phase transitions associated with the restructuring of the symmetry of the system. In fact, he connected quantum mechanics with statistical mechanics, and his work received fundamental
mental meaning. They are applicable in combustion processes, and in electronics, and in the description cosmic phenomena And nuclear interactions. Wilson studied a wide class of critical phenomena and created general theory phase transitions of the second order.
Introduction.
Phases are called homogeneous different parts of physical and chemical systems. A substance is homogeneous when all parameters of the state of the substance are the same in all its volumes, the dimensions of which are large compared to interatomic states. Mixtures of different gases always form one phase if they are in equal concentrations throughout the entire 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 conditions of pressure and temperature under which a substance is in equilibrium in different phases. For example, when a gas is liquefied in a state of phase equilibrium, the volume can be anything, and the transition temperature is related to the saturated 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 the points of melting, boiling and sublimation (or sublimation) take place. Sublimation is the transition of a substance from a solid to a gaseous state and can be observed, for example, in the shells of comet 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 comet head. When approaching the Sun, the comet's core and shells begin to heat up, the probability of sublimation increases, and desublimation decreases. Gases escaping from the comet's nucleus carry along solid particles, the comet's head increases in volume and becomes gas-dust in composition.
Phase transitions of the first and second order.
Phase transitions come in several types. 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 changes.
3) 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. In fact, during the transition of the condensed phase into a phase with a lower density, it is necessary to impart a certain amount of energy in the form of heat, which will be used 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 transform the adhesive forces, the intensity of thermal movement will not change, and as a result the temperature will remain constant. With such a transition, the degree of disorder, and therefore entropy, increases. If the process goes in the opposite direction, then latent heat is released. Phase transitions of the first order include: the transformation of a solid into a liquid (melting) and the reverse process (crystallization), the liquid into vapor (evaporation, boiling). One crystal modification into 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 paramagnetic state. Metals such as iron, cobalt, nickel and gadolinium stand out for their ability to become highly magnetized and to remain magnetized 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 magnetic field- these are paramagnetic. Phase transitions of the second, third, and so on kinds are associated with the order of those derivatives of the thermodynamic potential? φ that experience finite measurements at the transition point. This classification of phase transformations is associated with the work of the theoretical physicist Paul Ernest (1880 -1933). Thus, 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 = -T(?ph 2 /?T 2), compressibility = -(1/V 0)(? 2 f/ ?p 2), coefficient of thermal expansion b=(1/V 0)(? 2 f/?Tp), while the first derivatives remain continuous. This means no release (absorption) of heat and no change in specific volume (φ - thermodynamic potential).
State phase equilibrium characterized by a certain relationship between the temperature of phase transformation and pressure. Numerically, this dependence for phase transitions is given by the Clapeyron-Clausius equation: p/T=q/TV. Research at low temperatures is a very important branch of physics. The fact is that in this way you can get rid of the interference associated with chaotic thermal motion and study phenomena in a “pure” form. This is especially important when studying quantum laws. Usually, due to chaotic thermal motion, averaging occurs physical quantity By a large number her different meanings and quantum leaps are “smeared”.
Low temperatures ( cryogenic temperatures), in physics and cryogenic technology, the temperature range is below 120°K (0°c=273°K); the work of Carnot (worked on a heat engine) and Clausius laid the foundation for research into the properties of gases and vapors, or technical thermodynamics. In 1850, Clausius noticed that saturated water vapor partially condenses when expanding, and when compressed it goes into a superheated state. A special contribution to the development of this scientific discipline contributed by Renu. 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.
Phase transitions, transitions of a substance from one phase to another when the state parameters that characterize thermodynamic equilibrium change. The temperature value, or any other physical quantity, at which phase transitions occur in a one-component system is called the transition point. During phase transitions of the first order, the properties expressed by the first derivatives of G with respect to pressure p, t-re T and other parameters change abruptly with continuous changes in these parameters. In this case, transition heat is released or absorbed. In a one-component system, the transition temperature T 1 related to blood pressure r 1 Clapeyron-Clausius 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 another phase and the occurrence of phase transitions with terminal speed. In the absence of stable nuclei, the overheated (supercooled) phase is in a state of metastable equilibrium. The same phase can exist (albeit metastable) on both sides of the transition point (however, crystalline phases cannot be overheated above the temperature or sublimation). At point F. p. Type I Gibbs energy G as a function is continuous, and both phases can coexist for as long as desired, that is, so-called phase separation occurs (for example, the coexistence of both it or and for a given total volume of the system).
First-order phase transitions are widespread phenomena in nature. These include gas and liquid phase, melting and solidification, and (desublimation) from the gas to solid phase, most polymorphic transformations, some structural transitions in solids, for example, the formation of martensite in - . In pure materials, a sufficiently strong magnetic field causes first-order phase transitions from the superconducting to the normal state.
During phase transitions of the second kind, the quantity itself G and first derivatives G By T, p and other parameters and states change continuously, and the second derivatives (respectively, the coefficient and thermal expansion) with a continuous change in the parameters change abruptly or are singular. Heat is not released or absorbed, hysteresis phenomena and metastable states are absent. Phase transitions of the second kind, 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 Neel point) with the appearance of spontaneous magnetization (respectively in the entire lattice or in each of magnetic sublattices); transition - with the appearance of spontaneous. the appearance of an ordered state in solids (in ordering alloys); smectic transition 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 a superconducting state in the absence of a magnetic field.
Phase transitions can be associated with changes in pressure. Many substances at low pressures crystallize into loosely packed structures. For example, the structure is a series of layers widely spaced from each other. At sufficiently high pressures, such loose structures correspond to large values Gibbs energy, and lower values correspond to equilibrium close-packed phases. Therefore, at high pressures, graphite transforms into diamond. Quantum 4 He and 3 He remain liquid at normal pressure down to the lowest of reached temperatures near absolute zero. The reason for this is weak interaction and the large amplitude of their “zero oscillations” (high probability quantum tunneling from one fixed position to another). However, the increase 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 higher symmetry than below the transition point, therefore, second-order phase transitions are interpreted as a point of change in symmetry. For example, in a ferromagnet, above the Curie point, the directions of the spin magnetic moments of the particles are distributed chaotically, therefore the simultaneous rotation of all spins around the same axis by the same angle does not change the physical state. properties of the system. Below the transition point, the spins have a preferential orientation, and their joint rotation in the above sense changes the direction of the magnetic moment of the system. In a two-component alloy, the atoms of which 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 arranged in an orderly manner: ...ABAB... Shifting such a lattice by a period leads to the replacement of all A's by B's 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. a quantity that changes continuously during phase transitions of the second kind and is called. order parameter. For pure liquids this parameter is density, for solutions - composition, for ferro- and ferrimagnets - spontaneous magnetization, for ferroelectrics - spontaneous electrical polarization, for alloys - the fraction of ordered ones 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 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, characteristic of second-order phase transitions, is also observed at the critical point on the curves of first-order phase transitions. The similarity turns out to be 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 density of the substance from critical value: when moving along a critical isochore from the side high temperatures the gas is homogeneous and the deviation of the density from the critical value is zero, and below the critical temperature the substance stratifies into two phases, in each of which the deviation of the density from the critical value is not 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 like near the critical point. This is associated with critical phenomena at points of second-order phase transitions: an anomalous increase in the magnetic susceptibility of ferromagnets and the dielectric susceptibility of ferroelectrics (an analogue is the increase near the critical point of the liquid-vapor transition); 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. Dynamic processes also change significantly, which is associated with the very slow resorption of the resulting fluctuations. For example, near the liquid-vapor critical point the line of Rayleigh light scattering narrows; near the Curie and Néel points in ferromagnets and antiferromagnets, respectively, spin diffusion slows down (the spread of excess magnetization occurring according to the laws of diffusion). The average size of fluctuations (correlation radius) increases as the phase transitions of the second order are approached 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 the remaining parts. On the contrary, far from the transition point of the second kind, fluctuations are statistically independent and random changes in state in a given part of the system do not affect the properties of its other parts.
