Chapter 6 Water Vapor As a kind of working medium, water vapor has many advantages, such as proper therme nuclear power plants and many other places. Water vapor is also used as a heat transfer medium in various heat-exchangers. In thermodynamic systems, water vapor is usually not far away from liquid and often experiences phase changes during working processes. Thus, it can not be treated gas. In engineering calculations, the thermodynamic properties of water and water vapor are usually obtained by using water vapor charts and tables It needs to mention that working mediums used in refrigeration engineering, such as ammonia, Freon, etc, and liquefied petroleum gases in gas engineering, such as propane, butane, etc have similar thermodynamic properties with water vapor and follow the same rule of phase changes as water vapor, but with different phase change parameters. If we can grasp the property of water vapor and its phase change characteristics, it may help us to comprehend the properties of other vapors very easily Therefore, we choose water vapor as a representative to discuss. The water vapor generation process at constant pressure is introduced firstly. Then, the water vapor chart and tables are also introduced. In addition, we emphasize how to use them to solve practical problems 6.1 Vaporization and condensation Any kind of substance, including water, may undergo various phase change processes. The process involving a phase change from liquid to vapor is called vaporization. The intensity of vapor increases as the temperature of the liquid increases. There are two ways of vaporization: evaporation and boiling. Evaporation occurs at the liquid-vapor interface when the vapor pressure is less than the saturation pressure of the liquid at a given temperature. Boiling, on the other hand, occurs at the solid-liquid interface when a liquid is brought into contact with a surface maintained at a temperature T sufficiently above the saturation temperature T of the liquid. The boiling process is characterized by the rapid motion of vapor bubbles that form at the solid-liquid interface, detaching from the surface when they reach a certain size, and attempting to rise to the free surface of the liquid. However evaporation involves no bubble formation or bubble motion The process involving a change from the vapor to liquid phase is called condensation. It consumes energy during vaporization process and releases heat during condensation process If the liquid is placed in a closed vacuum vessel, it vaporizes faster than it condenses due to the low vapor concentration in the space of vapor side at the beginning. Gradually, the vapor molecule accumulates and its density increases continuously, and the number of molecules returning to the liquid surface also increases. Thus, the vaporization rate decreases gradually and the condensation rate increases.As these two rates become equal, vaporization and condensation will reach a dynamic equilibrium. This equilibrium state is called the saturated state. At this state, the vapor pressure called saturated pressure and the temperature is called saturated temperature. The liquid and vapor at saturated state is called saturated liquid and saturated vapor, respectively. The rate of vaporization depends on the temperature of the liquid and the rate of condensation is related to the apor molecular density. This molecule density is proportional to vapor pressure. Thus, the rate of condensation depends on the vapor pressure. That is, the temperature at which water starts boiling depends on the pressure; therefore, if the pressure is fixed, so is the boiling temperature. At a gi pressure, the temperature at which a pure substance changes phase is called the saturation temperature T. Likewise, at a given temperature, the pressure at which a pure substance changes
Chapter 6 Water Vapor As a kind of working medium，water vapor has many advantages, such as proper thermodynamic properties, non-toxic, odorless, cheap, and so on. It is widely used in steam turbines, steam engines, nuclear power plants and many other places. Water vapor is also used as a heat transfer medium in various heat-exchangers. In thermodynamic systems, water vapor is usually not far away from liquid and often experiences phase changes during working processes. Thus, it can not be treated as an ideal gas. In engineering calculations, the thermodynamic properties of water and water vapor are usually obtained by using water vapor charts and tables. It needs to mention that working mediums used in refrigeration engineering, such as ammonia, Freon, etc., and liquefied petroleum gases in gas engineering, such as propane, butane, etc. have similar thermodynamic properties with water vapor and follow the same rule of phase changes as water vapor, but with different phase change parameters. If we can grasp the property of water vapor and its phase change characteristics, it may help us to comprehend the properties of other vapors very easily. Therefore, we choose water vapor as a representative to discuss. The water vapor generation process at constant pressure is introduced firstly. Then, the water vapor chart and tables are also introduced. In addition, we emphasize how to use them to solve practical problems. 6.1 Vaporization and Condensation Any kind of substance, including water, may undergo various phase change processes. The process involving a phase change from liquid to vapor is called vaporization. The intensity of vaporization increases as the temperature of the liquid increases. There are two ways of vaporization: evaporation and boiling. Evaporation occurs at the liquid–vapor interface when the vapor pressure is less than the saturation pressure of the liquid at a given temperature. Boiling, on the other hand, occurs at the solid–liquid interface when a liquid is brought into contact with a surface maintained at a temperature T sufficiently above the saturation temperature Ts of the liquid. The boiling process is characterized by the rapid motion of vapor bubbles that form at the solid–liquid interface, detaching from the surface when they reach a certain size, and attempting to rise to the free surface of the liquid. However, evaporation involves no bubble formation or bubble motion. The process involving a change from the vapor to liquid phase is called condensation. It consumes energy during vaporization process and releases heat during condensation process. If the liquid is placed in a closed vacuum vessel, it vaporizes faster than it condenses due to the low vapor concentration in the space of vapor side at the beginning. Gradually, the vapor molecule accumulates and its density increases continuously, and the number of molecules returning to the liquid surface also increases. Thus, the vaporization rate decreases gradually and the condensation rate increases. As these two rates become equal, vaporization and condensation will reach a dynamic equilibrium. This equilibrium state is called the saturated state. At this state, the vapor pressure is called saturated pressure and the temperature is called saturated temperature. The liquid and vapor at saturated state is called saturated liquid and saturated vapor, respectively. The rate of vaporization depends on the temperature of the liquid and the rate of condensation is related to the vapor molecular density. This molecule density is proportional to vapor pressure. Thus, the rate of condensation depends on the vapor pressure. That is, the temperature at which water starts boiling depends on the pressure; therefore, if the pressure is fixed, so is the boiling temperature. At a given pressure, the temperature at which a pure substance changes phase is called the saturation temperature Ts . Likewise, at a given temperature, the pressure at which a pure substance changes
phase is called the saturation pressure Boiling can only occur when the temperature reaches the saturation temperature, which is corresponding to the specified pressure, or when the pressure drops below the saturation pressure corresponding to the specified temperature. It is clear that T, increases with Ps. Thus, a substance higher pressures boils at higher temperatures ts=f(Ps) 6.2 Phase Change Process of Water In this section, we mainly focus on the phase change process of a substance from liquid to vapor. As a familiar substance, water is chosen to demonstrate the basic principles involved. Remember, however, that all pure substances exhibit the same general behavior 6.2. 1 Phase Change Process of water (1)Pre-heat stage: compressed liquid to saturated liquid Consider a piston-cylinder device containing liquid water at 20C and I atm pressure(state 1, Fig 6-1(a)). Under this condition, water exists in the liquid phase, and it is called a compressed liquid, or a sub-cooled liquid, meaning that it is not about to vaporize. Heat is now transferred to the water and thus its temperature rises to, say, 60C. As the temperature rises, the liquid water expands slightly, and thus its specific volume increases. To accommodate this expansion, the piston moves up slightly. The pressure in the cylinder remains constant at I atm during this process since it is determined by the outside barometric pressure and the weight of the piston, both of which are constant. Water is still compressed liquid at this state since it has not started to vaporize. As more heat is transferred, the temperature keeps rising until it reaches 100C (state 2, Fig. 6-1(b)). At this point, water is still a liquid, but any heat addition will cause some of the liquid to vaporize. That is, a phase-change process from liquid to vapor is about to take place. a liquid that is about to vaporize is called a saturated liquid. Therefore, state 2 is the saturated liquid state (2)Vaporization stage: saturated liquid to saturated vapor Once boiling starts, the temperature stops rising until the liquid has completely vaporized. That is, the emperature will remain constant during the entire phase-change process if the pressure is held constant This can easily be verified by placing a thermometer into pure boiling water on top of a stove. At sea level(p=l atm), the thermometer will always read 100C if the pan is uncovered or covered with a weightless lid. During a boiling process, the only change observed is a large increase in the volume and a steady decline in the liquid level as a result of more liquid turning to vapor. Midway about the vaporization line(state 3, Fig. 6-1(c), the cylinder contains equal amounts of liquid and vapor. As heat is continuously transferred in, the vaporization process continues until the last drop of liquid is vaporized (state 4, Fig 6-1(d). At this point the entire cylinder is filled with vapor that is on the orderline of the liquid phase. Any heat loss from this vapor will cause some of the vapor to condense A vapor that is about to condense is called a saturated vapor. Therefore, state 4 is a saturated vapor state. A substance at states between 2 and 4 is referred to as a saturated liquid-vapor mixture since the liquid and vapor phases coexist in equilibrium at these states. The amount of energy absorbed during vaporization is called the latent heat of vaporization and is equivalent to the energy released during condensation. Once the phase-change process completes, the water turns back to a single phase egion again, this time vapor
99 phase is called the saturation pressure Boiling can only occur when the temperature reaches the saturation temperature, which is corresponding to the specified pressure, or when the pressure drops below the saturation pressure corresponding to the specified temperature. It is clear that Ts increases with s p . Thus, a substance at higher pressures boils at higher temperatures. ( ) s ps t = f （6-1） 6.2 Phase Change Process of Water In this section, we mainly focus on the phase change process of a substance from liquid to vapor. As a familiar substance, water is chosen to demonstrate the basic principles involved. Remember, however, that all pure substances exhibit the same general behavior. 6.2.1 Phase Change Process of Water (1) Pre-heat stage: compressed liquid to saturated liquid Consider a piston–cylinder device containing liquid water at 20°C and 1 atm pressure (state 1, Fig. 6–1(a)). Under this condition, water exists in the liquid phase, and it is called a compressed liquid, or a sub-cooled liquid, meaning that it is not about to vaporize. Heat is now transferred to the water and thus its temperature rises to, say, 60°C. As the temperature rises, the liquid water expands slightly, and thus its specific volume increases. To accommodate this expansion, the piston moves up slightly. The pressure in the cylinder remains constant at 1 atm during this process since it is determined by the outside barometric pressure and the weight of the piston, both of which are constant. Water is still a compressed liquid at this state since it has not started to vaporize. As more heat is transferred, the temperature keeps rising until it reaches 100°C (state 2, Fig. 6–1(b)). At this point, water is still a liquid, but any heat addition will cause some of the liquid to vaporize. That is, a phase-change process from liquid to vapor is about to take place. A liquid that is about to vaporize is called a saturated liquid. Therefore, state 2 is the saturated liquid state. (2) Vaporization stage: saturated liquid to saturated vapor Once boiling starts, the temperature stops rising until the liquid has completely vaporized. That is, the temperature will remain constant during the entire phase-change process if the pressure is held constant. This can easily be verified by placing a thermometer into pure boiling water on top of a stove. At sea level ( p = 1 atm), the thermometer will always read 100°C if the pan is uncovered or covered with a weightless lid. During a boiling process, the only change observed is a large increase in the volume and a steady decline in the liquid level as a result of more liquid turning to vapor. Midway about the vaporization line (state 3, Fig. 6-1(c)), the cylinder contains equal amounts of liquid and vapor. As heat is continuously transferred in, the vaporization process continues until the last drop of liquid is vaporized (state 4, Fig. 6–1(d)). At this point, the entire cylinder is filled with vapor that is on the borderline of the liquid phase. Any heat loss from this vapor will cause some of the vapor to condense. A vapor that is about to condense is called a saturated vapor. Therefore, state 4 is a saturated vapor state. A substance at states between 2 and 4 is referred to as a saturated liquid–vapor mixture since the liquid and vapor phases coexist in equilibrium at these states. The amount of energy absorbed during vaporization is called the latent heat of vaporization and is equivalent to the energy released during condensation. Once the phase-change process completes, the water turns back to a single phase region again, this time vapor
(c) (e) Figure 6-1 Phase Change Process of Water at Constant Pressure To analyze this mixture of saturated liquid and saturated vapor properly, we need to know the proportions of the liquid and vapor phases in the mixture. This is done by defining a new property called the quality x as the ratio of the mass of vapor to the total mass of the mixture where Quality has significance for saturated mixtures only. It has no meaning for compressed liquid or superheated vapor. Its value is between 0 and 1. The quality of a system that consists of saturated liquid is O, and the quality of a system consisting of saturated vapor is I (3)Superheat stage: saturated vapor to superheated vapor At the saturated vapor state 4, further transfer of heat results in an increase in both the temperature and the specific volume(Fig 6-1(e). At state 5, the temperature of the vapor is, let us say, 150C; and if ome heat is transferred from the vapor, the temperature may drop by somewhat but no condensation will take place as long as the temperature remains above 100oC (for p=l atm). a vapor that is not about to condense(i.e, not a saturated vapor) is called a superheated vapor Therefore, water at state 5 is a superheated vapor. The temperature difference between superheated vapor and saturated vapor is called the degree of superheat, that is At=t-t 6.2.2 Property Diagrams for Phase-Change Processes phase-change process of water at I atm pressure was described in detail in section 6. 2. 1. However, the variations of propertie during phase-change processes can be more d vapor easily studied and understood with the help of property diagrams. Now we repeat the above wet vapor pressures to develop the p-vand the T-sdiagrams for water Figure 6-2 p-v Diagram of Phase Change As I kg compressed liquid of water is heated at constant pressure, it follows a orizontal line on the p-v diagram, that is, the isobaric line changing from ao, a', a, a"to a, which oresents the state of unsaturated liquid, saturated liquid, saturated liquid and vapor mixture, saturated vapor and superheated vapor, respectively. Under other pressures, the isobaric lines can be obtained bo-b-b-b-b, do-d'-d
100 Figure 6-1 Phase Change Process of Water at Constant Pressure To analyze this mixture of saturated liquid and saturated vapor properly, we need to know the proportions of the liquid and vapor phases in the mixture. This is done by defining a new property called the quality x as the ratio of the mass of vapor to the total mass of the mixture: vapor total m x m = where, m m m total liquid vapor = + Quality has significance for saturated mixtures only. It has no meaning for compressed liquid or superheated vapor. Its value is between 0 and 1. The quality of a system that consists of saturated liquid is 0, and the quality of a system consisting of saturated vapor is 1. (3) Superheat stage: saturated vapor to superheated vapor At the saturated vapor state 4, further transfer of heat results in an increase in both the temperature and the specific volume (Fig. 6–1(e)). At state 5, the temperature of the vapor is, let us say, 150°C; and if some heat is transferred from the vapor, the temperature may drop by somewhat but no condensation will take place as long as the temperature remains above 100°C (for p = 1 atm). A vapor that is not about to condense (i.e., not a saturated vapor) is called a superheated vapor. Therefore, water at state 5 is a superheated vapor. The temperature difference between superheated vapor and saturated vapor is called the degree of superheat, that is s t = t −t . 6.2.2 Property Diagrams for Phase-Change Processes The phase-change process of water at 1 atm pressure was described in detail in section 6.2.1. However, the variations of properties during phase-change processes can be more easily studied and understood with the help of property diagrams. Now we repeat the above process at different pressures to develop the p v − and the T s − diagrams for water. As 1 kg compressed liquid of water is heated at constant pressure, it follows a horizontal line on the p v − diagram, that is, the isobaric line changing from 0 to x a a a a a 、 、 、 , which represents the state of unsaturated liquid, saturated liquid, saturated liquid and vapor mixture, saturated vapor and superheated vapor, respectively. Under other pressures, the isobaric lines can be obtained, such as 0 x b b b b b − − − − , 0 x d d d d d − − − − .... Connecting saturated liquid state points of Figure 6-2 p v − Diagram of Phase Change Processes
a、b、d"… and saturated vapor state at different pressures will form the saturated liquid line(x=0)and saturated vapor line(x=1). These two lines d, d superheated meet at the critical point C, forming a dome as shown in Fig. 6-2. All the compressed liquid states are located in the region to the wet vapor left of the saturated liquid line, called the compressed liquid region. All the Figure 6-3T-s Diagram of Phase Change Processes located to the ight of the saturated vapor line, called the superheated vapor region. In these two regions, the substance exists in a single phase, liquid or vapor. All the states that involve both phases in equilibrium are located under the dome, called the saturated liquid-vapor mixture region, or the wet region At the critical point, there is no longer difference between saturated liquid and saturated vapor The temperature, pressure, and specific volume of a substance at the critical point are called the critical temperature Te, critical pressure pe and critical specific c volume espectively. At pressures above the critical pressure, there is not a distinct phase change process. Instead, the specific volume of the substance continually increases, and at all times there is only one phase present. Eventually, it resembles a vapor, but we can never tell when the change has occurred. Above the critical state, there is no line that separates the compressed liquid region and the superheated vapor region. However, it is customary to refer to the substance as superheated vapor at temperatures above the critical temperature and as compressed liquid at temperatures below the critical temperature Critical properties of a substance are determined by the type of the substances, each substance has nly a group of critical properties. The critical properties of water vapor are t=373990,p=22064 MPa and 1=0003106m3/kg Similarly, the T-sdiagram of water vapor can be drawn, as shown in Fig. 6-3. The same haracteristics of the p-vand the T-sdiagram can be summarized as the following There are two lines on the diagram, which are the saturated liquid line (x=0) and saturated vapor line (x=0), and these two lines meet at one point: the critical point; and the two lines divide region into three region; during a phase-change process from liquid to vapor, substance will experience five kinds of states: unsaturated liquid state, saturated liquid state, wet vapor, saturated vapor state and superheated vapor state 6.3 Water Vapor Tables The ideal-gas equation of state is pv= RT. Water vapor differs from ideal gases and does not follow this equation. The equation of state for water vapor is very complicated and seldom directly used in practical engineering calculations. Therefore, property tables and charts are often compiled and plotted on the basis of experimental and theoretical data for practical application In the following, steam tables are used to demonstrate the use of thermodynamic property tables Property tables of other substances are used in the same manner. For various substances, the thermodynamic properties are listed in more than one table. In fact, a separate table is prepared for each region of interest, such as the superheated vapor, compressed liquid, and saturated(mixture) regions
101 a b d 、 、 …and saturated vapor states a b d 、 、 … ... at different pressures will form the saturated liquid line（ x = 0 ）and the saturated vapor line（ x =1 ）. These two lines meet at the critical point C, forming a dome as shown in Fig. 6-2. All the compressed liquid states are located in the region to the left of the saturated liquid line, called the compressed liquid region. All the superheated vapor states are located to the right of the saturated vapor line, called the superheated vapor region. In these two regions, the substance exists in a single phase, liquid or vapor. All the states that involve both phases in equilibrium are located under the dome, called the saturated liquid–vapor mixture region, or the wet region. At the critical point, there is no longer difference between saturated liquid and saturated vapor. The temperature, pressure, and specific volume of a substance at the critical point are called the critical temperature Tc , critical pressure c p and critical specific volume, respectively. At pressures above the critical pressure, there is not a distinct phase change process. Instead, the specific volume of the substance continually increases, and at all times there is only one phase present. Eventually, it resembles a vapor, but we can never tell when the change has occurred. Above the critical state, there is no line that separates the compressed liquid region and the superheated vapor region. However, it is customary to refer to the substance as superheated vapor at temperatures above the critical temperature and as compressed liquid at temperatures below the critical temperature. Critical properties of a substance are determined by the type of the substances, each substance has only a group of critical properties. The critical properties of water vapor are c t = 373.99 ℃, c p = 22.064 MPa and c v = 0.003106 m3 /kg. Similarly, the T s − diagram of water vapor can be drawn, as shown in Fig. 6-3. The same characteristics of the p − v and the T − s diagram can be summarized as the following: There are two lines on the diagram, which are the saturated liquid line （ x = 0 ） and saturated vapor line （ x = 0 ）; and these two lines meet at one point: the critical point; and the two lines divide the entire region into three regions: unsaturated liquid region, wet region and superheated vapor region; during a phase-change process from liquid to vapor, substance will experience five kinds of states: unsaturated liquid state, saturated liquid state, wet vapor, saturated vapor state and superheated vapor state. 6.3 Water Vapor Tables The ideal-gas equation of state is pv RT = . Water vapor differs from ideal gases and does not follow this equation. The equation of state for water vapor is very complicated and seldom directly used in practical engineering calculations. Therefore, property tables and charts are often compiled and plotted on the basis of experimental and theoretical data for practical application. In the following, steam tables are used to demonstrate the use of thermodynamic property tables. Property tables of other substances are used in the same manner. For various substances, the thermodynamic properties are listed in more than one table. In fact, a separate table is prepared for each region of interest, such as the superheated vapor, compressed liquid, and saturated (mixture) regions. Figure 6-3 T s − Diagram of Phase Change Processes
6.3. 1 Reference state and Reference values The values of u, h, and s cannot be measured directly, and they are calculated from measurable properties using the relations between thermodynamic properties. However, those relations give the changes in properties, not the values of properties at specified states. Therefore, we need to choose a convenient reference state and assign a value of zero for a convenient property or properties at that state. For water, the state of saturated liquid at 0.01 C is taken as the reference state and the internal energy and entropy are assigned to be zero values at this state. That is, for saturated water at 1o =tm =0.01C and Po=Pn=611659 Pa, o=0 kJ/kg, so=0 kJ/(kg. K). At this point the specific volume of water v=0.001 000 21 m/kg and the enthalpy h=0.611 7 J/kg, which approaches 0 kJ For refrigerant-134a, the state of saturated liquid at-40oC is taken as the reference state, and the enthalpy and entropy are assigned to be zero at that state. Note that sometimes different tables list different values for some properties at the same state as a result of using a different reference state However, in thermodynamics we are concerned with the changes in properties, and the reference state chosen is of no consequence in calculations as long as we use values from a single consistent set of tables or charts 6.3.2 Types of Steam Tables Steam tables are divided into a thermodynamic properties table for saturated liquid and saturated vapor and a thermodynamic properties table for unsaturated liquid and superheated vapor. In these tables, The subscript'is used to denote the properties of saturated liquid, and the subscript is to denote the properties of saturated vapor. For example, represents the specific volume of saturated liquid and y is the specific volume of saturated vapor The properties of saturated liquid and saturated vapor for water are listed in Tables A-I and A-2 n these two tables, the thermodynamic properties of saturated liquid and saturated vapor, including the specific volume v, v, specific enthalpy h, h and specific entropy s, s are listed and the latent heat of vaporization r is also given. The only difference between two tables is that properties are listed according to the pressure in Table A-1 and according to the temperature in Table A-2. It means they are based on different independent variables. Thus, it is more convenient to use Table A-l in the Appendix when pressure is given and to use Table A-2 when temperature is given Since the compressed liquid region and superheated region are single-phase regions (liquid or vapor phase only), temperature and pressure are no longer independent of each other and they can superheated vapor table is illustrated in Table A-3. In this table, the properties are listed against temperature for selected pressures starting with the saturated vapor data. The saturation temperature is given in parentheses following the pressure value. This table gives out the enthalpy, entropy and specific volume of the unsaturated water and superheated vapor. The data above the bold line in the table are the properties of unsaturated water, and the data below this line are properties of superheated In these tables, the internal energy u is not listed, as it can be determined by using the definition quation of the enthalpy, u=h-pr Water vapor tables are tables with discrete data If the data of the state properties to be found are not listed in the table, linear interpolation calculation must be done based on the properties of
102 6.3.1 Reference State and Reference Values The values of u, h, and s cannot be measured directly, and they are calculated from measurable properties using the relations between thermodynamic properties. However, those relations give the changes in properties, not the values of properties at specified states. Therefore, we need to choose a convenient reference state and assign a value of zero for a convenient property or properties at that state. For water, the state of saturated liquid at 0.01°C is taken as the reference state, and the internal energy and entropy are assigned to be zero values at this state. That is, for saturated water at 0 tp t t = = 0.01 ℃ and 0 tp p p = = 611.659 Pa, 0 u = 0 kJ/kg , 0 s = 0 kJ/(kg K) . At this point, the specific volume of water 0 v = 0.001 000 21 m3 /kg and the enthalpy 0 h = 0.611 7 J/kg, which approaches 0 kJ / kg. For refrigerant-134a, the state of saturated liquid at -40°C is taken as the reference state, and the enthalpy and entropy are assigned to be zero at that state. Note that sometimes different tables list different values for some properties at the same state as a result of using a different reference state. However, in thermodynamics we are concerned with the changes in properties, and the reference state chosen is of no consequence in calculations as long as we use values from a single consistent set of tables or charts. 6.3.2 Types of Steam Tables Steam tables are divided into a thermodynamic properties table for saturated liquid and saturated vapor and a thermodynamic properties table for unsaturated liquid and superheated vapor. In these tables, The subscript ′ is used to denote the properties of saturated liquid, and the subscript 〞is to denote the properties of saturated vapor. For example, ' v represents the specific volume of saturated liquid and " v is the specific volume of saturated vapor. The properties of saturated liquid and saturated vapor for water are listed in Tables A-1 and A-2. In these two tables, the thermodynamic properties of saturated liquid and saturated vapor, including the specific volume v v , , specific enthalpy h h , and specific entropy s s , are listed and the latent heat of vaporization r is also given. The only difference between two tables is that properties are listed according to the pressure in Table A-1 and according to the temperature in Table A-2. It means they are based on different independent variables. Thus, it is more convenient to use Table A–1 in the Appendix when pressure is given and to use Table A–2 when temperature is given. Since the compressed liquid region and superheated region are single-phase regions (liquid or vapor phase only), temperature and pressure are no longer independent of each other and they can conveniently be used as the two independent properties. The format of the compressed liquid and superheated vapor table is illustrated in Table A-3. In this table, the properties are listed against temperature for selected pressures starting with the saturated vapor data. The saturation temperature is given in parentheses following the pressure value. This table gives out the enthalpy, entropy and specific volume of the unsaturated water and superheated vapor. The data above the bold line in the table are the properties of unsaturated water, and the data below this line are properties of superheated vapor. In these tables, the internal energy u is not listed, as it can be determined by using the definition equation of the enthalpy, u = h − pv . Water vapor tables are tables with discrete data. If the data of the state properties to be found are not listed in the table, linear interpolation calculation must be done based on the properties of
neighboring states. But we can not use the properties to do interpolation calculations to get the state properties of wet vapor based on the properties of the states on different sides of the bold line in the table for thermodynamic properties of unsaturated water and superheated steam Variation of properties of compressed liquid with pressure is very mild. 100 times increase in the pressure often causes properties to change only less than 1 percent. This is because the compressed liquid properties depend on temperature much more strongly than they do on pressure. In the absence of compressed liquid data, a general approximation is to treat compre ssed liquid as saturated liquid at 6.3.3 Saturated Liquid-Vapor Mixture A saturated mixture can be treated as a combination of the saturated liquid and the saturated vapor To analyze this mixture properly, we need to know the quality x, that is the ratio of the mass of vapor to the total mass of the mixture For saturated mixtures, quality can serve as one of the two independent intensive properties eeded to describe a state. Note x=m, / motal that the properties of the saturated liquid are the same whether it exists alone or in a mixture with saturated vapor:. Then the properties of this"mixtur will simply be the average properties of the saturated liquid-vapor mixture under consideration Thus, at a given pressure, or a given temperature, the properties of a saturated mixture can be ulated by the following formula Specific volume of wet vapor Vr=xv+(1-x)v (6-2) Enthalpy of wet vapor h, =xh"+(1-x)h (6-3) Entropy of wet vapor Sx=xs+(1-x)s 4 where h, vand s represent enthalpy, specific volume, entropy of saturated liquid, respectively. And h, v"and s"represent enthalpy, specific volume, entropy of saturated vapor, respect The internal energy of saturated liquid-vapor mixture u is determined by u,=h 6. 4 The Enthalpy -Entropy Diagram(h-s Diagram)for Steam On T-s and p-v diagrams, the area enclosed by process curves and the axes of coordinates indicates the amount of heat addition/rejection and work output/input, but it is inconvenient for use of calculation. If using enthalpy-entropy diagram (h-s diagram), the length of lines can represent the amount of heat and work directly It is very intuitive, and thus it has been widely used in engineering calculations. The h-s diagram for steam is shown in Fig 6-4. The h-s diagram is constructed follows the enthalpy is chosen to be the axis of dinate and the origin of coordinates is assumed to be the state Fig 6-4 h-s Diagram for Water Steam of water at the triple point, where s. =0 and 1=0. Making use of the data taken from the steam tables, the saturated liquid line
103 / v total x m m = Fig.6-4 h − s Diagram for Water Steam neighboring states. But we can not use the properties to do interpolation calculations to get the state properties of wet vapor based on the properties of the states on different sides of the bold line in the table for thermodynamic properties of unsaturated water and superheated steam,. Variation of properties of compressed liquid with pressure is very mild. 100 times increase in the pressure often causes properties to change only less than 1 percent. This is because the compressed liquid properties depend on temperature much more strongly than they do on pressure. In the absence of compressed liquid data, a general approximation is to treat compressed liquid as saturated liquid at the given temperature. 6.3.3 Saturated Liquid–Vapor Mixture A saturated mixture can be treated as a combination of the saturated liquid and the saturated vapor. To analyze this mixture properly, we need to know the quality x, that is the ratio of the mass of vapor to the total mass of the mixture. For saturated mixtures, quality can serve as one of the two independent intensive properties needed to describe a state. Note that the properties of the saturated liquid are the same whether it exists alone or in a mixture with saturated vapor. Then the properties of this “mixture” will simply be the average properties of the saturated liquid–vapor mixture under consideration. Thus, at a given pressure, or a given temperature, the properties of a saturated mixture can be calculated by the following formula. Specific volume of wet vapor (6-2) Enthalpy of wet vapor (6-3) Entropy of wet vapor (6-4) where h , v and s represent enthalpy, specific volume, entropy of saturated liquid, respectively. And h , v and s represent enthalpy, specific volume, entropy of saturated vapor, respectively. The internal energy of saturated liquid-vapor mixture u is determined by x x x u h pv = − 6.4 The Enthalpy - Entropy Diagram ( h s − Diagram) for Steam On T − s and p − v diagrams, the area enclosed by process curves and the axes of coordinates indicates the amount of heat addition/rejection and work output/input, but it is inconvenient for use of calculation. If using enthalpy-entropy diagram ( h − s diagram), the length of lines can represent the amount of heat and work directly. It is very intuitive, and thus it has been widely used in engineering calculations. The h − s diagram for steam is shown in Fig.6-4. The h − s diagram is constructed as follows: the enthalpy is chosen to be the axis of ordinate and the entropy is the abscissa. The origin of coordinates is assumed to be the state of water at the triple point, where 0 0 s h = = 0 and 0 . Making use of the data taken from the steam tables, the saturated liquid line v xv x v x = + (1− ) hx = xh+ (1− x)h s xs x s x = + (1− )
x=0 and saturated vapor linex=1, meeting at the critical point C, are firstly plotted on the diagram. The saturated liquid line initiates from the origin of coordinates. In the wet region the isobars and isotherms are identical and are inclined straight lines. In the superheated region the isobars and isotherms diverge: the isobars run upwards and the isotherms turn to approach horizontal lines. In the wet region, lines of constant quality (x=const)are also plotted, which merge at the critical point C. Isochors(constant-volume lines) are also plotted on the h-s diagram, which run more steeply ds, compared with the isobars, as shown by the dotted line in Fig.6- It is convenient to use h-s diagram to determine the properties of water vapor. However, the accuracy of the readings depends on the person who uses it. Therefore, in practice, it is often to analyze thermodynamic processes of water vapor with the aid of h-s diagram and tables for water vapor simultaneously to simplify the calculations and to ensure the accuracy Usually, the entire h-s diagram is just partly given out. It is the part of the wet region with quality greater than 0.6 because the lines in the region with quality less than 0.6 is too dense and the data seldom used in projects. The h-s diagram of steam for application in engineering practice is hown in Appendix Figure 2 6.5 Thermodynamic Processes of Water Vapor The main purpose of analyzing thermodynamic processes of water vapor is to determine the final state and state properties of the process and to determine the thermodynamic energy and enthalpy changes of steams to obtain the energy conversion relations, including those between work output and heat ddition during the process. In general, steam tables and h-s diagram are used. The analysis is based on the first and the second laws of thermodynamics. Here we just discuss reversible processes. The (1)Based on the given conditions, determine the initial state and related properties (2)Based on the characteristics of the process and one of the properties given for the final state determine the final state and its properties (3) Based on the initial and final states, calculate the q, Au and w during the process Energy conversion relationships of water vapor are discussed respectively for the four basic thermodynamic processes as following 6.5.1 Isochoric process Durin isochoric (constant-volume) process, when heat is transferred to water, its pressure and temperature increase. The work output is zero as the volume remains constant. The heat addition leads to the increase in the internal energy of the water. And the increment of internal energy is equal to the heat addition. On h-s diagram, the process is depicted by the curve 1-2 in Fig. 6-5 The work output can be calculated by w=pdv=0 le amount of heat addition is The change in internal energy of the steam is △a=h2-h1-(P2-P1) The technical work available is w,=-]vdp=v(P1-P2)
104 x = 0 and saturated vapor line x =1, meeting at the critical point C, are firstly plotted on the diagram. The saturated liquid line initiates from the origin of coordinates. In the wet region the isobars and isotherms are identical and are inclined straight lines. In the superheated region the isobars and isotherms diverge: the isobars run upwards and the isotherms turn to approach horizontal lines. In the wet region, lines of constant quality ( x =const) are also plotted, which merge at the critical point C. Isochors (constant-volume lines) are also plotted on the h − s diagram, which run more steeply upwards, compared with the isobars, as shown by the dotted line in Fig.6-4. It is convenient to use h − s diagram to determine the properties of water vapor. However, the accuracy of the readings depends on the person who uses it. Therefore, in practice, it is often to analyze thermodynamic processes of water vapor with the aid of h − s diagram and tables for water vapor simultaneously to simplify the calculations and to ensure the accuracy. Usually, the entire h − s diagram is just partly given out. It is the part of the wet region with quality greater than 0.6 because the lines in the region with quality less than 0.6 is too dense and the data seldom used in projects. The h − s diagram of steam for application in engineering practice is shown in Appendix Figure 2. 6.5 Thermodynamic Processes of Water Vapor The main purpose of analyzing thermodynamic processes of water vapor is to determine the final state and state properties of the process and to determine the thermodynamic energy and enthalpy changes of steams to obtain the energy conversion relations, including those between work output and heat addition during the process. In general, steam tables and h − s diagram are used. The analysis is based on the first and the second laws of thermodynamics. Here we just discuss reversible processes. The analyzing procedure is as following: ⑴ Based on the given conditions, determine the initial state and related properties. ⑵ Based on the characteristics of the process and one of the properties given for the final state, determine the final state and its properties. ⑶ Based on the initial and final states, calculate the q u w , and during the process. Energy conversion relationships of water vapor are discussed respectively for the four basic thermodynamic processes as following. 6.5.1 Isochoric Process During an isochoric (constant-volume) process, when heat is transferred to water, its pressure and temperature increase. The work output is zero as the volume remains constant. The heat addition leads to the increase in the internal energy of the water. And the increment of internal energy is equal to the heat addition. On h s − diagram, the process is depicted by the curve 1-2 in Fig.6-5. The work output can be calculated by 0 2 1 w = pdv = The amount of heat addition is q = u The change in internal energy of the steam is ( ) 2 1 p2 p1 u = h − h −v − The technical work available is = − = − 2 1 1 2 w vdp v( p p ) t
h Fig 6-5 Isochoric Process of Water Vapor Fig 6-6 Isobaric Process of Water Vapor 6.5.2 Isobaric Process On h-s diagram, the isobaric(constant-pressure) process is depicted by the curve 1-2 in Fig. 6-6 The change in internal energy of the steam is v2=v 1) The work output is w=p(V2-n)=q-△ The technical work available is PI-p The amount of heat addition is 6.5.3 Isothermal Process On h-s diagram, the isothermal (constant-temperature) process is depicted by the curve 1-2 in Fig. 6-7 The change in internal energy of steam is Fig 6-7 Isothermal Process M=l2-l1=(h2-P22)-(-P1n1) The amount of heat addition is 7(S2-S1) The expansion work output is The technical work available is 6.5. 4 Adiabatic Process The adiabatic process is realized without heat addition or rejection and the entropy of the working medium during a reversible adiabatic(isentropic) process remains constant. That is, s=const(as shown by a straight line 1-2 in Fig. 6-8). Superheated steam turns into saturated vapor, and further into wet vapor. An irreversible process is shown by the dotted line 1-2 in Fig. 6-9. During an adiabatic expansion process, the pressure and the temperature of the steam decreases, however, the entropy Icreases Under isentropic conditions, it is easy to determine the final state properties on h-s diagram The amount of heat addition is equal to zero, that is
105 Fig .6-5 Isochoric Process of Water Vapor Fig. 6-6 Isobaric Process of Water Vapor Fig. 6-7 Isothermal Process 6.5.2 Isobaric Process On h s − diagram, the isobaric (constant-pressure) process is depicted by the curve 1-2 in Fig.6-6. The change in internal energy of the steam is ( ) 2 1 2 1 2 1 u = u −u =h −h − p v −v The work output is w= p(v2 − v1 ) = q − u The technical work available is = − = − 2 1 1 2 w vdp v( p p ) t The amount of heat addition is q = h2 − h1 6.5.3 Isothermal Process On h s − diagram, the isothermal (constant-temperature) process is depicted by the curve 1-2 in Fig.6-7. The change in internal energy of steam is ( ) ( ) 2 1 2 2 2 1 1 1 u = u −u = h −p v − h − p v The amount of heat addition is ( ) 2 1 q =T s − s The expansion work output is w= q −u The technical work available is wt = q − h 6.5.4 Adiabatic Process The adiabatic process is realized without heat addition or rejection and the entropy of the working medium during a reversible adiabatic (isentropic) process remains constant. That is, s = const (as shown by a straight line 1-2 in Fig. 6-8). Superheated steam turns into saturated vapor, and further into wet vapor. An irreversible process is shown by the dotted line 1-2 in Fig. 6-9. During an adiabatic expansion process, the pressure and the temperature of the steam decreases, however, the entropy increases. Under isentropic conditions, it is easy to determine the final state properties on h s − diagram. The amount of heat addition is equal to zero, that is
q The work output or input during an adiabatic process can be determined from the following The change in internal energy is M=(h2-P2V2)-(h-Pv1) The technical work available h Fig. 6-8 Re (Isentropic Process K Example 6-11 Steam expands isothermally at t=300'Cfrom P,=1 MPa to p2=0.1MPa Determine the amount of heat added to the steam, the change in internal energy and the expansion (Solution] From the steam table, we can get to know the water is superheated vapor at state"I 1=300 C and P,=1 MPa. The other properties of th state V1=0.25793m3/kg,h=30504kJkg,S1=71216kJkg Draw an isothermal line through the initial point"Iand it meets the isobar of p,=0. 1 MPa at point We can find h,=3 073. 8 kJ/kg,s,=8.214 8 kJ/kg. K)when P2=0. 1 MPa and t=300 C The amount of the heat addition can be determined by q=7(s2-s1)=573×(82148-7.1216)=6264kJkg e change in internal energy of the steam is equal to △a=(h2-P2V2)-(h-P11) (3073.8 0.1×10°×26388 )-(305041×10×0.25793 1000 1000 The expansion work output is =q-A=6264-17.5=6089kJ/ks K Example 6-21 Superheated vapor at 8 MPa and 500 Experiences an isentropic expansion process to P2=0.1 MPa. Determine the final state of the steam, the change in internal energy and the work Solution: We can find on the h-s diagram that at the end of expansion process, the steam becomes saturated liquid-vapor mixture with the quality of x=0.84 The initial properties of the superheated vapor at 8 MPa and 500C are h=3400kJ/kg,n1=0045m3/kg
106 Fig. 6-8 Reversible Adiabatic Process Fig. 6-9 Irreversible Adiabatic Process (Isentropic Process) The work output or input during an adiabatic process can be determined from the following equation ( ) ( ) 1 2 1 1 1 2 2 2 w = u −u = h − p v − h − p v The change in internal energy is ( ) ( ) 2 2 2 1 1 1 u = h − p v − h − p v The technical work available is wt = −h 【Example 6-1】 Steam expands isothermally at t = 300 ℃from p1 =1 MPa to p2 = 0.1 MPa. Determine the amount of heat added to the steam, the change in internal energy and the expansion work output. 【Solution】From the steam table, we can get to know the water is superheated vapor at state “1”, t = 300 ℃ and p1 =1 MPa. The other properties of this state are 3 1 v = 0.257 93 m /kg , 1 h = 3 050.4 kJ/kg , 1 s = 7.121 6 kJ/kg . Draw an isothermal line through the initial point “1”and it meets the isobar of 2 p = 0.1 MPa at point “2”.We can find 2 h = 3 073.8 kJ/kg ， 2 s = 8.214 8 kJ/(kg K) when 2 p = 0.1 MPa and t = 300 ℃， The amount of the heat addition can be determined by 2 1 q T s s = − = − = ( ) 573 (8.214 8 7.121 6) 626.4 kJ/kg The change in internal energy of the steam is equal to 2 2 2 1 1 1 6 6 ( ) ( ) 0.1 10 2.638 8 1 10 0.257 93 (3 073.8 ) (3 050.4 ) 1 000 1 000 17.5 kJ/kg = − − − u h p v h p v = − − − = The expansion work output is w= q −u = 626.4−17.5= 608.9 kJ/kg 【Example 6-2】 Superheated vapor at 8 MPa and 500℃experiences an isentropic expansion process to p2 = 0.1 MPa. Determine the final state of the steam, the change in internal energy and the work output by using the h s − diagram Solution: We can find on the h s − diagram that at the end of expansion process, the steam becomes saturated liquid-vapor mixture with the quality of x = 0.84 The initial properties of the superheated vapor at 8 MPa and 500℃ are 1 h = 3 400 kJ/kg; 1 v = 0.045 m3 /kg q = 0
The final properties at p,=0. 1 MPa are h2=2135kJ/kg,v2=1.5m3/k The change in internal energy amounts to △=h2-h-(P22-P)=2135-340(0.1×10×1.58×10°×045 1000 000 The expansion work is equal to =-△a=1055kJ/kg Chapter 7 Atmospheric Air 7.1 Atmospheric Air and state Properties 7. 1. 1 Definition of Atmospheric air(Moist air) Air is a mixture of nitrogen, oxygen, and small amounts of some other gases. Air in the atmosphere
107 The final properties at 2 p = 0.1 MPa are 2 h = 2 135 kJ/kg ; 3 2 v = 1.5 m /kg The change in internal energy amounts to 6 6 2 1 2 2 1 1 0.1 10 1.5 8 10 0.045 ( ) 2 135 3 400 ( ) 1000 1000 -1 055 kJ/kg u h h p v p v = − − − = − − − = The expansion work is equal to w u = − =1 055 kJ/kg Chapter 7 Atmospheric Air 7.1 Atmospheric Air and State Properties 7.1.1 Definition of Atmospheric air (Moist air) Air is a mixture of nitrogen, oxygen, and small amounts of some other gases. Air in the atmosphere