PROPERTIES OF PURE SUBSTANCES

Transcription

1 PROPERTIES OF PURE SUBSTANCES

2 Pure Substance A pure substance is one that has a homogeneous and invariable chemical composition. It may exist in more than one phase, but the chemical composition is the same in all phases. Example: liquid water, a mixture of liquid water and water vapor (steam), and a mixture of ice and liquid water are all pure substances; every phase has the same chemical composition. In contrast, a mixture of liquid air and gaseous air is not a pure substance because the composition of the liquid phase is different from that of the vapor phase. Sometimes a mixture of gases, such as air, is considered a pure substance as long as there is no change of phase. Strictly speaking, this is not true. a mixture of gases such as air exhibits some of the characteristics of a pure substance as long as there is no change of phase.

3 Vapor-Liquid-Solid Phase Equilibrium Figure: Constant-pressure change from liquid to vapor phase for a pure substance. Consider as a system 1 kg of water contained in the piston/cylinder arrangement shown in Fig. a. and maintain a pressure of 0.1 MPa in the cylinder and that the initial temperature is 20 C. With Q water T appreciably, (0 0 C T C ) specific volume,υ slightly, pressure P = constant. Continuing the Q, phase change starts at T = C, P and T remains constant, υ with heating upto last drop of liquid has vaporized. With further Q, T ( T > C) υ and P = constant.

4 Figure: Temperature volume diagram for water showing liquid and vapor phases (not to scale).

5 Some Terminology Saturation temperature designates the temperature at which vaporization takes place at a given pressure. This pressure is called the saturation pressure for the given temperature. For a pure substance there is a definite relation between saturation pressure and saturation temperature. It is shown by a typical curve, called the vapor-pressure curve If a substance exists as liquid at the saturation temperature and pressure, it is called a saturated liquid. If the temperature of the liquid is lower than the saturation temperature for the existing pressure, it is called either a subcooled liquid (implying that T T sat (P)) or a compressed liquid (implying that the pressure, P > P sat (T)). When a substance exists as part liquid and part vapor at the saturation temperature, its quality, x is defined as the ratio of the mass of vapor to the total mass. Exam: if the mass of the vapor is 0.2 kg and the mass of the liquid is 0.8 kg, the quality is 0.2 or 20%.

6 The quality may be considered an intensive property. Quality has meaning only when the substance is in a saturated state, that is, at saturation pressure and temperature. If a substance exists as vapor at the saturation temperature, it is called saturated vapor. (Sometimes dry saturated vapor is used to emphasize that the quality is 100%.). When the vapor is at a temperature greater than the saturation temperature, it is said to exist as superheated vapor. The pressure and temperature of superheated vapor are independent properties, since the temperature may increase while the pressure remains constant. Actually, the substances we call gases are highly superheated vapors. At the critical point the saturated-liquid and saturated-vapor states are identical. The temperature, pressure, and specific volume at the critical point are called the critical temperature, critical pressure, and critical volume. Coexistent phases are separated by an interface, called the phase boundary, of finite thickness across which the property values change uniformly. A system in which two phases coexist in equilibrium is called saturated.

7 T v and P-v diagram for the two-phase liquid vapor region showing the quality specific volume relation.

8 By convention, the subscript f the subscript g is used to designate a property of a saturated liquid and a property of a saturated vapor All of the liquid present is at state f with specific volume v f and all of the vapor present is at state g with v g. The total volume is the sum of the liquid volume and the vapor volume The average specific volume of the system v is then in terms of the definition of quality x = m vap /m. Now the quality x can be viewed as the fraction (v v f )/v f g of the distance between saturated liquid and saturated vapor, as indicated in the Fig.

9 The general shape of the P-v diagram of a pure substance is very much like the T-v diagram, but the T constant lines on this diagram have a downward trend,

10 Extending the Diagrams to Include the Solid Phase

11 P-v diagram of a substance that expands on freezing (such as water).

12 The basic principles discussed in conjunction with the liquid vapor phasechange process apply equally to the solid liquid and solid vapor phase-change processes Most substances contract during a solidification (i.e., freezing) process (exception is water). Consider another experiment with the piston/cylinder arrangement. Suppose that the cylinder contains 1 kg of ice at 20 C, 100 kpa. When heat is transferred to the ice, Pressure, P = constant, sp. vol m, υ slightly T until it reaches 0 C. (at which point the ice melts and the temperature remains constant). In this state the ice is called a saturated solid. ( For most substances the specific volume increases during this melting process, but for water the specific volume of the liquid is less than the specific volume of the solid.) When all the ice has melted, further Q T.

13 The fact that water expands upon freezing has vital consequences in nature. If water contracted on freezing as most other substances do, the ice formed would be heavier than the liquid water, and it would settle to the bottom of rivers, lakes, and oceans instead of floating at the top. The sun s rays would never reach these ice layers, and the bottoms of many rivers, lakes, and oceans would be covered with ice at times, seriously disrupting marine life. If the initial pressure of the ice at 20 C is kpa. Heat transfer to the ice results in an increase in temperature to 10 C. At this point, however, the ice passes directly from the solid phase to the vapor phase in the process known as sublimation. Further heat transfer results in superheating of the vapor.

14 Thermodynamic Surfaces (P-v-T Surface) P v T Ssurface for a substance that expands on freezing (such as water)

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16 In these diagrams the pressure, specific volume, and temperature are plotted on mutually perpendicular coordinates, and each possible equilibrium state is thus represented by a point on the surface. All points along a quasi-equilibrium process lie on the P v T surface, since such a process always passes through equilibrium states. The regions of the surface that represent a single phase the solid, liquid, and vapor phases are indicated. These surfaces are curved. The two-phase regions the solid liquid, solid vapor, and liquid vapor regions are ruled surfaces. the two-phase regions as surfaces perpendicular to the P-T plane that is they are made up of straight lines parallel to the specific-volume axis. in the twophase region, lines of constant pressure are also lines of constant temperature. Notice that for a substance such as water, which expands on freezing, the freezing temperature decreases with an increase in pressure. For a substance that contracts on freezing, the freezing temperature increases as the pressure increases.

17 P-T diagram (Phase diagram) of a pure substance

18 Finally, consider an initial pressure of the ice of kpa and a temperature of 20 C. Through heat transfer, let the temperature increase until it reaches 0.01 C. At this point, however, further heat transfer may cause some of the ice to become vapor and some to become liquid, for at this point it is possible to have the three phases in equilibrium. This point is called the triple point, defined as the state in which all three phases may be present in equilibrium. The states on the triple line of a substance have the same pressure and temperature but different specific volumes. The P-T diagram is often called the phase diagram since all three phases are separated from each other by three lines. Along the sublimation line the solid and vapor phases are in equilibrium, along the fusion (melting) line, the solid and liquid phases are in equilibrium, and along the vaporization line the liquid and vapor phases are in equilibrium. The only point at which all three phases may exist in equilibrium is the triple point.

19 The vaporization line ends at the critical point because there is no distinct change from the liquid phase to the vapor phase above the critical point. This is the state at which the densities of the liquid and the vapor phases become equal and, consequently, where the physical interface between the liquid and the vapor disappears. Substances existing under these conditions are called gases. A substance in the vapor phase that does not meet the definition of a gas is called a superheated vapor (sometimes just vapor). Consider a solid in state A, as shown in P-T diagram. When the temperature increases but the pressure (which is less than the triple-point pressure) is constant, the substance passes directly from the solid to the vapor phase. Along the constant-pressure line EF, the substance passes from the solid to the liquid phase at one temperature and then from the liquid to the vapor phase at a higher temperature. The constant-pressure line CD passes through the triple point, and it is only at the triple point that the three phases may exist together in equilibrium. At a pressure above the critical pressure, such as GH, there is no sharp distinction between the liquid and vapor phases. Although we have made these comments with specific reference to water (only because of our familiarity with water), all pure substances exhibit the same general behavior.

20 Figure: Water phase diagram.

21 A pure substance can exist in a number of different solid phases. A transition from one solid phase to another is called an allotropic transformation (a term that comes from the Greek words allos, meaning related to, and trope meaning forms of the same substance ). Example: graphite and diamond are allotropic forms of carbon.. When subjected to high pressures, water can form at least 15 solid phases. These phases differ by their crystalline structure, ordering, and density. (In 2009, ice XV was found at extremely high pressures and 143 C. Figure 3.8 shows a more complete p-t phase diagram for water including 7 of its 15 known solid phases. Each intersection of three phase transition lines forms a new triple point. The figure shows a number of solid phases for water. A pure substance can have a number of triple points, but only one triple point has a solid, liquid, and vapor equilibrium. Other triple points for a pure substance can have two solid phases and a liquid phase, two solid phases and a vapor phase, or three solid phases.

22 Independent Properties Of A Pure Substance The number of degrees of freedom (independent properties) within a heterogeneous mixture of pure substances is given by Gibbs s phase rule as Example: a homogeneous (P = 1) pure substance (C = 1) requires f = = 2 intensive properties to fix its state. a homogeneous (P = 1) mixture of two pure substances (C = 2) requires f = = 3 intensive properties to fix its state. The case of a two-phase (P = 2) pure substance (C = 1), however, is misleading, because f = = 1, but this simply means that each phase requires one intensive property to fix its state. Hence, two independent properties are required to fix the state of the complete two-phase system. To find the state of a mixture of two phases, we need to know how much of each phase is present, that is, the composition of the mixture. The phase composition in a liquid-vapor mixture is given by the thermodynamic property called the quality of the mixture,

23 Tables Of Thermodynamic Properties Tables of thermodynamic properties of many substances are available, and in general, all these tables have the same form. In this section we will refer to the steam tables. The steam tables in Appendix B (according to Van Wylen )consist of five separate tables. Listing of the steam tables.

24 The saturated-liquid and saturated-vapor region, as seen in Fig. is listed according to the values of T in Table B.1.1 and according to the values of P (T and P are not independent in the two-phase regions) in Table B.1.2.

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27 The region of superheated vapor is given in Table B.1.3.

28 The region of compressed liquid is given in TableB.1.4.

29 The compressed-solid region not presented in Appendix B. The saturated-solid and saturated-vapor region is listed according to T in Table B.1.5, but the saturated-solid and saturated-liquid region, the third phase boundary line, is not listed in Appendix B.

30 Problem-1: Determine the phase for each of the following water states using the tables in Appendix B and indicate the relative position in the P v, T v, and P T diagrams. a. 120 C, 500 kpa b. 120 C, 0.5 m 3 /kg

31 From Table B.1.1, at 120 C, the saturation pressure is kpa. P > P sat So we have a compressed liquid, point a as shown in Fig. That is above the saturation line for 120 C. From Table B.1.2 with 500 kpa, the saturation temperature is C, T < T sat So we would say that it is a subcooled liquid. That is to the left of the saturation line for 500 kpa, as seen in the P T diagram.

32 (b) From Table B.1.1 with 120 C and notice that so the state is a two-phase mixture of liquid and vapor.

33 Problem-2: Determine the temperature and quality (if defined) for water at a pressure of 300 kpa and at each of these specific volumes: a. 0.5 m 3 /kg b. 1.0 m 3 /kg

34 (a) At P = 300 kpa, T sat = C, v f = m 3 /kg, and v g = m 3 /kg. v f < v (=0.5 m 3 /kg) < v g So the state is a two-phase mixture of liquid and vapor 0.5 = x , x = (b) v = 1.0 m 3 /kg > v g, the superheated vapor region. in which quality is undefined. T is found by linear interpolation between 300 C and 400 C. T = C.

35 Problem-3: A rigid vessel contains saturated ammonia vapor at 20 C. Heat is transferred to the system until the temperature reaches 40 C. What is the final pressure?

36 Since the volume does not change during this process, the specific volume also remains constant. From the ammonia tables, V g, 20 0 C = v 1 = v 2 = m 3 /kg and v g, 40 0 C = m 3 /kg v = m 3 /kg > v g, 40 0 C So, the final state the ammonia is superheated vapor. P 2 = 945 kpa

37 Problem-4: A vessel contains having a volume of 0.4 m 3 contains 2.0 kg of a liquid vapor and water vapor mixture in equilibrium at a pressure of 600 kpa. Calculate a) The volume and mass of liquid b) The volume and mass of vapor