Diagram of the transition of water to steam. Phase states and transformations of water. Ice Melting Curve VI

The state diagram (or phase diagram) is a graphic representation of the relationship between the quantities characterizing the state of the system and phase transformations in the system (transition from solid to liquid, from liquid to gaseous, etc.).

For one-component systems, state diagrams are usually used, showing the dependence of phase transformations on temperature and pressure; they are called state diagrams in P-t coordinates.

On fig. 10.1 shows in schematic form (without strict adherence to scale) a diagram of the state of water. Any point on the diagram corresponds to certain values ​​​​of temperature and pressure.

Rice. 10.1. Diagram of the state of water in the area of ​​low pressures

The diagram shows those states of water that are thermodynamically stable at certain temperatures and pressures. It consists of three curves that delimit all possible temperatures and pressures into three regions corresponding to ice, liquid and vapor.

Curve OA represents the dependence of the pressure of saturated water vapor on temperature: the points of the curve show those pairs of temperature and pressure values ​​at which liquid water and water vapor are in equilibrium with each other. The OA curve is called the liquid-vapor equilibrium curve or boiling curve.

OS curve - solid state - liquid equilibrium curve, or melting curve, - shows those pairs of temperature and pressure values ​​at which ice and liquid water are in equilibrium.

RH curve - equilibrium curve solid state - steam, or sublimation curve. It corresponds to those pairs of temperature and pressure values ​​at which ice and water vapor are in equilibrium.

All three curves intersect at point O. The coordinates of this point are the only pair of temperature and pressure values ​​at which all three phases can be in equilibrium: ice, liquid water and steam. She bears the name triple point.

The triple point corresponds to a water vapor pressure of 0.610 kPa (4.58 mm Hg) and a temperature of 0.0 GS.

The water state diagram is important in the development of technological regimes for obtaining food products. For example, as follows from the diagram, if ice is heated at a pressure of less than 0.610 kPa (4.58 mm Hg), then it directly goes into steam. This is the basis for the development of methods for obtaining food products by freeze-drying.

One of the features of water that distinguishes it from other substances is the decrease in the melting point of ice with increasing pressure. This circumstance is reflected in the diagram. The OC melting curve on the state diagram of water goes up to the left, while for almost all other substances it goes up to the right.

The transformations that occur with water at atmospheric pressure are reflected in the diagram by points or segments located on the horizontal corresponding to 101.3 kPa (760 mm Hg). So, the melting of ice or the crystallization of water corresponds to point D, the boiling of water corresponds to point E, the heating or cooling of water corresponds to segment DE, etc.

The state of water has been studied in a wide range of temperatures and pressures. At high pressures, the existence of at least ten crystalline modifications of ice has been established. The most studied is ice I - the only modification of ice found in nature.

The presence of various modifications of the substance - polymorphism leads to the complication of state diagrams.

Phase diagram of water in coordinates R - T shown in Fig.15. It consists of 3 phase fields- areas of various R, T- values ​​at which water exists in the form of a certain phase - ice, liquid water or steam (indicated in the figure by the letters L, W and P, respectively). These phase fields are separated by 3 boundary curves.

Curve AB - evaporation curve, expresses the dependence vapor pressure of liquid water on temperature(or, conversely, represents the dependence of the boiling point of water on external pressure). In other words, this line corresponds to a two-phase balance.

Liquid water ↔ steam, and the number of degrees of freedom calculated from the phase rule is WITH= 3 – 2 = 1. Such an equilibrium is called monovariant. This means that for a complete description of the system, it is sufficient to define only one variable- either temperature or pressure, since for a given temperature there is only one equilibrium pressure and for a given pressure - only one equilibrium temperature.

At pressures and temperatures corresponding to points below the line AB, the liquid will evaporate completely, and this region is the vapor region. To describe a system in a given single-phase region, two independent variables are needed: temperature and pressure ( WITH = 3 – 1 = 2).

At pressures and temperatures corresponding to points above line AB, the vapor is completely condensed into a liquid ( WITH= 2). The upper limit of the AB evaporation curve is at point B, which is called the critical point (for water 374.2ºС and 218.5 atm.). Above this temperature, the liquid and vapor phases become indistinguishable (the liquid/vapor interface disappears), so F = 1.

AC line - this ice sublimation curve (sometimes called the sublimation line), reflecting the dependence water vapor pressure above ice on temperature. This line corresponds to the monovariant equilibrium ice ↔ vapor ( WITH= 1). Above the AC line lies the region of ice, below the region of steam.

Line AD - melting curve, expresses the dependence melting temperature of ice on pressure and corresponds to the monovariant equilibrium ice ↔ liquid water. For most substances, the line AD deviates from the vertical to the right, but the behavior of water is anomalous: liquid water occupies a smaller volume than ice. An increase in pressure will cause a shift in equilibrium towards the formation of liquid, i.e., the freezing point will decrease.

Studies pioneered by Bridgman to determine the course of the ice melting curve at high pressures showed that all existing crystalline modifications of ice, with the exception of the first, are denser than water. Thus, the upper limit of the AD line is point D, where ice I (ordinary ice), ice III, and liquid water coexist in equilibrium. This point is at -22ºС and 2450 atm.

Rice. 15. Phase diagram of water

The example of water shows that the phase diagram does not always have such a simple character, as shown in Fig.15. Water can exist in the form of several solid phases, which differ in their crystal structure (see Fig. 16).

Rice. 16. Expanded phase diagram of water in a wide range of pressure values.

The triple point of water (a point reflecting the balance of three phases - liquid, ice and steam) in the absence of air is at 0.01ºС ( T = 273,16K) and 4.58 mmHg. Number of degrees of freedom WITH= 3-3 = 0 and such an equilibrium is called invariant.

In the presence of air, the three phases are in equilibrium at 1 atm. and 0ºС ( T = 273,15K). The decrease in the triple point in air is caused by the following reasons:

1. The solubility of air in liquid water at 1 atm, which leads to a decrease in the triple point by 0.0024ºС;

2. Increasing pressure from 4.58 mmHg. up to 1 atm, which reduces the triple point by another 0.0075ºС.

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C \u003d 3 - F,

If there is 1 phase in equilibrium, then C = 2, say that the system bivariant;

2 phase C \u003d 1, system monovariant;

3 phase C \u003d 0, system invariant.

A diagram expressing the dependence of the state of a system on external conditions or on the composition of the system is called phase diagram. The relationship between pressure ( R), temperature ( T) and volume ( V) phases can be represented by a three-dimensional phase diagram. Each point (called figurative point) on such a diagram depicts some equilibrium state. It is usually more convenient to work with sections of this diagram by a plane r - T(at V = const) or plane p-v(at T = const). Let us analyze in more detail the case of a section by a plane r - T(at V=const).

Consider, as an example, the phase diagram of a one-component system - water (Fig. 8).

Phase diagram of water

Phase diagram of water in coordinates r - T presented in Fig.8. It is made up of 3 phase fields- areas of different ( p, T)-values ​​at which water exists in the form of a certain phase - ice, liquid water or steam (indicated in Fig. 8 by the letters L, W and P, respectively). For these single-phase regions, the number of degrees of freedom is two, the equilibrium is bivariant ( C \u003d 3 - 1 \u003d 2). This means that in order to describe the system, two independent variables - temperature and pressure. These variables can be changed in these areas independently, without changing the type and number of phases.

The phase fields are separated by 3 boundary curves.

Curve AB - evaporation curve, expresses dependence vapor pressure of liquid water on temperature(or, conversely, represents the dependence of the boiling point of water on pressure). In other words, this line corresponds two-phase liquid water-steam equilibrium, and the number of degrees of freedom calculated by the phase rule is C \u003d 3 - 2 \u003d 1. Such a balance monovariant. This means that for a complete description of the system, it is sufficient to define only one variable either temperature or pressure. The second variable is dependent, it is given by the shape of the curve AB . Thus, for a given temperature, there is only one equilibrium pressure, or for a given vapor pressure, only one equilibrium temperature.

At pressures and temperatures corresponding to points below the line AB, the liquid will evaporate completely, and this region is the vapor region.

At pressures and temperatures corresponding to points above line AB, the vapor is completely condensed into a liquid ( C = 2). The upper limit of the AB evaporation curve is at point B, which is called critical point(for water 374 o C and 218 atm). Above this temperature, the liquid and vapor phases become indistinguishable (a clear liquid/vapor interface disappears), so Ф=1.

AC line- thisice sublimation curve(sometimes called the sublimation line), reflecting the dependence water vapor pressure above ice on temperature. This line corresponds monovariant ice-vapor equilibrium ( C=1). Above the AC line lies the region of ice, below the region of steam.

Line AD - melting curve, expresses dependence melting temperature of ice on pressure and corresponds monovariant ice-liquid water equilibrium. For most substances, the AD line deviates from the vertical to the right, but the behavior of water is anomalous: liquid water occupies a smaller volume than ice. Based on the Le Chatelier principle, it can be predicted that an increase in pressure will cause a shift in the equilibrium towards the formation of a liquid, i.e. the freezing point will drop.

Fig.8. Phase diagram of water

Studies carried out by Bridgman to determine the course of the ice melting curve at high pressures showed that there is seven different crystalline modifications of ice, each of which, with the exception of the first, denser than water. Thus, the upper limit of the line AD is point D, where ice I (ordinary ice), ice III and liquid water are in equilibrium. This point is at -22 0 C and 2450 atm.

Triple point of water(a point reflecting the balance of three phases - liquid, ice and steam) in the absence of air is at 0.0100 o C and 4.58 mm Hg. Number of degrees of freedom WITH=3-3=0 and such an equilibrium is called invariant. When any parameter is changed, the system ceases to be three-phase.

In the presence of air, the three phases are in equilibrium at 760 mm Hg. and at 0 o C. The decrease in the temperature of the triple point in air is caused by the following reasons:

1. the solubility of the gaseous components of air in liquid water at 1 atm, which leads to a decrease in the triple point by 0.0024 o C;

2. increase in pressure from 4.58 mm Hg. up to 1 atm, which reduces the triple point by another 0.0075 o C.

First, let's agree that the term "water" will mean H 2 O in any of its possible phase states.

In nature, water can be in three states: solid phase (ice, snow), liquid phase (water), gaseous phase (steam).

Consider water without energy interaction with the environment, i.e. in an equilibrium state.

Steam is always present at the surface of ice or liquid. The contacting phases are in thermodynamic equilibrium: fast molecules fly out of the liquid phase, overcoming surface forces, and slow molecules pass from the vapor phase into the liquid phase.

In a state of equilibrium, each temperature corresponds to a certain vapor pressure - total (if only vapor is present above the liquid) or partial (if there is a mixture of vapor with air or other gases). A vapor that is in equilibrium with the liquid phase from which it was formed is called saturated vapor, and the temperature corresponding to it is called the saturation temperature, and the pressure–saturation pressure.

Now consider the nonequilibrium states of water:

a) Let the vapor pressure over the liquid decrease below the saturation pressure. In this case, the equilibrium is disturbed, an uncompensated transition of the substance from the liquid phase to the gaseous phase occurs through the interface due to the fastest molecules.

The process of uncompensated transition of a substance from a liquid phase to a gaseous one is called evaporation.

The process of uncompensated transition of a substance from the solid phase to the gas phase is called sublimation or sublimation.

The intensity of evaporation or sublimation increases with the intensive removal of the resulting vapor. In this case, the temperature of the liquid phase decreases due to the escape of molecules with the highest energy from it. This can be achieved without lowering the pressure, simply by blowing the air flow.

b) Let there be a supply of heat to a liquid in an open vessel. In this case, the temperature, and, accordingly, the pressure of saturated vapor above the liquid increases and can reach the total external pressure (Р=Р n). those. conditions are created for the formation of steam in the thickness of the liquid.

The process of transition of a substance from the liquid phase to the vapor phase directly inside the liquid is called boiling.

The process of nucleation of vapor bubbles in the bulk of a liquid is complex. For water to boil, it is necessary to have centers of vaporization on the surface of heat supply - depressions, protrusions, irregularities, etc. At the heating surface, during boiling, the temperature difference between water and saturated steam at the pressure prevailing here depends on the intensity of heat supply and can reach tens of degrees.

The action of the forces of surface tension of the liquid causes overheating of the liquid at the interface when it boils by 0.3-1.5 ° C in relation to the temperature of the saturated vapor above it.

Any process of transition of a substance from a liquid phase to a vapor phase is called vaporization.

The process opposite to vaporization, i.e. the uncompensated transition of a substance from a vapor phase to a liquid phase is called condensation.

At constant vapor pressure, condensation occurs (like boiling) at a constant temperature and is the result of heat removal from the system.

The process opposite to sublimation, i.e. the transition of a substance from the vapor phase directly to the solid phase is called desublimation.

Recall that the previously introduced concepts of saturated vapor and saturation temperature, transferred to the boiling process, explain the equality of vapor and liquid temperatures during boiling. In this case, both the pressure and the temperature of the liquid and vapor phases are the same.

The liquid phase of water at its boiling point is called a saturated liquid..

Steam at the boiling point (saturation) is called dry saturated steam..

A two-phase mixture of "liquid + steam" in a state of saturation is called wet saturated steam.

In thermodynamics, this term extends to two-phase systems in which saturated vapor can be above the liquid level or represent a mixture of vapor with liquid droplets suspended in it. To characterize wet saturated steam, the concept of the degree of drynessX, which is the ratio of the mass of dry saturated steam, m s.n.p., to the total weight of the mixture, m cm \u003d m s.n.p + m zh.s.n, it with the liquid in a state of saturation:

The ratio of the mass of the liquid phase of water in a state of saturation to the mass of the mixture is called the degree of humidity(1-x):

The supply of heat to wet saturated steam at constant pressure leads to the transition of the liquid phase of the mixture into steam. In this case, the temperature of the mixture (saturation) cannot be increased until all the liquid has been converted to vapor. Further heat supply only to the vapor phase in the saturation state leads to an increase in the vapor temperature.

Steam above saturation temperature at a given pressure is called superheated steam. Superheated steam temperature difference t and saturated steam of the same pressure t n is called the degree of superheating of the steam Dt p \u003d t -t n.

With an increase in the degree of superheating of steam, its volume increases, the concentration of molecules decreases, in terms of its properties it approaches gases.

6.2. Phase diagrams P, t-, P, v- and T, s for H 2 O

To analyze various thermodynamic processes of changing the state of H 2 O, phase diagrams are widely used.

To get acquainted with the phase diagrams P, t- and P, v, imagine that in a cylinder under a piston that creates a constant pressure (Fig. 6.1), there is ice at an initial temperature t 1. Heat Q is supplied through the walls of the cylinder, the process of heating and phase transitions of H 2 O is shown in the t, Q-diagram. The ice is heated to the melting temperature t pl (process 1a), after which the ice melts at a constant temperature and turns into water (aa "), then the water is heated to the boiling (saturation) temperature t n (a" c), then the evaporation process takes place and the transformation of water into dry saturated steam (vv "), then the process of superheating the steam (v" 2) to a temperature t 2 takes place.

The same process (12) of obtaining superheated steam from ice at constant pressure is shown in Fig. 6.2 in the P,t coordinate system. Since the processes of melting (aa") and vaporization (vv") proceed at a constant temperature, in Fig. 6.2 they concentrate at points a and c. In the P,t-diagram, these points characterize the thermodynamic equilibrium of two-phase mixtures. Geometrically, the location of these points at different pressures and their corresponding temperatures is the line of phase transitions.

Line AB is the line of phase transition of the solid and liquid phases. This is an anomalous line, because For most substances, with increasing pressure, the melting point also increases, for water, on the contrary.

The AK line is the line of the phase transition of the liquid and vapor phases; with increasing pressure, the boiling (saturation) temperature of water and steam also increases.

With decreasing pressure, the difference between the melting and saturation temperatures decreases, and at point A the indicated curves converge. This point A is called the triple point of water; its coordinates determine the physical conditions(P o u t o) , at which all three phases of the substance are in thermodynamic equilibrium and can exist simultaneously. Parameters of the triple point of water: t about = 0.01 o C or 273.16 K And R o \u003d 611.2 Pa .

The AC curve located below the triple point is the line of phase transition and equilibrium of the solid and vapor phases, i.e. sublimation and desublimation line. So, at a pressure corresponding to the process de, when the solid phase is heated (de), at point c, the solid phase passes into vapor - sublimation, while cooling (process ed) at point c, the vapor passes into the solid phase - desublimation. In both cases, the transition bypasses the liquid phase.

The phase transition curves divide the entire field of the P,t-diagram into three zones: to the left of the BAC lines, the solid state zone (ice), between the VA and KA curves, the liquid zone, and to the right of the CAS, the superheated vapor zone. In this case, the line AK ends at the top with the point K, determined by the critical parameters. At pressures above the critical, there is no visible phase transition of liquid to vapor.

Water refers to substances that have several modifications of crystalline phases. Currently, six modifications of water ice are known. At pressures achieved in conventional technical devices, only one modification of ice is obtained. All other modifications can be obtained at high pressures. For such substances, the P,t-diagram has not one, but several triple points, since the equilibrium state of more than three phases of a pure substance is impossible. The main triple point in such a diagram is the one in which the equilibrium of the liquid, gaseous and one of the solid phases takes place (point A, Fig. 6.2).

For substances with a normal pattern of volume change(these include most of the substances found in nature, but water is not one of them.) at constant pressure, as the temperature increases, the volume continuously increases. For such substances, at P=const, the volume of the solid phase is less than the volume of liquid, and the volume of liquid is less than the volume of vapor. In this case, the volume change during the phase transition can be represented in Fig. 6.3.

At point 1 - a solid phase with a volume v 1, at point a - a solid phase at a melting temperature with a volume v t p, at point a "- a liquid phase at a melting temperature with a volume v l p, at point c - a liquid phase at a temperature saturation (boiling) with volume v", at point c" - steam with saturation temperature with volume v", at point 2 - superheated steam with volume v 2. The ratio of volumes v 2 >v">v">v f p >v t p >v 1, i.e. a normal regular decrease in volume is observed from v 2 - steam to v 1 - solid phase.

In accordance with this regularity, it is possible to construct a phase diagram Р,v for normal matter(fig.6.4). This is carried out by conducting experiments similar to process 12 (Fig. 6.3) at various constant pressures, as a result of which phase transition lines are obtained for a normal substance in the P, v-diagram (Fig. 6.4): DC - solid phase at the melting temperature; AE - liquid at the melting point; AK - liquid at saturation temperature (boiling point, x=0); КL – dry saturated steam (x=1), ВС – solid phase at sublimation temperature.

To the left of the line SVD is the region of the solid state; between the lines VD and AE - solid phase + liquid; between the lines AE and AK - the liquid area; between lines AK and KN - liquid + steam; between lines CB, BN and NL - solid + steam; to the right of the KL line is the vapor phase region. The BAN horizontal corresponds to the triple point of normal matter in the P,t-diagram.

The phase diagram T,s looks similar to the diagram P,v for normal matter(fig.6.5). Here, to the left of the line DBC is the solid phase, between the lines BD and AE is the two-phase state, solid + liquid, between AE and AK - liquid phase, between BC and NL - two-phase state, solid + steam; to the right of the line KL - superheated steam; between AK and KN - two-phase state liquid + steam in a state of saturation (wet saturated steam).

These phase diagrams cannot be extended entirely to water. Water– anomalous substance during its isobaric transition from a liquid to a solid state, the specific volume of water increases (ice floats on the surface of water). Therefore, in the P, v-diagram, the area of ​​the two-phase state ice+liquid partially superimposed on the zone of wet vapor and liquid.

On fig. 6.6 shows on an enlarged scale a part of the region of the phase diagram P,v for water in the zone of transition of the solid phase to the liquid phase at low temperatures. Here the horizontal line ABN is the isotherm corresponding to the triple point of water in the P,t-diagram. The AE vertical is the isotherm corresponding to the triple point temperature for liquid, and the BD vertical is the same ice isotherm. Between them is a zone of two-phase state liquid+ice.

The AMNL curve represents the liquid line at saturation temperature (x=0). With an increase in pressure and temperature, starting from the values ​​of the triple point of water A, the specific volume of boiling water first decreases, reaching a minimum at point M (about 4 ° C and 800 Pa), and with a further increase in pressure and temperature, the specific volume of boiling water continuously increases. At a temperature of about 8 ° C (point N), it reaches a specific volume at point A, and two isotherms of the liquid (0 and 8 ° C) coincide on the vertical NE. Similarly, above the MN line, the verticals will correspond to two isotherms of the liquid phase of water. As mentioned earlier, the liquid is a poorly compressible phase, therefore, in the water region, the isotherms are almost vertical straight lines.

The solid phase of water is also poorly compressible; isotherms for ice in the P,v-diagram are practically straight vertical lines. In addition, the volume of the solid phase at 0 ° C is close to the volume of ice in the melting state at temperatures below 0 ° C, and the volume of the liquid phase at 0 ° C is close to the volume of the liquid in the saturation state at negative temperatures. The dependence of the change in the melting point of ice on pressure is weakly expressed compared to the change in saturation temperature on pressure, so at -20 ° C ice melts at a pressure of 187.3 MPa, and at +20 ° C water boils at a pressure of 2.33 kPa. All of the above allows us to accept isotherms 0 ° C for liquid - line AE - and ice in the state of melting - BD in the P, v-diagram - as boundary curves between the liquid phase, the two-phase state ice+liquid and solid phase for all pressures above the triple point pressure of water. In this case, in the temperature range less than 0 ° C, the solid phase will be to the left of the BD line, and the liquid phase will be to the left of the AE line, because as the temperature decreases, the volume of both the liquid and solid phases decreases, and the melting pressure of ice is greater than the pressure of the triple point of water. However, these deviations within the pressures used in practice are very small.

The line of phase transition of ice directly into vapor (the sublimation line) is located at pressures below the triple point pressure - line BC. On this line, as the pressure decreases, the temperature of the ice and its volume decrease. To the left of the BC line is only the solid phase, to the right - solid + steam.

As a result, the phase diagram P,v for water has the form shown in Fig. 6.7, a. Here, to the left of the CBD line is the solid phase of water, to the left of the AK line is the liquid phase of water, and between the EABD lines is the two-phase state liquid+ice, between CBNL lines - two-phase state ice+steam, above the KL line - superheated steam. Due to the anomalous properties of water, there is an overlap of areas of different phase states of water in the P, v-diagram: the area of ​​the two-phase state ice+liquid EABD is superimposed on the EAMD liquid region and on the two-phase state region liquid + steam AMBA, in addition, there is an overlay on the area of ​​the solid phase to the left of the line BD. It should be noted that the image of these regions in Fig. 6.7, but for greater clarity, enlarged, not to scale. In reality, the volumes of liquid and ice are much smaller than at points A and B; at the same time, with a decrease in temperature and an increase in pressure, the volumes of these phase states decrease, i.e. To the left of the AE line, the liquid region increases with increasing pressure, and the solid phase, being to the left of the AE line, cannot be located to the left of the liquid phase of water at negative temperatures.

To illustrate the superposition of different phases of water in the P, v-diagram in fig. 6.7, a, b shows two isotherms (dashed lines) having a temperature greater than (t> t o) and less (t

Isotherm 1234 has a temperature less than 0 ° C and passes in the P, v-diagram on line 12 in the liquid region, on line 22 "- in the region of a two-phase state liquid+ice, on line 2"3 - in the area of ​​ice, on line 33" - in the area of ​​a two-phase state ice+steam, on line 3 "4 - in the area of ​​superheated steam.

Isotherm 567 has a temperature greater than 0 ° C and passes in the P, v-diagram on line 56 in the liquid region, on line 66 "in the region of a two-phase state liquid + steam, on line 6 "7 - in the area of ​​superheated steam.

The intersection points of these isotherms in the P,v-diagram indicate the superposition of different phase states of water on top of each other. At these points, these phase states have the same specific volumes at the same pressures and different temperatures. So the liquid on the isotherm 56 has the same specific volume with liquid+ice with one of the points on the 22" isotherm, and the ice on the 2"3 isotherm has the same volume with liquid + steam from one of the points on the 66" isotherm.

When constructing a phase T,s-diagram of water, the entropy reference point is chosen at the parameters of the triple point of water (t o =0.01 o C and P o =611.2 Pa) for a liquid in a state of saturation (x=0).

In the future, due to the small difference in the temperature of the triple point of water from 0 ° C, the value of zero degrees Celsius will be used mainly (it means the temperature of the triple point of water).

The entropies of the liquid phase of water at a temperature of 0 ° C for various pressures (from the pressure of the triple point of water and more) will have almost the same numerical values ​​close to zero. The equality of the entropies of the liquid phase of water at 0 ° C and different pressures is explained by the poor compressibility of the liquid phase of water. Since entropy, like any state parameter, is determined by two independent state parameters, then the equality of temperatures and specific volumes of liquid on the 0 ° C isotherm will correspond to the equality of enropies at these points. The deviations of the numerical entropy values ​​at these points from zero are thousandths of 1 kJ/(kg·K). Based on the foregoing, the isotherm of the liquid phase of water 0 o C in the T, s-diagram will represent point A (Fig. 6.8, a).

The specific heat of melting of ice is a positive value, so at 0 ° C it is 335 kJ / kg, therefore point B, corresponding to the solid phase at the temperature and pressure of the triple point of water, will be to the left of point A, i.e. with a negative value of entropy.

The anomalous properties of water will change the nature of its phase diagram T,s compared to the T,s diagram for a normal substance in the areas of liquid, solid and equilibrium two-phase solid + liquid And solid + steam states. First, these areas will be below the triple point isotherm of water, as ice can exist only at temperatures less than (or equal to) 0 o C. Secondly, they will be superimposed on the sublimation region, where the solid and vapor phases are located simultaneously. The liquid phase of water can also be at temperatures below 0 ° C, i.e. at these temperatures, there will again be an overlay in the T, s-diagram of the region of the liquid phase on the region of two-phase states liquid+ice And steam+ice.

The positive specific heat of ice melting and negative (in degrees Celsius) temperatures during the phase transition from ice to liquid explain the location of the boundary lines of phase transitions: BC is the sublimation line, AE is the liquid line at the melting temperature, BD is the ice line at the melting temperature (Fig. .6.8, a). The nature of the phase transition lines in this region is explained by the dependence of the isobaric heat capacity of liquid and ice on pressure (lines with lower heat capacity in the T, s diagram are steeper than lines with higher heat capacity). The BC sublimation line is flatter than the HP line, since the isobaric heat capacity of ice increases with decreasing pressure, and at the same temperatures, the pressure on the BC line is less than the pressure on the HP line. In turn, the VD line is steeper than the AE line, since at the same temperatures the isobaric heat capacity of ice is less than the heat capacity of the liquid.

The phase T,s-diagram for water will be presented in fig. 6.8, a. To the left of the line KAE there will be an area of ​​the liquid phase of water, between the lines DBAE - the area of ​​a two-phase state liquid+ice, between the lines T about BD - the area of ​​the solid phase, between the lines CBNL - the area solid phase+steam, above the KL line is the area of ​​superheated steam. Two-phase state area liquid+ice DBAE is superimposed on the area of ​​the two-phase state ice+steam CBNL.

In turn, on the region of the two-phase state steam+ice CBNL overlays the ice region CBD. In addition, on the region of ice and two-phase states ice+steam And liquid+ice superimposed area of ​​the liquid to the left of the line AE. On line BD there is an area of ​​ice in a state of melting, on line AE - liquids at a melting temperature, on line BC - an area of ​​sublimation, the boundary between ice and ferry+ice, on the line AK - the area of ​​liquid in a state of saturation, on the line KL - dry saturated steam. To visualize the phase transformations of water in the T, s-diagram in fig. 2.8, and the dotted line shows isobars with pressure greater than (P> P o) and less (P<Р o), чем давление в тройной точке воды. Те же изобары показаны на рис. 6.8, б в Р,t- диаграмме.

In the future, the main attention will be paid to the properties of the liquid and vapor phases of water at temperatures greater than or equal to 0 ° C. Therefore, in the phase diagrams, we will depict only these areas, i.e. in practice, this is the right side with respect to the vertical drawn through point A. In this case, in the P, v-diagram, the 0 ° C isotherm in the liquid region can be considered as the left boundary curve of the liquid phase, since it is almost vertical. In the T,s-diagram, the parameters of the triple point of the liquid phase of water are taken as the entropy reference point. Since the volume of the liquid phase of water at 0 o C is practically equal to its volume at the triple point, and the temperature of the triple point of water is very close to 0 o C, the constancy of these two parameters will give a constant value of the entropy of the liquid phase of water at various pressures and t = 0 o C Thus, all isobars in the area of ​​the liquid phase of water will come out of the point A in the T, s-diagram.

Thus, the main lines and processes for the liquid and vapor phases of water in the P, v-diagram can be presented in Fig. 6.9. Here, the subcritical isotherms in the liquid region (12) are close to vertical straight lines with a slight shift to the left. In the wet steam region (23), the isotherm coincides with the saturation isobar. In the region of superheated steam (34), the isotherm represents a downward convex curve. The critical isotherm has an inflection point at the critical point. Isotherms at t > t cr can also have an inflection point, which disappears at high temperatures.

Lines of constant entropies are curves convex downwards. Moreover, the lines s< s кр пересекают только линию x = 0, а линии s >s cr intersect only the line x = 1.

The construction of lines x=const corresponds to the ratio of segments:

The specific volume of liquid is very different from the specific volume of dry saturated steam. So at the triple point of water, the liquid (point A) has v o "= 0.00100022 m 3 / kg, and steam - v o" = 206.175 m 3 / kg, at the critical point v cr = 0.003147 m 3 / kg. At a pressure of 1 bar, v"=0.0010434 m 3 /kg, and v"=1.6946 m 3 /kg. As a result, the x=0 line is steeper than the x=1 line.

The image of the T, s-diagram for the liquid and vapor phases of water with the drawing of lines of the main processes and parameters will be given after a detailed study of the thermodynamic properties of the liquid and vapor phases of water.

The intermediate state of matter between the state of a real gas and liquid is commonly called vaporous or simply ferry. The transformation of liquid into vapor is phase transition from one aggregate state to another. During a phase transition, an abrupt change in the physical properties of a substance is observed.

An example of such phase transitions is the process boiling liquids with wet saturated steam and its subsequent transition to devoid of moisture dry saturated steam or reverse boiling process condensation saturated steam.

One of the main properties of dry saturated steam is that the further supply of heat to it leads to an increase in the temperature of the steam, i.e., its transition to the state of superheated steam, and the removal of heat leads to the transition to the state of wet saturated steam. IN

Phase states of water

Figure 1. Phase diagram for water vapor in T, s coordinates.

RegionI- gaseous state (superheated steam, which has the properties of a real gas);

RegionII– equilibrium state of water and saturated water vapor (two-phase state). Region II is also called the region of vaporization;

RegionIII- liquid state (water). Region III is bounded by the EK isotherm;

RegionIV– equilibrium state of solid and liquid phases;

RegionV– solid state;

Regions III, II and I are separated border lines AK (left line) and KD (right line). The common point K for the boundary lines AK and KD has special properties and is called critical point. This point has parameters pkr, vkr And T cr, at which boiling water passes into superheated steam, bypassing the two-phase region. Therefore, water cannot exist at temperatures above Tcr.

Critical point K has parameters:

pkr= 22.136 MPa; vkr\u003d 0.00326 m 3 / kg; tkr\u003d 374.15 ° С.

Values p, t, v And s for both boundary lines are given in special tables of thermodynamic properties of water vapor.

The process of obtaining water vapor from water

Figures 2 and 3 show the processes of heating water to a boil, vaporization and superheating of steam in p,v- And T, s-diagrams.

Initial state of liquid water under pressure p 0 and having a temperature of 0 °C, is depicted in the diagrams p,v And T, s dot A. When heat is supplied at p= const its temperature increases and the specific volume increases. At some point, the temperature of the water reaches the boiling point. In this case, its state is indicated by a dot b. With a further supply of heat, vaporization begins with a strong increase in volume. In this case, a two-phase medium is formed - a mixture of water and steam, called wet saturated steam. The temperature of the mixture does not change, since heat is spent on the evaporation of the liquid phase. The process of vaporization at this stage is isobaric-isothermal and is indicated on the diagram as a section bc. Then, at some point in time, all the water turns into steam, called dry saturated. This state is indicated in the diagram by a dot. c.

Figure 2. P, v diagram for water and steam.

Figure 3. T, s diagram for water and steam.

With a further supply of heat, the temperature of the steam will increase and the process of overheating of the steam will proceed. c - d. dot d indicates the state of superheated steam. Point distance d from the point With depends on the superheated steam temperature.

Indexing to designate quantities related to different states of water and steam:

• the value with the index "0" refers to the initial state of the water;
• the value with the index "′" refers to water heated to the boiling point (saturation);
• the value with index "″" refers to dry saturated steam;
• value with index " x» refers to wet saturated steam;
• the value without index refers to superheated steam.

Vaporization process at higher pressure p1 > p0 it can be noted that the point a, representing the initial state of water at a temperature of 0 ° C and a new pressure, remains practically on the same vertical, since the specific volume of water is almost independent of pressure.

Dot b'(the state of water at saturation temperature) shifts to the right by p,v-chart and climbs up on T,s-diagram. This is because as pressure increases, so does the saturation temperature and hence the specific volume of water.

Dot c'(state of dry saturated steam) shifts to the left, because with increasing pressure, the specific volume of steam decreases, despite an increase in temperature.

Connecting multiple points b And c at various pressures gives lower and upper boundary curves ak And kc. From p,v-diagram shows that as the pressure increases, the difference in specific volumes v″ And v′ decreases and at some pressure becomes equal to zero. At this point, called the critical point, the boundary curves converge ak And kc. State corresponding to a point k, is called critical. It is characterized by the fact that with it, steam and water have the same specific volumes and do not differ in properties from each other. Region lying in a curvilinear triangle bkc(V p,v-diagram), corresponds to wet saturated steam.

The state of superheated steam is represented by points lying above the upper boundary curve kc.

On T, s-chart area 0 abs' corresponds to the amount of heat required to heat liquid water to saturation temperature.

The amount of heat supplied, J / kg, equal to the heat of vaporization r, expressed by area s'bcs, and it has the relation:

r = T(s″ - s′).

The amount of heat supplied in the process of superheating water vapor is represented by the area s″cds.

On T, s- diagram shows that as the pressure increases, the heat of vaporization decreases and becomes equal to zero at the critical point.

Usually T, s-diagram is used in theoretical studies, since its practical use is greatly hindered by the fact that the amounts of heat are expressed by the areas of curvilinear figures.

Based on the materials of my lecture notes on thermodynamics and the textbook "Fundamentals of Energy". Author G. F. Bystritsky. 2nd ed., rev. and additional — M.: KNORUS, 2011. — 352 p.