Conditions of water.

Water can be in three states of aggregation, or phases - solid(ice), liquid (water itself), gaseous (water vapor). It is very important that, given the ranges of atmospheric pressure and temperature that actually exist on Earth, water can simultaneously be in different states of aggregation. In this respect, water differs significantly from other physical substances, which are found under natural conditions predominantly either in a solid (minerals, metals) or in a gaseous (O 2, N 2, CO 2, etc.) state.

Changes in the aggregate state of a substance are called phase transitions. In these cases, the properties of the substance (for example, density) change abruptly. Phase transitions are accompanied by the release or absorption of energy, called the heat of phase transition (“latent heat”).

The dependence of the aggregate state of water on pressure and temperature is expressed by the state diagram of water, or phase diagram (Fig. 5.1.1.).

The BB"O curve in Fig. 5.1.1 is called the melting curve. When passing through this curve from left to right, melting occurs

Rice. 5.1.1. Water diagram

I – VIII - various modifications of ice

ice, and from right to left - ice formation (crystallization of water). The OK curve is called the vaporization curve. When passing through this curve, boiling of water is observed from left to right, and condensation of water vapor is observed from right to left. The AO curve is called the sublimation curve, or sublimation curve. When crossing it from left to right, ice evaporates (sublimation), and from right to left, condensation into the solid phase (or sublimation) occurs.

At point O (the so-called triple point, at a pressure of 610 Pa and a temperature of 0.01 ° C or 273.16 K), water is simultaneously in all three states of aggregation.

The temperature at which ice melts (or water crystallizes) is called the temperature or melting point T pl. This temperature can also be called the temperature or freezing point T sub.

From the surface of water, as well as ice and snow, a certain number of molecules are constantly being torn off and carried into the air, forming water vapor molecules. At the same time, some of the water vapor molecules return back to the surface of water, snow and ice. If the first process predominates, then water evaporation occurs, if the second process occurs, water vapor condenses. The regulator of the direction and intensity of these processes is the humidity deficit - the difference between the elasticity of water vapor saturating the space at a given air pressure and temperature of the water surface (snow, ice), and the elasticity of the water vapor actually contained in the air, i.e. absolute air humidity. The content of saturated water vapor in the air and its elasticity increase with increasing temperature (at normal pressure) as follows. At a temperature of O°C, the content and elasticity of saturated water vapor are respectively 4.856 g/m3 and 6.1078 hPa, at a temperature of 20°C - 30.380 g/m3 and 23.373 hPa, at 40°C - 51.127 g/m3 and 73.777 hPa.

Evaporation from the surface of water (ice, snow), as well as moist soil, occurs at any temperature and the more intense it is, the greater the moisture deficit. With increasing temperature, the elasticity of water vapor saturating the space increases, and evaporation accelerates. An increase in evaporation also leads to an increase in the speed of air movement over the evaporating surface (i.e., wind speed in natural conditions), increasing the intensity of vertical mass and heat transfer.

When intense evaporation covers not only the free surface of the water, but also its thickness, where evaporation occurs from the inner surface of the resulting bubbles, the boiling process begins. The temperature at which the pressure of saturated water vapor is equal to external pressure is called the temperature or boiling point T bp.

At normal atmospheric pressure (1.013 105 Pa = 1.013 bar = 1 atm = 760 mm Hg), the freezing points of water (melting ice) and boiling points (condensation) correspond to 0 and 100 ° on the Celsius scale.

The freezing point Tzam and the boiling point of water Tbip depend on pressure (see Fig. 3.9.2.). In the range of pressure changes from 610 to 1.013 105 Pa (or 1 atm), the freezing temperature decreases slightly (from 0.01 to 0 ° C), then when the pressure increases to approximately 6 107 Pa (600 atm) T freezing temperature drops to -5 ° C, with an increase in pressure to 2.2 108 Pa (2,200 atm), Tdz decreases to -22 ° C. With a further increase in pressure, Tdz begins to increase rapidly. At very high pressure, special “modifications” of ice are formed (II-VIII), differing in their properties from regular ice(ice I).

At real atmospheric pressure on Earth fresh water freezes at a temperature of about 0 ° C. At maximum depths in the ocean (about 11 km), the pressure exceeds 108 Pa, or 1,000 atm (an increase in depth for every 10 m increases the pressure by approximately 105 Pa, or 1 atm). At this pressure, the freezing point of fresh water would be about -12° C.

To reduce the freezing point of water

its salinity influences.

1.4). An increase in salinity for every 10‰ reduces T by approximately 0.54° C:

T deputy = -0.054 S.

The boiling point decreases with decreasing pressure (see Fig. 3.9.2.). Therefore, at high altitudes in the mountains, water boils at a temperature lower than 100 ° C. With increasing pressure, T boil increases to the so-called “critical point”, when at p = 2.2 107 Pa and T boil = 374 ° C, water simultaneously has properties of both liquid and gas.

The diagram of the state of water illustrates two “anomalies” of water, which have a decisive influence not only on the “behavior” of water on Earth, but also on the natural conditions of the planet as a whole. Compared to substances that are compounds of hydrogen with elements that are in the same row as oxygen in the Periodic Table of Mendeleev - tellurium Te, selenium Se and sulfur S, the freezing and boiling points of water are unusually high. Considering the natural relationship between the freezing and boiling points and the mass number of the mentioned substances, one would expect water to have a freezing temperature of about -90° C, and a boiling point of about -70° C. Abnormally high values ​​of freezing and boiling temperatures predetermine the possibility of the existence of water on the planet as in solid and liquid states and serve as the determining conditions for the main hydrological and other natural processes on Earth.

Density of water

Density is the most important physical characteristic of any substance. It represents the mass of a homogeneous substance per unit volume:

where m is mass, V is volume. Density p has the dimension kg/m3.

The density of water, like other substances, depends primarily on temperature and pressure (and for natural waters, also on the content of dissolved and finely dispersed suspended solids) and changes abruptly during phase transitions. With increasing temperature, the density of water, like any other substance , in most of the range of temperature changes decreases, which is associated with an increase in the distance between molecules with increasing temperature. This pattern is violated only when ice melts and when water is heated in the range from 0 to 4° (more precisely 3.98° C). Two more very important “anatomies” of water are noted here: 1) the density of water in the solid state (ice) is less than in the liquid state (water), which is not the case for the vast majority of other substances; 2) in the water temperature range from 0 to 4 ° C, the density of water does not decrease with increasing temperature, but increases. Features of changes in water density are associated with a restructuring of the molecular structure of water. These two “anomalies” of water are of great hydrological importance: ice is lighter than water and therefore “floats” on its surface; reservoirs usually do not freeze to the bottom, since fresh water cooled to a temperature below 4° becomes less dense and therefore remains in the surface layer.

The density of ice depends on its structure and temperature. Porous ice may have a density much lower than indicated in Table 1.1. The snow density is even less. Freshly fallen snow has a density of 80-140 kg/m3, the density of compacted snow gradually increases from 140-300 (before the start of melting) to 240-350 (at the beginning of melting) and 300-450 kg/m3 (at the end of melting). Dense wet snow can have a density of up to 600-700 kg/m3. Snowflakes during melting have a density of 400-600, avalanche snow 500-650 kg/m3. The layer of water formed when ice and snow melts depends on the thickness of the ice or snow layer and its density. The amount of water in ice or snow is equal to:

h in = ah l r l / r

where h l is the thickness of the layer of ice or snow, r l is their density, p is the density of water, and is a multiplier determined by the ratio of the dimensions h in and h l: if the water layer is expressed in mm, and the thickness of ice (snow) in cm, then a=10, with the same dimension a=1.

The density of water also changes depending on the content of dissolved substances in it and increases with increasing salinity (Fig. 1.5). The density of sea water at normal pressure can reach 1025-1033 kg/m3.

The combined effect of temperature and salinity on the density of water at atmospheric pressure is expressed using the so-called equation of state of sea water. Such an equation in its simplest linear form is written as follows:

p = p o (1 - α 1 T + α 2 S)

where T is the water temperature, °C, S is the salinity of water, ‰, p o is the density of water at T = 0 and S = 0, α 1 and α 2 are parameters.

An increase in salinity also leads to a decrease in the temperature of greatest density (°C) according to the formula

T max.pl = 4 - 0.215 S.

Rice. 5.2.1. Dependence of the density of water at normal atmospheric pressure on the temperature and salinity of the water.

An increase in salinity for every 10‰ reduces Tmax by approximately 2° C. The dependence of the temperature of maximum density and freezing temperature on water salinity is illustrated by the so-called Helland-Hansen graph (see Fig. 3.10.1.).

The relationship between the temperatures of highest density and freezing influence the nature of the process of water cooling and vertical convection - mixing caused by differences in density. Cooling of water as a result of heat exchange with air leads to an increase in the density of water and, accordingly, to the lowering of denser water down. Warmer and less dense waters rise in its place. The process of vertical density convection occurs. However, for fresh and brackish waters with a salinity of less than 24.7‰, this process continues only until the water reaches its highest density temperature (see Fig. 1.4). Further cooling of the water leads to a decrease in its density, and vertical convection stops. Salt waters at S>24.7‰ are subject to vertical convection until they freeze.

Thus, in fresh or brackish waters in winter, in the near-bottom horizons, the water temperature is higher than on the surface, and, according to the Helland-Hansen graph, always above the freezing temperature. This circumstance is of great importance for the preservation of life in water bodies at depths. If water had the same temperature of greatest density and freezing, like all other liquids, then reservoirs could freeze to the bottom, causing the inevitable death of most organisms.

An “anomalous” change in the density of water with a change in temperature entails the same “anomalous” change in the volume of water: with an increase in temperature from 0 to 4 ° C, the volume of chemically pure water decreases, and only with a further increase in temperature does it increase; the volume of ice is always noticeably greater than the volume of the same mass of water (remember how pipes burst when water freezes).

The change in the volume of water when its temperature changes can be expressed by the formula

V T1 = V T2 (1 + β DT)

where V T1 is the volume of water at temperature T1, V T2 is the volume of water at T2, β is the coefficient of volumetric expansion, which takes negative values ​​at temperatures from 0 to 4 ° C and positive values ​​at water temperatures above 4 ° C and less than 0 ° C ( ice) (see table 1.1),

Pressure also has some effect on the density of water. The compressibility of water is very small, but at great depths in the ocean it still affects the density of water. For every 1000 m of depth, the density due to the influence of the pressure of the water column increases by 4.5-4.9 kg/m3. Therefore, at maximum ocean depths (about 11 km), the density of water will be approximately 48 kg/m 3 greater than on the surface, and at S = 35‰ it will be about 1076 kg/m 3. If water were completely incompressible, the level of the world's oceans would be 30 m higher than it actually is. The low compressibility of water makes it possible to significantly simplify the hydrodynamic analysis of the movement of natural waters.

The influence of fine suspended sediment on the physical characteristics of water and, in particular, on its density has not yet been sufficiently studied. It is believed that the density of water can only be influenced by very fine suspended matter at their exceptionally high concentration, when water and sediment can no longer be considered in isolation. Thus, some types of mudflows, containing only 20-30% water, are essentially a clay solution with increased density. Another example of the influence of small sediments on density is the waters of the Yellow River flowing into the Yellow Sea Bay. With a very high content of fine sediment (up to 220 kg/m3), river turbid waters have a density 2-2.5 kg/m3 greater than sea water (their density at actual salinity and temperature is about 1018 kg/m3). Therefore, they “dive” to depth and descend along the seabed, forming a “dense” or “turbidity” flow.

5. Phase transformations and state diagram of water

A state diagram (or phase diagram) is graphic image dependencies between quantities characterizing the state of the system and phase transformations in the system (transition from solid to liquid, from liquid to gaseous, etc.). Phase diagrams are widely used in chemistry. For single-component systems, phase diagrams are usually used to show the dependence phase transformations on temperature and pressure, they are called phase diagrams in P---T coordinates

Figure 5 shows a diagram of the state of water in schematic form. Any point on the diagram corresponds to certain values ​​of temperature and pressure.

In liquid state - water

Hard - ice

Gaseous - steam

The diagram shows those states of water that are thermodynamically stable at certain values ​​of temperature and pressure. It consists of three curves that separate all possible temperatures and pressures into three regions corresponding to ice, liquid and steam.

ice = steam (OA curve)

ice = liquid (RH curve)

liquid = steam (OC curve)

O - freezing point of water

For water, the critical temperature is 374 degrees Celsius. At normal pressure, the liquid and vapor phases of water are in equilibrium with each other at 100 degrees Celsius, because in this case, the vapor pressure above the liquid is compared with the external pressure and the water boils. The intersection of the three curves occurs at point O - the triple point, at which all three phases are in equilibrium with each other.

Let's look at each of the curves in more detail. Let's start with the OA curve separating the vapor region from the liquid region. Let's imagine a cylinder from which air has been removed, after which a certain amount of clean water, free of dissolved substances, including gases, is introduced into it; the cylinder is equipped with a piston, which is fixed in a certain position. After some time, part of the water will evaporate, and saturated steam will exist above its surface. You can measure its pressure and make sure that it does not change over time and does not depend on the position of the piston. If we increase the temperature of the entire system and measure the saturated vapor pressure again, it will turn out that it has increased. By repeating such measurements at different temperatures, we will find the dependence of the pressure of saturated water vapor on temperature. The OA curve is a graph of this relationship: 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 - coexist. The OA curve is called the liquid-vapor equilibrium curve or boiling curve. Table 5 shows the values ​​of saturated water vapor pressure at several temperatures.

Table 5 Temperature	Saturated steam pressure	Temperature	Saturated steam pressure
		mmHg Art.			mmHg Art.

Molecular physics of water in its three states of aggregation

Fig. 5.2 Diagram of aggregative states of water in the region of triple point A. I - ice. II - water. III -- water vapor.

Water is found in natural conditions in three states: solid - in the form of ice and snow, liquid - in the form of water itself, gaseous - in the form of water vapor. These states of water are called aggregate states, or solid, liquid and vapor phases, respectively. The transition of water from one phase to another is caused by changes in its temperature and pressure. In Fig. shows a diagram of the states of aggregation of water depending on temperature t and pressure P. From Fig. 5.2 it is clear that in region I water is found only in solid form, in region II - only in liquid form, in region III - only in the form of water vapor . Along the AC curve it is in a state of equilibrium between solid and liquid phases (ice melting and water crystallization); along the AB curve - in a state of equilibrium between the liquid and gaseous phases (evaporation of water and condensation of steam); along the AD curve - in equilibrium between the solid and gaseous phases (sublimation of water vapor and sublimation of ice).

The equilibrium of phases according to Fig. 5.2 along the curves AB, AC and AD must be understood as dynamic equilibrium, i.e. along these curves the number of newly formed molecules of one phase is strictly equal to the number of newly formed molecules of another phase.

If, for example, we gradually cool water at any pressure, then in the limit we will find ourselves on the AC curve, where water will be observed at the corresponding temperature and pressure. If we gradually heat ice at different pressures, we will find ourselves on the same AC equilibrium curve, but on the ice side. Similarly, we will have water and water vapor, depending on which side we approach the AB curve.

All three curves of the state of aggregation - AC (curve of the dependence of the melting temperature of ice on pressure), AB (curve of the dependence of the boiling temperature of water on pressure), AD (curve of dependence of the vapor pressure of the solid phase on temperature) - intersect at one point A, called triple point. By modern research, the values ​​of the saturation vapor pressure and temperature at this point are respectively equal: P = 610.6 Pa (or 6.1 hPa = 4.58 mm Hg), t = 0.01°C (or T = 273.16 TO). In addition to the triple point, the AB curve passes through two more characteristic points - the point corresponding to the boiling of water at normal air pressure with coordinates P = 1.013 10 5 Pa and t = 100°C, and the point with coordinates P = 2.211 10 7 Pa and t cr = 374.2°C, corresponding to the critical temperature - the temperature only below which water vapor can be converted into a liquid state by compression.

Curves AC, AB, AD related to the processes of transition of a substance from one phase to another are described by the Clapeyron-Clausius equation:

where T is the absolute temperature corresponding to each curve, respectively, to the temperature of evaporation, melting, sublimation, etc.; L -- specific heat respectively evaporation, melting, sublimation; V 2 - V 1 is the difference in specific volumes, respectively, when moving from water to ice, from water vapor to water, from water vapor to ice. A detailed solution of this equation regarding the pressure of saturated water vapor e 0 above the surface of water - curve AB and ice - curve AD, can be found in the course of general meteorology.

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Subtitles

All phase transitions considered were isobaric; in particular, the phase transitions of water in the last videos occurred at a pressure at sea level equal to one atmosphere. In reality everything is different. IN real world Nowhere is a constant pressure of 1 atmosphere maintained. 1 atmosphere is the pressure at sea level on Earth. Pressure depends on the size of the planet, on the thickness of the atmosphere, on the conditions in which gases, liquids and solids. So, here is a phase diagram. I'll write it down. " Phase diagram" There are several forms of chart recording. This is the most popular of them, which shows states of aggregation and transitions between them when temperature and pressure change. This is a diagram for water. The pressure value is plotted along the ordinate axis. Let me sign it. The x-axis is temperature, and the areas of the diagram correspond to different states of aggregation: solid, liquid... liquid and, finally, gas. Let's see what state of aggregation a temperature of 0 degrees corresponds to. So, the temperature is 0 degrees Celsius and the pressure is 1 atmosphere. This point corresponds to them on the graph. This is the boundary between a solid and a liquid at a pressure of 1 atmosphere. The pressure here is 1 atmosphere. This corresponds to the well-known fact that ice melts at 0 degrees. What happens if we increase the pressure? Ice will melt at a lower temperature. Let's increase the pressure, for example, to 10 atmospheres, which is 10 times more than the pressure at sea level. The temperature at which a solid turns into a liquid will decrease. If the pressure is reduced, such as being in Denver, which is a mile above sea level, the freezing temperature will increase by about 1 degree. This isn't quite the right scale, but the point is that the ice will freeze faster, that is, at a higher temperature, in Denver than at the bottom of the Dead Sea or Death Valley, which are located below sea level. The area to the right of the purple line corresponds to gas. Let's return to atmospheric pressure. This is a diagram for water. We know how it behaves at a pressure of 1 atmosphere. I'll draw the line. At a pressure of 1 atmosphere and a temperature of 0 degrees, solid ice turns into liquid water. Moving along this line, we enter an area of ​​high temperature. At this point on the graph the temperature is 100 degrees. At this temperature and pressure of 1 atmosphere, liquid water turns into water vapor, that is, it boils. This is the boiling point of water. What if you lower your blood pressure? Let's head to Denver again. Here's Denver. Although no, we need something more visual. It would be better if it was Mount Everest, there the pressure is low. As pressure decreases, the freezing point increases and the boiling point decreases, so it is easier to boil water at the top of Everest than at its foot or in the lowlands of Death Valley. Imagine a liquid. It contains millions of molecules that are located very close, but at the same time have sufficient kinetic energy to move relative to each other. Molecules move - liquid flows. Molecules do not evaporate, do not jump out, because air presses on them from above. I have already talked about air pressure. The pressure created by gas molecules depends on their temperature, as well as on their kinetic energy. Gas molecules are on top and do not allow liquid molecules to jump out. They prevent them from separating from each other and turning into gas. The greater the pressure, the more difficult it is for molecules to escape. Now let's transfer the liquid into a vacuum, surface of the moon where there is no air, and shake slightly. These molecules are still attracted to each other, but in the absence of external pressure, a small push is enough for them to turn into gas. The lower the pressure, the easier it is for a liquid, even a solid, to become a gas. Even solids evaporate. This requires very low pressure. Look at the left side of the graph. It's practically a vacuum. Take the ice to the surface of the Moon, to an area with the desired temperature, I’m sure it’s minus there, but I don’t remember exactly how much, the ice will evaporate, turning into steam. In deep vacuum conditions, the molecules of a substance only need the slightest push to begin to evaporate. And this can happen not only on the Moon. To make it clearer, consider the phase diagram of carbon dioxide. Here she is, look. This is carbon dioxide. We exhale it, green plants consume it. And this substance behaves differently at 1 atmosphere than water. Please note that the scale is not maintained here. The distances between 1 and 5 atmospheres and between five and seventy-three are not actually equal. The scale here is also inconsistent. If it was important, I would probably use a logarithmic scale. But let's return to carbon dioxide. Here is solid carbon dioxide, here is a gas, and here is a liquid substance. At a pressure of one atmosphere, that is, at sea level, for example, as in New Orleans, if you create a temperature of -80 degrees Celsius, carbon dioxide will freeze. You've encountered this. I’m not sure if it’s still used in smoke generators, but everyone has heard about dry ice. This is solid carbon dioxide. At atmospheric pressure at sea level at a temperature of -78.5 degrees, it sublimates. Sublimation is the transition from solid to liquid. I'll write this down. Therefore, there is no such thing as liquid carbon dioxide. I've never seen anything like this. To make carbon dioxide liquid, you need a pressure of 5 atmospheres, that is, 5 times higher than the pressure at sea level. This is possible on Jupiter or Saturn, where the pressure is enormous due to gravity and the thickness of the atmosphere. Liquid carbon dioxide occurs naturally on gas giant planets. And on Earth, dry ice sublimes. It is a synonym for sublimation. From solid to gaseous state, bypassing liquid. There is something else interesting, and you may have already noticed it. This point is called the triple point because at five atmospheres and minus 56 degrees Celsius, carbon dioxide is in a state of equilibrium between ice, liquid and gas. A little bit of each of them. You can push a substance towards one of the states by changing the conditions. And here is the triple point for water. At pressure lower than atmospheric. This is 611 pascals, which is about 200 times less than one atmosphere. At this pressure and temperature just above 0, the triple point of water is located. Here the water is in equilibrium between these three states. There is another interesting point here. Critical point. Sounds serious and important, doesn't it? If you raise the temperature or pressure even higher, you get a supercritical fluid. Sounds cool. Everything beyond that is a supercritical fluid. With high temperature and pressure. Temperature turns it into a gas, but pressure turns it into a liquid—it's both. Supercritical water is used as a solvent. It behaves like liquid water, substances can be dissolved in it, and it can also penetrate solids and seep anywhere to remove some kind of contaminant or dissolve some kind of salt. Supercritical fluids are very interesting. And the reason I showed you these diagrams is because pressure can change just as much as the temperature of a substance. At 100 degrees Celsius or even 110 at sea level, water will be a gas. Here's the 110 degree mark, and that's water vapor. Now let's increase the pressure, for example, go deeper underground or to the bottom of the ocean, and the water vapor will condense into liquid. If you move to lower temperatures, you can see the opposite of sublimation. I think I wrote down its name. Oh, no. He's gone. It's similar to condensation, but I forgot its name. This is a transition from a gaseous state directly to a solid, bypassing the liquid. The benefit of these diagrams is that they allow one to predict the behavior of a substance as pressure and temperature change. Subtitles by the Amara.org community

Elements of a phase diagram

Triple points

№	Phases			Pressure	Temperature		Note
				MPa	°C	K
1	Steam	Water	Ice Ih	611.657 Pa	0,01	273,16
2	Steam	Ice Ih	Ice XI	0	−201,0	72,15
3	Water	Ice Ih	Ice III	209,9	−21,985	251,165
4	Ice Ih	Ice II	Ice III	212,9	−34,7	238,45
5	Ice II	Ice III	Ice V	344,3	−24,3	248,85
6	Ice II	Ice VI	Ice XV	~ 800	−143	130	For D2O
7	Water	Ice III	Ice V	350,1	−16,986	256,164
8	Water	Ice IV	Ice XII	~ 500-600	~ −6	~ 267
9	Ice II	Ice V	Ice VI	~ 620	~ −55	~ 218
10	Water	Ice V	Ice VI	632,4	0.16	273,32
11	Ice VI	Ice VIII	Ice XV	~ 1500	−143	130	For D2O
12	Ice VI	Ice VII	Ice VIII	2100	~ 5	~ 278
13	Water	Ice VI	Ice VII	2216	81,85	355
14	Ice VII	Ice VIII	Ice X	62 000	−173	100
15	Water	Ice VII	Ice X	47 000	~ 727	~ 1000

Ice sublimation curve

P = A ⋅ e x p (− B / T) , (\displaystyle P=A\cdot exp(-B/T),) A = 3.41 ⋅ 10 12 P a ; B = 6130 K. (\displaystyle A=3.41\cdot 10^(12)~\mathrm (Pa) ;\quad B=6130~\mathrm (K) .)

The error of this formula is no more than 1% in the temperature range 240-273.16 K and no more than 2.5% in the temperature range 140-240 K.

More accurately, the sublimation curve is described by the formula recommended by the IAPWS (English) Russian(English) International Association for the Properties of Water and Steam - International Association for the Study of the Properties of Water and Steam) :

ln ⁡ P P 0 = T 0 T ∑ i = 1 3 a i (T T 0) b i , (\displaystyle \ln (\frac (P)(P_(0)))=(\frac (T_(0))(T ))\sum _(i=1)^(3)a_(i)\left((T \over T_(0))\right)^(b_(i)),) P 0 = 611, 657 P a ; T0 = ​​273.16 K; a 1 = − 21, 2144006; b 1 = 0.003333333; a 2 = 27, 3203819; b 2 = 1, 20666667; a 3 = − 6, 1059813; b 3 = 1 , 70333333. (\displaystyle (\begin(matrix)~P_(0)=611.657~\mathrm (Pa) ;&T_(0)=273.16~\mathrm (K) ;\\a_(1 )=-21.2144006;&b_(1)=0.003333333;\\a_(2)=27.3203819;&b_(2)=1.20666667;\\a_(3)=-6.1059813;&b_( 3)=1.70333333.\end(matrix)))

Ice melting curve Ih

P P 0 = 1 + ∑ i = 1 3 a i [ 1 − (T T 0) b i ] , (\displaystyle (\frac (P)(P_(0)))=1+\sum _(i=1)^( 3)a_(i)\left,) P 0 = 611, 657 P a ; T0 = ​​273.16 K; a 1 = 1 195 393, 37; b 1 = 3, 00; a 2 = 80 818, 3159; b 2 = 25, 75; a 3 = 3338, 2686; b 3 = 103, 75; (\displaystyle (\begin(matrix)~P_(0)=611.657~\mathrm (Pa) ;&T_(0)=273.16~\mathrm (K) ;\\a_(1)=1~195~393 ,37;&b1=3.00;\\a_(2)=80~818.3159;&b2=25.75;\\a_(3)=3~338.2686;&b3=103.75;\end( matrix)))

Ice melting curve III

Melting curve ice III begins at the point of minimum solidification temperature of water (251.165 K; 208.566 MPa), where ordinary ice turns into structural modification III, and ends at the point (256.164 K; 350.1 MPa), where the boundary of phases III and V passes.

P P 0 = 1 − 0 , 299948 [ 1 − (T T 0) 60 ] , (\displaystyle (\frac (P)(P_(0)))=1-0.299948\left,) P 0 = 208.566 M P a ; T0 = ​​251.165 K. (\displaystyle P_(0)=208.566~\mathrm (MPa) ;\quad T_(0)=251.165~\mathrm (K) .)

Ice melting curve V

The melting curve of ice V begins at the point (256.164 K; 350.1 MPa), at the boundary of phases III and V, and ends at the point (273.31 K; 632.4 MPa), where the boundary of phases V and VI passes.

P P 0 = 1 − 1 , 18721 [ 1 − (T T 0) 8 ] , (\displaystyle (\frac (P)(P_(0)))=1-1.18721\left,) P 0 = 350.1 M P a ; T0 = ​​256.164 K. (\displaystyle P_(0)=350.1~\mathrm (MPa) ;\quad T_(0)=256.164~\mathrm (K) .)

Ice melting curve VI

The melting curve of ice VI begins at the point (273.31 K; 632.4 MPa), at the boundary of phases V and VI, and ends at the point (355 K; 2216 MPa), where the boundary of phases VI and VII passes.

P P 0 = 1 − 1 , 07476 [ 1 − (T T 0) 4 , 6 ] , (\displaystyle (\frac (P)(P_(0)))=1-1.07476\left,) P 0 = 632.4 M P a ; T0 = ​​273.31 K. (\displaystyle P_(0)=632.4~\mathrm (MPa) ;\quad T_(0)=273.31~\mathrm (K) .)

Ice melting curve VII

The melting curve of ice VII begins at the point (355 K; 2216 MPa), at the boundary of phases VI and VII, and ends at the point (715 K; 20.6 GPa), where the boundary of phase VII passes.

ln ⁡ P P 0 = ∑ i = 1 3 a i (1 − (T T 0) b i) , (\displaystyle \ln (\frac (P)(P_(0)))=\sum _(i=1)^( 3)a_(i)\left(1-\left((T \over T_(0))\right)^(b_(i))\right),) P 0 = 2216 M P a ; T0 = ​​355 K; a 1 = 1, 73683; b 1 = − 1 ; a 2 = − 0, 0544606; b 2 = 5 ; a 3 = 8, 06106 ⋅ 10 − 8; b 3 = 22. (\displaystyle (\begin(matrix)~P_(0)=2216~\mathrm (MPa) ;&T_(0)=355~\mathrm (K) ;\\a_(1)=1, 73683;&b_(1)=-1;\\a_(2)=-0.0544606;&b_(2)=5;\\a_(3)=8.06106\cdot 10^(-8);&b_( 3)=22.\end(matrix)))

Water vapor saturation curve

The water vapor saturation curve begins at the triple point of water (273.16 K; 611.657 Pa) and ends at the critical point (647.096 K; 22.064 MPa). It shows the boiling point of water at a specified pressure or, equivalently, the pressure of saturated water vapor at a specified temperature. At the critical point, the density of water vapor reaches the density of water and, thus, the difference between these states of aggregation disappears.

β 2 θ 2 + n 1 β 2 θ + n 2 β 2 + n 3 β θ 2 + n 4 β θ + n 5 β + n 6 θ 2 + n 7 θ + n 8 = 0 , (\displaystyle \beta ^(2)\theta ^(2)+n_(1)\beta ^(2)\theta +n_(2)\beta ^(2)+n_(3)\beta \theta ^(2)+n_( 4)\beta \theta +n_(5)\beta +n_(6)\theta ^(2)+n_(7)\theta +n_(8)=0,) θ = T T 0 + n 9 T T 0 − n 10 ; T 0 = 1 K ; (\displaystyle \theta =(T \over T_(0))+(\frac (n_(9))((T \over T_(0))-n_(10)));\quad T_(0)= 1~\mathrm (K) ;) β = (P P 0) 0, 25; P 0 = 1 M P a ; (\displaystyle \beta =\left((\frac (P)(P_(0)))\right)^(0.25);\quad P_(0)=1~\mathrm (MPa) ;) n0 = 1, 0; (\displaystyle n_(0)=1.0;) n 1 = 1167, 0521452767; (\displaystyle n_(1)=1167.0521452767;) n 2 = − 724213, 16703206; (\displaystyle n_(2)=-724213,16703206;) n 3 = − 17, 073846940092; (\displaystyle n_(3)=-17.073846940092;) n 4 = 12020, 82470247; (\displaystyle n_(4)=12020.82470247;) n 5 = − 3232555, 0322333; (\displaystyle n_(5)=-3232555.0322333;) n 6 = 14, 91510861353; (\displaystyle n_(6)=14.91510861353;) n 7 = − 4823, 2657361591; (\displaystyle n_(7)=-4823.2657361591;) n8 = 405113, 40542057; (\displaystyle n_(8)=405113,40542057;) n 9 = − 0, 23855557567849; (\displaystyle n_(9)=-0.23855557567849;) n 10 = 650, 17534844798. (\displaystyle n_(10)=650,17534844798.)

For a given absolute temperature value T, the normalized value is calculated θ and odds quadratic equation

A = θ 2 + n 1 θ + n 2 ; (\displaystyle A=\theta ^(2)+n_(1)\theta +n_(2);) B = n 3 θ 2 + n 4 θ + n 5 ; (\displaystyle B=n_(3)\theta ^(2)+n_(4)\theta +n_(5);) C = n 6 θ 2 + n 7 θ + n 8 , (\displaystyle C=n_(6)\theta ^(2)+n_(7)\theta +n_(8),)

after which the value is found β

β = − B − B 2 − 4 A C 2 A (\displaystyle \beta =(\frac (-B-(\sqrt (B^(2)-4AC)))(2A)))

and absolute pressure value:

P = P 0 β 4 . (\displaystyle P=P_(0)\beta ^(4).)

Saturated water vapor pressure (kPa) at various temperatures

T°C	0	1	2	3	4	5	6	7	8	9
0	0,6112	0,6571	0,7060	0,7581	0,8135	0,8726	0,9354	1,002	1,073	1,148
10	1,228	1,313	1,403	1,498	1,599	1,706	1,819	1,938	2,065	2,198
20	2,339	2,488	2,645	2,811	2,986	3,170	3,364	3,568	3,783	4,009
30	4,247	4,497	4,759	5,035	5,325	5,629	5,947	6,282	6,632	7,000
40	7,384	7,787	8,209	8,650	9,112	9,594	10,10	10,63	11,18	11,75
50	12,35	12,98	13,63	14,31	15,02	15,76	16,53	17,33	18,17	19,04
60	19,95	20,89	21,87	22,88	23,94	25,04	26,18	27,37	28,60	29,88
70	31,20	32,57	34,00	35,48	37,01	38,60	40,24	41,94	43,70	45,53
80	47,41	49,37	51,39	53,48	55,64	57,87	60,17	62,56	65,02	67,56
90	70,18	72,89	75,68	78,57	81,54	84,61	87,77	91,03	94,39	97,85
100	101,4

see also

Links

• IAPWS. Website of the International Association for the Study of the Properties of Water.

The state of water has been studied over 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 a substance - polymorphism - leads to a complication of state diagrams.

Phase diagram of water in coordinates R - T is presented in Fig. 6. 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, F and P, respectively). These phase fields are separated by 3 boundary curves.

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

liquid water is vapor, and the number of degrees of freedom calculated using the phase rule is WITH= 3 - 2 = 1. This equilibrium is called monovariant. This means that for a complete description of the system it is enough to determine only one variable- either temperature or pressure, because for a given temperature there is only one equilibrium pressure and for a given pressure there is only one equilibrium temperature.

At pressures and temperatures corresponding to points below line AB, the liquid will completely evaporate, and this region is the region of vapor. 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 liquid ( WITH= 2). The upper limit of the evaporation curve AB 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), therefore F = 1.

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

Line AD - melting curve, expresses the dependence ice melting temperature versus pressure and corresponds to the monovariant equilibrium ice ↔ liquid water. For most substances, the AD line deviates from the vertical to the right, but the behavior of water

Fig.6. Phase diagram of water

anomalous: liquid water occupies less 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 first carried out by Bridgman to determine the course of the melting curve of ice 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.

The triple point of water (a point reflecting the equilibrium of three phases - liquid, ice and steam) in the absence of air is located at 0.0100ºС ( T = 273,16K) and 4.58 mm Hg. Number of degrees of freedom WITH= 3-3 = 0 and such an equilibrium is called invariant.

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

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

In Fig. Figure 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 region of low pressures

The diagram shows those states of water that are thermodynamically stable at certain values ​​of temperature and pressure. It consists of three curves that separate all possible temperatures and pressures into three regions corresponding to ice, liquid and steam.

The OA curve represents the dependence of saturated water vapor pressure 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-liquid equilibrium curve, or melting curve, - shows those pairs of temperature and pressure values ​​at which ice and liquid water are in equilibrium.

OB curve - solid state - vapor equilibrium curve, 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. It's called triple point.

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

The state diagram of water is important when developing 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 turns into steam. This is the basis for the development of methods for producing food products by freeze drying.

One of the features of water that distinguishes it from other substances is that the melting point of ice decreases with increasing pressure. This circumstance is reflected in the diagram. The OC melting curve on the water diagram 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 on the diagram by points or segments located on the horizontal line corresponding to 101.3 kPa (760 mm Hg). Thus, the melting of ice or the crystallization of water corresponds to point D, the boiling of water - to point E, the heating or cooling of water - to the segment DE, etc.