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