(5) The dry air and the water vapor fill the entire room. Therefore, the volume of every gas is equal to the volume of the room that is V=k 5×3=75m3 The masses of the dry air and the water vapor can be determined by using the ideal-gas relation to each gas individually P。97.624×75 =8561k Ra70.287×298 1.296k R7461.5×298 From the above examples, we can find that the state properties of moist air can be determined through analytical method if p, t and o of the moist air are specified. It indicates that at least three independent properties are required to determine the state of moist air, including two independent intensive properties and a parameter that reflects the amount of water vapor, such as the relative humidity, the humidity ratio, etc. p and T can be measured directly. Then, how to obtain the third properties, such as ta, P,, o, d etc, which reflect the amount of water vapor in the moist air? 7.2 The Measurement of Relative Humidity humidity is not only necessary to determine the properties of moist air, but also of great significance for industrial and gricultural measurement and control. weather forecasting Ordinary thermometer aerospace, micro-environment and other fields. However they can not be measured directly. It requires a long Wet-bulb saturation temperature indirectly. But it is difficult to realize. In practice, the wet-bulb temperaturet, is taken as a substitution for the adiabatic saturation temperature flow 一 Thus, the dry-bulb and wet-bulb thermometer are used to measure the relative humidity of the moist air indirectly Wet-bulb temperature is measured by using a thermometer whose bulb is covered with a cotton wick Fig 7-3 A Simple Arrangement to saturated into water and letting the air blow over the wick, Measure the Wet-bulb Temperature as shown in Figure 7-3. The temperature measured in this manner is called the wet-bulb temperature t,, and it is commonly used for air-conditioning principle involved is as following when unsaturated air passes over the wet wick. some of the ater in the wick difference between the air and the water After a while, the heat loss from the water by evaporation equals to the heat gain from the air, and the water temperature tends to be Fig7-4 The Relation among Dry-bulb Temperature, Wet-bulb temperature and Relative Humidity of Moist Air
113 Fig.7-3 A Simple Arrangement to Measure the Wet-bulb Temperature (5) The dry air and the water vapor fill the entire room. Therefore, the volume of every gas is equal to the volume of the room, that is, 3 V V V a v room = = = = 5 5 3 75 m The masses of the dry air and the water vapor can be determined by using the ideal-gas relation to each gas individually. 97.624 75 85.61 0.287 298 a a a a p V m R T = = = kg 2 376 75 1.296 461.5 298 v v v v p V m R T = = = kg From the above examples，we can find that the state properties of moist air can be determined through analytical method if p t, and of the moist air are specified. It indicates that at least three independent properties are required to determine the state of moist air, including two independent intensive properties and a parameter that reflects the amount of water vapor, such as the relative humidity, the humidity ratio, etc. p T and can be measured directly. Then, how to obtain the third properties, such as d , , , v t p d etc, which reflect the amount of water vapor in the moist air? 7.2 The Measurement of Relative Humidity The measurement of relative humidity and specific humidity is not only necessary to determine the properties of moist air, but also of great significance for industrial and agricultural measurement and control, weather forecasting, aerospace, micro-environment and other fields. However, they can not be measured directly. It requires a long channel in adiabatic saturator to measure the adiabatic saturation temperature indirectly. But it is difficult to realize. In practice, the wet-bulb temperature w t is taken as a substitution for the adiabatic saturation temperature. Thus, the dry-bulb and wet-bulb thermometer are used to measure the relative humidity of the moist air indirectly. Wet-bulb temperature is measured by using a thermometer whose bulb is covered with a cotton wick saturated into water and letting the air blow over the wick, as shown in Figure 7-3. The temperature measured in this manner is called the wet-bulb temperature w t , and it is commonly used for air-conditioning applications. The principle involved is as following: when unsaturated air passes over the wet wick, some of the water in the wick evaporates. As a result, the temperature of the water drops, creating a temperature difference between the air and the water. After a while, the heat loss from the water by evaporation equals to the heat gain from the air, and the water temperature tends to be （ p = 101325 Pa ） Fig.7-4 The Relation among Dry-bulb Temperature, Wet-bulb temperature and Relative Humidity of Moist Air
stable. The reading of the thermometer at this point is the wet-bulb temperature. Typically, when the wind speed is greater than 4 m/s, the difference between the wet-bulb temperature measured and the diabatic saturation temperature is very slight At a certain total pressure of the moist air, the relative humidity is only the function of the dry-bulb and wet-bulb temperatures t, and t, Figure 7-4 shows the relation among the dry-bulb temperature, the wet-bulb temperature and the relative humidity of the moist air at the 101 325 Pa. In fact, the process of the wet bulb temperature measurement is similar to the adiabatic humidifying process. The amount of moisture in the moist air can be calculated, and the relative humidity is then obtained using eq (7-7). Fig 7-4 gives out the results. Since the wet bulb temperature can be easily easured, it is often used to measure the relative humidity of the moist air indirectly In addition to the measurement methods above, the humidity-sensitivity characteristic of various materials varying with the humidity is applied to make some hygrometers. Electric hygrometer makes use of electrical characteristic of some materials, such as resistors, capacitors sensitivity to humidity and moisture, Optical hygrometer makes use of the water vapor absorbing spectrum to measure humidity. Today, hand-held electronic humidity measurement devices based on the capacitance change in a thin polymer film as it absorbs water vapor are widely used They are capable of sensing and displaying the relative humidity digitally with I percent accuracy 7.3 Psychrometric Chart (h-d Chart) It needs three separate properties to determine the state of moist air. Typically, the state of the atmospheric air at a given pressure is completely specified by two independent intensive properties Other properties can be calculated easily in terms of the relations introduced above. However, it may involve tedious calculations and incur errors. Therefore. there is a clear motivation to do these calculations once and to present the data in the form of easily readable charts. Such charts are called psychrometric charts(h-d charts). It is a plot of specific humidity versus enthalpy. It shows lines of constant dry-bulb temperature, relative humidity, etc, for the atmospheric air. They are widely used in air-conditioning engineering The h-d chart of the moist air for a fixed pressure is shown in Figure 7-5. It can clearly reflect various properties of the moist air. It is usually plotted for moist air at barometric pressure of 101325Pa but it can be used with sufficient accuracy for other pressures close to the basic one. On this chart enthalpy h, kJ/(kg dry air), is chosen to be the vertical axis, and the specific humidity, g/(kg dry air) -to be the horizontal axis. For the convenience of arranging various lines on the chart, the axes of coordinates are arranged at an angle of 135 c
114 stable. The reading of the thermometer at this point is the wet-bulb temperature. Typically, when the wind speed is greater than 4 m/s, the difference between the wet-bulb temperature measured and the adiabatic saturation temperature is very slight. At a certain total pressure of the moist air, the relative humidity is only the function of the dry-bulb and wet-bulb temperatures 1 and w t t . Figure 7-4 shows the relation among the dry-bulb temperature, the wet-bulb temperature and the relative humidity of the moist air at the 101 325 Pa. In fact, the process of the wet bulb temperature measurement is similar to the adiabatic humidifying process. The amount of moisture in the moist air can be calculated, and the relative humidity is then obtained using eq. (7-7). Fig.7-4 gives out the results. Since the wet bulb temperature can be easily measured, it is often used to measure the relative humidity of the moist air indirectly. In addition to the measurement methods above, the humidity-sensitivity characteristic of various materials varying with the humidity is applied to make some hygrometers. Electric hygrometer makes use of electrical characteristic of some materials, such as resistors, capacitors sensitivity to humidity and moisture; Optical hygrometer makes use of the water vapor absorbing spectrum to measure humidity. Today, hand-held electronic humidity measurement devices based on the capacitance change in a thin polymer film as it absorbs water vapor are widely used. They are capable of sensing and displaying the relative humidity digitally with 1 percent accuracy. 7.3 Psychrometric Chart ( h d − Chart) It needs three separate properties to determine the state of moist air. Typically, the state of the atmospheric air at a given pressure is completely specified by two independent intensive properties. Other properties can be calculated easily in terms of the relations introduced above. However, it may involve tedious calculations and incur errors. Therefore, there is a clear motivation to do these calculations once and to present the data in the form of easily readable charts. Such charts are called psychrometric charts ( h − d charts). It is a plot of specific humidity versus enthalpy. It shows lines of constant dry-bulb temperature, relative humidity, etc, for the atmospheric air. They are widely used in air-conditioning engineering. The h − d chart of the moist air for a fixed pressure is shown in Figure 7-5. It can clearly reflect various properties of the moist air. It is usually plotted for moist air at barometric pressure of 101325Pa, but it can be used with sufficient accuracy for other pressures close to the basic one. On this chart, enthalpy h , kJ/ (kg dry air), is chosen to be the vertical axis, and the specific humidity d , g/(kg dry air) —to be the horizontal axis. For the convenience of arranging various lines on the chart, the axes of coordinates are arranged at an angle of 135℃
水蒸气分压力5 附图2 大气 Fig. 7-5 Psychrometric Chart On the chart there is a curve called the saturation line. all the states of saturated air are located refore, it is also the curve of 100 percent relative humidity There are the following lines illustrated on the h-d chart (I)Lines of constant specific humidity and lines of constant enthalpy(Isenthalpic lines) raight lines vertical to the horizontal (lines of constant enthalpy )are parallel straight lines in an angle of 135c with the horizontal axis (2) Lines of constant dry-bulb temperature(Isotherm lines) Enthalpy of the moist air h=1.01t +0.001d (2501+1.86r)kJ/(kg dry air) shows that at a certain dry-bulb temperature, h is linear with d. The slopes of the constant dry-bulb temperature lines are slightly different from each other. The higher the temperature, the larger the intercept and the slope of constant dry-bulb temperature lines have. It means that constant dry-bulb temperature lines are not parallel However, since 1.861 2501, they are nearly parallel (3)Constant relative humidity lines(o lines) From d=622 9 -, we know that the relative humidity at a certain total pressure is a function of d and t. The relative humidity line =0 is corresponding to the longitudinal axis(vertical axis),it indicates the state of the dry air(d=0); the relative humidity =100% line is of the saturated air line Other constant relative-humidity curves generally have the same shape as that of the saturated air. The unsaturated air situates between the vertical axis and saturated moist air line. as shown in Figure 7-5 For moist air with the same specific humidity, the higher the dry-bulb temperature, the smaller is the value of o. Thus, the closer the constant relative humidity line approaches to the vertical axis Noted that when the total pressure of moist air is 10 Pa, the corresponding saturated temperature is 99.63 C. When the dry bulb temperature (299. C, the saturation vapor pressure is equal to the total pressure of the moist air, that is, P.=p. In other words, on the h-d chart for the total pressure 115
115 Fig.7-5 Psychrometric Chart On the chart, there is a curve called the saturation line. All the states of saturated air are located on this curve. Therefore, it is also the curve of 100 percent relative humidity. There are the following lines illustrated on the h − d chart: (1) Lines of constant specific humidity and lines of constant enthalpy (Isenthalpic lines) Constant specific humidity lines are straight lines vertical to the horizontal axis and isenthalpic lines (lines of constant enthalpy) are parallel straight lines in an angle of 135℃ with the horizontal axis. ⑵ Lines of constant dry-bulb temperature (Isotherm lines) Enthalpy of the moist air h t d t = + + 1.01 0.001 (2501 1.86 ) kJ/ (kg dry air) shows that at a certain dry-bulb temperature, h d is linear with . The slopes of the constant dry-bulb temperature lines are slightly different from each other. The higher the temperature, the larger the intercept and the slope of constant dry-bulb temperature lines have. It means that constant dry-bulb temperature lines are not parallel. However, since 1.86 2501 t , they are nearly parallel. ⑶ Constant relative humidity lines( lines) From 622 s s p d p p = − , we know that the relative humidity at a certain total pressure is a function of d t and . The relative humidity line = 0 is corresponding to the longitudinal axis (vertical axis), it indicates the state of the dry air ( d = 0 ); the relative humidity =100% line is of the saturated air line. Other constant relative-humidity curves generally have the same shape as that of the saturated air. The unsaturated air situates between the vertical axis and saturated moist air line, as shown in Figure 7-5. For moist air with the same specific humidity, the higher the dry-bulb temperature, the smaller is the value of . Thus, the closer the constant relative humidity line approaches to the vertical axis. Noted that when the total pressure of moist air is 105 Pa, the corresponding saturated temperature is 99.63 ℃. When the dry bulb temperature t 99.63 ℃, the saturation vapor pressure is equal to the total pressure of the moist air, that is, s p p = . In other words, on the h d − chart for the total pressure
10Pa, lines of constant turn upwards vertically after they intersect with the isotherm linet=9963C when the temperature is higher than 99.63 C (4)Constant vapor pressure lines Eq(7-5),d=622-P,, shows that at a fixed total pressure, when p, <<p, there is a one-to-one spondence relation between the vapor pressure P, and the specific humidity d h-d chart, another horizontal axis on the top of the horizontal axis of d is given, as shown in Figure 7-5, or a transformation line between constant d and constant p, is given, as shown in(A-) (5)Dew point temperature lines and wet-bulb temperature lines Dew point temperature(lines of td=constant), is the temperature of moist air cooled to be saturated at constant vapor pressures. Thus, lines of constant dew-point temperature are equivalent to lines of constant specific humidity. The dew-point temperature of atmospheric air at any point on the chart can be determined by drawing a vertical line(a line of d =constant or p,= constant) from the point to the saturated curve. The temperature value at the intersection point is the dew-point temperature Lines of constant wet-bulb temperature have a downhill appearance to the right. They lie very nearly parallel to the lines of constant enthalpy(in kJ/kg dry air). Therefore, the constant-enthalpy lines are deemed as constant wet-bulb-temperature lines. The wet bulb temperature of atmospheric air at any point can be determined by drawing a line of constant enthalpy from the point to the saturated curve on the chart. The temperature value at the intersection point is the wet-bulb temperature For saturated air, the dry-bulb, wet-bulb, and dew-point temperatures are identical (6) Heat and moisture ratio line The psychrometric chart also serves as a valuable aid in visual izing the air conditioning process During air conditioning processes of moist air, the heat and moisture exchange processes occur simultaneously and uniformly. The process 1-2 proceeds along a line connecting the initial state point I with the final state point 2 on the h-d chart. The slope of the line is referred to as the ratio of the change in enthalpy to that of the moisture, denoted by e d=1000-4 (7-13) The ratio of the change in enthalpy to that of the moisture reflects the inclination extent of the line 1-2, so it is also called shape factor. It shows the direction and characteristics of the heat and moisture exchange process On the h-d chart, for all kinds of processes, regardless of its initial and final states, the processes lines are parallel with each other as long as the ratios of the change in enthalpy to that of the moisture are the same. Therefore, on some h-d chart, in the lower part on the right side, series of lines of constant ratio of change in enthalpy to that of the moisture are drawn with slopes corresponding to starting from a randomly chosen initial point When the ratio of the change in enthalpy to that of the moisture, E, of the process is known, process line can be drawn from the initial state point I parallel to the line of a on the h-d chart When any property of the final state is given, for example, the dry-bulb temperature, then the intersection point of the isotherm line t, and the process line is the final state point 2. And then, it is easy to determine other properties of the final state. Therefore, it is very convenient to make use of the heat and humidity ratio a line to analyze thermodynamic processes of moist air Various air-conditioning processes can be illustrated on the psychrometric chart The isenthalpic 116
116 105Pa, lines of constant turn upwards vertically after they intersect with the isotherm line t =99.63℃ when the temperature is higher than 99.63 ℃. (4) Constant vapor pressure lines Eq. (7-5), 622 v v p d p p = − , shows that at a fixed total pressure, when v p p , there is a one-to-one correspondence relation between the vapor pressure pv and the specific humidity d . Typically, on the h d − chart, another horizontal axis on the top of the horizontal axis of d is given, as shown in Figure 7-5, or a transformation line between constant d and constant pv is given, as shown in (A- ). (5) Dew point temperature lines and wet-bulb temperature lines Dew point temperature (lines of d t =constant), is the temperature of moist air cooled to be saturated air at constant vapor pressures. Thus, lines of constant dew-point temperature are equivalent to lines of constant specific humidity. The dew-point temperature of atmospheric air at any point on the chart can be determined by drawing a vertical line (a line of d = constant or v p = constant) from the point to the saturated curve. The temperature value at the intersection point is the dew-point temperature. Lines of constant wet-bulb temperature have a downhill appearance to the right. They lie very nearly parallel to the lines of constant enthalpy (in kJ/kg dry air). Therefore, the constant-enthalpy lines are deemed as constant wet-bulb-temperature lines. The wet bulb temperature of atmospheric air at any point can be determined by drawing a line of constant enthalpy from the point to the saturated curve on the chart. The temperature value at the intersection point is the wet-bulb temperature. For saturated air, the dry-bulb, wet-bulb, and dew-point temperatures are identical. (6) Heat and moisture ratio line The psychrometric chart also serves as a valuable aid in visualizing the air conditioning process. During air conditioning processes of moist air, the heat and moisture exchange processes occur simultaneously and uniformly. The process 1-2 proceeds along a line connecting the initial state point 1 with the final state point 2 on the h d − chart. The slope of the line is referred to as the ratio of the change in enthalpy to that of the moisture, denoted by , 2 1 2 1 2 1 2 1 1000 1000 1000 h h h h h d d d d d − − = = = − − （7-13） The ratio of the change in enthalpy to that of the moisture reflects the inclination extent of the line 1-2, so it is also called shape factor. It shows the direction and characteristics of the heat and moisture exchange process. On the h d − chart, for all kinds of processes, regardless of its initial and final states, the processes lines are parallel with each other as long as the ratios of the change in enthalpy to that of the moisture are the same. Therefore, on some h d − chart, in the lower part on the right side, series of lines of constant ratio of change in enthalpy to that of the moisture are drawn with slopes corresponding to starting from a randomly chosen initial point. When the ratio of the change in enthalpy to that of the moisture, ,of the process is known, the process line can be drawn from the initial state point 1 parallel to the line of on the h d − chart. When any property of the final state is given, for example, the dry-bulb temperature, then the intersection point of the isotherm line 2 t and the process line is the final state point 2. And then, it is easy to determine other properties of the final state. Therefore, it is very convenient to make use of the heat and humidity ratio line to analyze thermodynamic processes of moist air. Various air-conditioning processes can be illustrated on the psychrometric chart. The isenthalpic
lines and constant specific humidity lines divide the h-d chart into four regions, as shown in Figure 7-6. If the initial state of moist air is indicated with the oint 1, the final state point may fall into the following four regions. The characteristics of the process vary with which region the final state point is in (1)>0 n region I, then both the enthalpy and the humidity ratio of the moist air increase during the process, that is Ah>0, Ad>0 if in region Il, then the enthalpy increases, but the humidity ratio decreases during the process, that IS A >oad<o if in region Ill, then both the enthalpy and the Figure 7-6 Characteristics of processes in humidity ratio of the moist air decrease during the four regions on h-d chart process, that is Ah<0, Ad<0 if in regionlV, then the enthalpy decreases but the humidity ratio increases during the process, that K Example 7-31 Moist Air is at atmospheric pressure B=0. 1 MPa and temperature t=30C with relative humidity = 60%. Determine the dew point temperature, the enthalpy, the humidity ratio and the vapor pressure of the moist air (Solution On psychrometric chart(h-d chart)of the moist air at the fixed atmospheric pressure B=0.1 MPa, we can find the position of the state, t=30C and =60%, other related properties can be obtained as Humidity ratio d=16.2 g/(kg h=71.5 g/kg dry air) Vapor pressure by intersecting the line of d=16.2 g/(kg dry air) with p,=f(d) line reads p, =2 500 Pa Dew-point temperature by intersecting the line of d=16.2 g/(kg dry air) with the line of saturated air 100%reads the dew-point temperature to be 21.5 C, that is t, =215C K Example 7-41 A room contains air at,=20 C,,=50%. 10 persons are reading some books in the room. Each person emits heat 530 kJ/h and moisture 80 gh. The heat transferred through the envelope and emitted by equipment into the room is 4 700 kJ/h and the moisture added is at the rate of 1200 g/h. The actual temperature of air supplied into the room is t,=12C. Determine the properties of the supply air, the mass of moist air enters the room per hour. Assume the local atmospheri pressure is B=0.1 MPa. ( Solution] The heat transferred into room per hour is Q=10×530+4700=10000kJ/h 2=20℃ The moisture added to the room per hour is The ratio of enthalpy change to moisture change is wt=12℃ =10001=-=1000×2=100x10000500 w1=12℃ Point 2 can be determined by the intersecting point of 117
117 Figure 7-6 Characteristics of processes in four regions on h d − chart lines and constant specific humidity lines divide the h d − chart into four regions, as shown in Figure 7-6. If the initial state of moist air is indicated with the point 1, the final state point may fall into the following four regions. The characteristics of the process vary with which region the final state point is in: if in region I, then both the enthalpy and the humidity ratio of the moist air increase during the process, that is h d 0, 0 ; if in region II, then the enthalpy increases, but the humidity ratio decreases during the process, that is h d 0, 0 ; if in region Ⅲ, then both the enthalpy and the humidity ratio of the moist air decrease during the process, that is h d 0, 0 ; if in regionⅣ, then the enthalpy decreases but the humidity ratio increases during the process, that is h d 0, 0 . 【Example 7-3】 Moist Air is at atmospheric pressure B = 0.1 MPa and temperature t = 30 ℃ with relative humidity = 60% . Determine the dew point temperature, the enthalpy, the humidity ratio and the vapor pressure of the moist air. 【Solution】 On psychrometric chart ( h d − chart) of the moist air at the fixed atmospheric pressure B = 0.1 MPa, we can find the position of the state, t = 30 ℃ and = 60% , other related properties can be obtained as, Humidity ratio d =16.2 g/(kg ) dry air Enthalpy h = 71.5 g/(kg ) dry air Vapor pressure by intersecting the line of d =16.2 g/(kg ) dry air with ( ) v p f d = line reads 2 500 Pa v p = . Dew-point temperature by intersecting the line of d =16.2 g/(kg dry air) with the line of saturated air =100% reads the dew-point temperature to be 21.5℃,that is 21.5 d t = ℃. 【Example 7-4】 A room contains air at 2 t = 20 ℃, 2 = 50% . 10 persons are reading some books in the room. Each person emits heat 530 kJ/h and moisture 80 g/h. The heat transferred through the envelope and emitted by equipment into the room is 4 700 kJ/h and the moisture added is at the rate of 1200 g/h. The actual temperature of air supplied into the room is 1 t = 12 ℃. Determine the properties of the supply air, the mass of moist air enters the room per hour. Assume the local atmospheric pressure is B = 0.1 MPa. 【Solution】 The heat transferred into room per hour is totally equal to Q=10×530+4700=10 000 kJ/h The moisture added to the room per hour is W=80×10+1200=2 000 g/h The ratio of enthalpy change to moisture change is 10 000 1 000 1 000 1 000 5 000 2 000 a a h Q m h d m d W = = = = = Point 2 can be determined by the intersecting point of Fig.7-7 Schematic for Example 7-4