normally contains some water vapor(or moisture)and is usually referred to as atmospheric air(or moist air). In contrast, air that contains no water vapor is called dry air(air without moisture). It is often convenient to treat atmospheric air as a mixture of water vapor and dry air. Although the amount of water vapor is small, it can not be ignored. The amount of water vapor in the air has significant impact on thermal comfort and many processes such as drying. Therefore, we can not treat moist air simply as dry air for analysis and calculation As dry air is far away from its critical point, it can be regarded as an ideal gas. Atmospheric air contains a very small amount of water vapor and the partial pressure of water vapor is very low. Thus, the water vapor in the atmospheric air can also be treated as ideal gas. That is, atmospheric air can be treated as a binary mixture of ideal gases, dry air and water vapor. However, phase change of water vapor in the atmospheric air often occurs, such as condensing, frosting, snowing, hailing, etc. Thus, it is not exactly the same as an ideal-gas mixture. Therefore, it needs some special state properties in order to describe the characteristics of moist air, such as the phase change of the water vapor and changes of the amount of water vapor 7.1.2 State of Atmospheric Air and its State Properties (1)The pressure of moist air As the Dalton law of partial pressure stated, the pressure of atmospheric air p is the sum of the partial pressure of the dry air pa and the partial pressure of the water vapor p,, that he partial pressure of water vapor reflects the amount of water vapor in moist air. It is referred to as apor pressure. The more moisture the atmospheric air contains, the higher the vapor pressure it has When there is no phase change in water vapor, both the dry air and the water vapor satisfy the ideal-gas relation. Tha Pv=raT Pv=RT where. T is thermodynamic temperature of the atmospheric air K:R,=2870J/(kg. K)and R,=4615J/(kg.K)are the gas constants of the dry air and the water vapor, respectively; v is the specific volume of moist air, m/kg In ventilation and air conditioning or drying processes, atmospheric air is often taken as the working fluid, where the total pressure of the moist air is the local atmospheric pressure. And eq (7-1) can be written as B=p=P+p The local atmospheric pressure varies with altitude, location, season and weather conditions, especially the altitude of a place (2) Saturated air and unsaturated Air When the temperature of the moist air ist, the corresponding saturated vapor pressure is p, (t) fo the moist air. If pr <Ps(t), then water vapor in the moist air is superheated vapor at the state A,as shown in Figure 7-1. The moist air at this point is known as unsaturated air. The unsaturated air is a mixture of dry air and superheated water vapor. Maintaining the temperature t constant, increasing the vapor pressure by adding some water vapor into the air, the state of the moist air changes from A towards C, as shown in Figure 7-1. When it reaches C on the saturated vapor line, P,=P,(),water vapor in the moist air becomes saturated vapor. At this point, the moist air is called saturated
108 normally contains some water vapor (or moisture) and is usually referred to as atmospheric air (or moist air). In contrast, air that contains no water vapor is called dry air (air without moisture). It is often convenient to treat atmospheric air as a mixture of water vapor and dry air. Although the amount of water vapor is small, it can not be ignored. The amount of water vapor in the air has significant impact on thermal comfort and many processes such as drying. Therefore, we can not treat moist air simply as dry air for analysis and calculation. As dry air is far away from its critical point, it can be regarded as an ideal gas. Atmospheric air contains a very small amount of water vapor and the partial pressure of water vapor is very low. Thus, the water vapor in the atmospheric air can also be treated as ideal gas. That is, atmospheric air can be treated as a binary mixture of ideal gases, dry air and water vapor. However, phase change of water vapor in the atmospheric air often occurs, such as condensing, frosting, snowing, hailing, etc. Thus, it is not exactly the same as an ideal-gas mixture. Therefore, it needs some special state properties in order to describe the characteristics of moist air, such as the phase change of the water vapor and changes of the amount of water vapor. 7.1.2 State of Atmospheric Air and its State Properties (1) The pressure of moist air As the Dalton law of partial pressure stated, the pressure of atmospheric air p is the sum of the partial pressure of the dry air pa and the partial pressure of the water vapor pv , that is p = pa + pv （7-1） The partial pressure of water vapor reflects the amount of water vapor in moist air. It is referred to as vapor pressure. The more moisture the atmospheric air contains, the higher the vapor pressure it has. When there is no phase change in water vapor, both the dry air and the water vapor satisfy the ideal-gas relation. That is, a a p v R T = v v p v R T = where, T is the thermodynamic temperature of the atmospheric air, K; R a = 287.0 J / kg K ( ) and R v = 461.5 J / kg K ( ) are the gas constants of the dry air and the water vapor, respectively; v is the specific volume of moist air, m3 /kg. In ventilation and air conditioning or drying processes, atmospheric air is often taken as the working fluid, where the total pressure of the moist air is the local atmospheric pressure. And eq. (7-1) can be written as B p p p = = + a v The local atmospheric pressure varies with altitude, location, season and weather conditions, especially the altitude of a place. （2）Saturated air and unsaturated Air When the temperature of the moist air is t , the corresponding saturated vapor pressure is p (t) s for the moist air. If p p (t) v s , then water vapor in the moist air is superheated vapor at the state A, as shown in Figure 7-1. The moist air at this point is known as unsaturated air. The unsaturated air is a mixture of dry air and superheated water vapor. Maintaining the temperature t constant, increasing the vapor pressure by adding some water vapor into the air, the state of the moist air changes from A towards C, as shown in Figure 7-1. When it reaches C on the saturated vapor line, p p (t) v = s , water vapor in the moist air becomes saturated vapor. At this point, the moist air is called saturated air
Saturated air is a mixture of dry air and saturated water vapor. Due to P,(t)is the maximal vapor pressure at the temperaturet, the amount of water vapor in the moist air reaches the maximum at point C. It can not increase any more, even if water vapor is sprayed into the air, it will drop out as water droplets. That is to say, saturated air is the air that can not hold any more moisture (3)Condensation and dew point temperature Figure 7-1 P-v and T-s diagram of the water vapor in moist air If unsaturated moist air at point A is cooled continuously at a fixed water vapor pressure and reaches oint B on the saturated vapor line, then the water vapor begins to condense. This phenomenon is known as condensation and the point b is called the dew-point. Temperature at this point is called the dew-point temperature, denoted by t. In other words, it is the temperature at which condensation begins when the air is cooled at constant pressure. And the dew point temperature is the saturation temperature corresponding to the vapor pressure, that is, Id=tsar(Pr) When it reaches the dew point, it becomes saturated air. If the temperature of the moist air continues to drop, then condensation is incurred. And the state of the moist air will change along the saturated vapor line, as shown by the curve B-D in Figure 7-1. At the same time, as the temperature drops, the vapor pressure also decreases (4)Dry-bulb temperature and adiabatic saturation temperature Dry-bulb temperature is the ordinary temperature of the moist air. The dry-bulb temperature of water apor and dry air are the same. It is denoted as'I. As shown in Figure 7-2, when the unsaturated with a certain amount of moisture at temperature t, flows through a long insulated evaporate into the moist air. During this process, the moisture contained by the air stream increases and temperature decreases as the result of providing the latent heat of vaporization to the water when it evaporates into the air. If the channel is long enough ig 7-2 Adiabatic Saturated Temperature the air stream may exit as saturated air(p=100%)at temperature t,, which is called the adiabatic saturation temperature. This device is called adiabatic saturator. During the evaporation process, water absorbs heat so that the air temperature drops. In general, the adiabatic saturation temperature is lower than the dry-bulb temperature of the moist air The adiabatic saturation temperature is a state property. It only depends on the state of the inlet moist (5) Relative humidity of moist air At a given temperature, the more water vapor(moisture) the moist air holds, the higher the vapor
109 Saturated air is a mixture of dry air and saturated water vapor. Due to p (t) s is the maximal vapor pressure at the temperature t , the amount of water vapor in the moist air reaches the maximum at point C. It can not increase any more, even if water vapor is sprayed into the air, it will drop out as water droplets. That is to say, saturated air is the air that can not hold any more moisture. (3) Condensation and dew point temperature If unsaturated moist air at point A is cooled continuously at a fixed water vapor pressure and reaches point B on the saturated vapor line, then the water vapor begins to condense. This phenomenon is known as condensation and the point B is called the dew-point. Temperature at this point is called the dew-point temperature, denoted by d t . In other words, it is the temperature at which condensation begins when the air is cooled at constant pressure. And the dew point temperature is the saturation temperature corresponding to the vapor pressure, that is, ( ) d sat pv t = t （7-2） When it reaches the dew point, it becomes saturated air. If the temperature of the moist air continues to drop, then condensation is incurred. And the state of the moist air will change along the saturated vapor line, as shown by the curve B-D in Figure 7-1. At the same time, as the temperature drops, the vapor pressure also decreases. (4) Dry-bulb temperature and adiabatic saturation temperature Dry-bulb temperature is the ordinary temperature of the moist air. The dry-bulb temperature of water vapor and dry air are the same. It is denoted as ‘ t ’. As shown in Figure 7-2, when the unsaturated moist air with a certain amount of moisture at temperature 1 t flows through a long insulated channel containing a pool of water, water may evaporate into the moist air. During this process, the moisture contained by the air stream increases and its temperature decreases as the result of providing the latent heat of vaporization to the water when it evaporates into the air. If the channel is long enough, the air stream may exit as saturated air ( =100%) at temperature 2 t , which is called the adiabatic saturation temperature. This device is called adiabatic saturator. During the evaporation process, water absorbs heat so that the air temperature drops. In general, the adiabatic saturation temperature is lower than the dry-bulb temperature of the moist air. The adiabatic saturation temperature is a state property. It only depends on the state of the inlet moist air. ⑸ Relative humidity of moist air At a given temperature, the more water vapor (moisture) the moist air holds, the higher the vapor Figure 7-1 p − v and T − s diagram of the water vapor in moist air Fig.7-2 Adiabatic Saturated Temperature
pressure p, it possesses. As stated, maintaining the temperature constant, the increase in the amount of moisture will cause the vapor pressure to rise. When it eventually reaches P,(0), the moist air becomes saturated air. And the amount of moisture reaches the maximum value at the specified temperature Generally, the ratio of the amount of moisture the atmospheric air holds at a given temperature to the maximum amount the air can hold at the same temperature is defined as relative humidity denoted as o. In terms of this definition and the ideal-gas relation, it is expressed as m、PH/RT_P mas、p2F/RTp where, P, and p, are the vapor pressure and the saturated vapor pressure of the atmospheric air at temperature t, respectively. The vapor pressure of saturated air at a given temperature is equal to the uration pressure of water at that temperature. Relative humidity can also be expressed as the ratio of the vapor pressure to the saturation pressure of water vapor at that temperatur The relative humidity ranges from 0 for dry air to I for saturated air. It reflects the extent the air approaches the saturated air at the same temperature. The lower the value the less water vapor it holds, the more water vapor it can absorb, and the drier it is. Note that the amount of moisture the air can hold depends on its temperature. Therefore, the relative humidity of air changes with temperatur even when the amount of moisture it holds remains constant (6)Specific humidity(Humidity ratio) In ventilation and air conditioning or drying processes, it is often required to adjust the amount of ater vapor in the moist air. If a unit mass or a unit volume of moist air is chosen as the datum, it may bring some trouble because the mass or the volume will change during a process in which the temperature and the amount of moisture in the moist air changes as well. However, the amount of dry air does not change during energy and mass exchange processes. Therefore, the calculation of the properties of moist air is based on per unit mass of dry air The amount of water vapor in the air can be specified directly by the mass of water vapor present in per unit mass of dry air. This is called absolute or specific humidity(also called humidity ratio) denoted as d d=-(kg water vapor/kg dry air) Since there are m-P, V and ma Ra p RT substituting them into eq (7-4) yields the calculation T equation of the humidity ratio P R 622-Px=622-9P,(g water vapor/kg dry air) (7-5) R,P p-pr p-pp (7) Density and specific volume of moist air The density of moist air is the ratio of its total mass to its total volume that is According to the ideal-gas equation of state, we can get As we know, pa=p-p. Substituting these formulas above into eq(7-6), we can obtain 110
110 pressure v p it possesses. As stated, maintaining the temperature constant, the increase in the amount of moisture will cause the vapor pressure to rise. When it eventually reaches () s p t , the moist air becomes saturated air. And the amount of moisture reaches the maximum value at the specified temperature. Generally, the ratio of the amount of moisture the atmospheric air holds at a given temperature to the maximum amount the air can hold at the same temperature is defined as relative humidity, denoted as . In terms of this definition and the ideal-gas relation, it is expressed as v sat,v / = / v v v s v s m p V R T p m p V R T p = = (7-3) where, v p and s p are the vapor pressure and the saturated vapor pressure of the atmospheric air at temperature t , respectively. The vapor pressure of saturated air at a given temperature is equal to the saturation pressure of water at that temperature. Relative humidity can also be expressed as the ratio of the vapor pressure to the saturation pressure of water vapor at that temperature. The relative humidity ranges from 0 for dry air to 1 for saturated air. It reflects the extent the air approaches the saturated air at the same temperature. The lower the value , the less water vapor it holds, the more water vapor it can absorb, and the drier it is. Note that the amount of moisture the air can hold depends on its temperature. Therefore, the relative humidity of air changes with temperature even when the amount of moisture it holds remains constant. (6) Specific humidity (Humidity ratio) In ventilation and air conditioning or drying processes, it is often required to adjust the amount of water vapor in the moist air. If a unit mass or a unit volume of moist air is chosen as the datum, it may bring some trouble because the mass or the volume will change during a process in which the temperature and the amount of moisture in the moist air changes as well. However, the amount of dry air does not change during energy and mass exchange processes. Therefore, the calculation of the properties of moist air is based on per unit mass of dry air. The amount of water vapor in the air can be specified directly by the mass of water vapor present in per unit mass of dry air. This is called absolute or specific humidity (also called humidity ratio) denoted as d. (kg water vapor/kg dry air) v a m d m = (7-4) Since there are v v v p V m R T = and a a a p V m R T = , substituting them into eq.(7-4) yields the calculation equation of the humidity ratio, 622 622 (g water vapor/kg dry air) v a v v v s v a a a v s p R p M p p d R p p M p p p p = = = = − − (7-5 ) (7) Density and specific volume of moist air The density of moist air is the ratio of its total mass to its total volume, that is a v a v m m m V V + = = = + (7-6) According to the ideal-gas equation of state, we can get R T p a a a = ， v v v p R T = As we know, pa = p − pv . Substituting these formulas above into eq. (7-6 ), we can obtain
p=pa+, 0.0013152 Ra T It indicates that the density of moist air is less than that of dry air. And the higher the temperature the lighter the moist air is. At a fixed atmospheric pressure, the density of moist air is related to temperature and the specific humidity The specific volume of moisture air is defined as oold (7-8) Obviously, it is different from pv (8)Enthalpy of moist Air In most practical applications, the amount of dry air in the air-water vapor mixture remains constant, but the amount of water vapor changes. Therefore, the enthalpy of the atmospheric air is expressed per unit mass of dry air instead of per unit mass of moist air. It is the sum of the enthalpies of dry air and the water vapor H=mhtmh (7-9) h=H-m,+m, y =h+0.001dh Selecting the enthalpy at0 C as the datum point, the dry air enthalpy atoC is zero and thus the enthalpy of the dry air at the temperaturet is ha=Cp. /=1.olf kJ/kg: For water vapor, the specific heat at constant pressure c,,=1.86 kJ/(kg. K)and the latent heat of vaporization at 0C is r=2501 k/kg. Thus, the enthalpy of the water vapor at the temperature t is 2501+1.86t Therefore, the total enthalpy of moist air per unit mass dry air is h=1.0t+0.001d(2501+1.861)kJ/( kg dry ai I Example 7-11 10 000 m atmospheric air is at B=0. 1 MPa, t=30C and =60%.Determine the dew point temperaturet,, the humidity ratiod, the density p and the specific volume, the total enthalpy h and the mass m of the moist air. (Solution(1)The dew point temperature t p,=P,=0.6×4242=2545P From the steam table, we can obtain that the saturation temperature of water vapor corresponding to p,=2 545 Pa is 21.5C, which is the dew point temperature of the moist air. That is t=21.5℃ (2)The humidity ratio =16.24 g/(kg dry air) P (3)The density p and the specific volume v of the moist air The density p of the moist air is determined as following, l11
111 0.001315 v a v a p p R T T = + = − (7-7) It indicates that the density of moist air is less than that of dry air. And the higher the temperature, the lighter the moist air is. At a fixed atmospheric pressure, the density of moist air is related to temperature and the specific humidity. The specific volume of moisture air is defined as, 1 0.001d v + = (7-8) Obviously, it is different from v =1 . (8) Enthalpy of moist Air In most practical applications, the amount of dry air in the air–water vapor mixture remains constant, but the amount of water vapor changes. Therefore, the enthalpy of the atmospheric air is expressed per unit mass of dry air instead of per unit mass of moist air. It is the sum of the enthalpies of dry air and the water vapor. H m h m h = + a a v v （7-9） 0.001 a a v v a v a a H m h m h h h d h m m + = = = + Selecting the enthalpy at 0 ℃ as the datum point, the dry air enthalpy at 0 ℃ is zero and thus the enthalpy of the dry air at the temperature t is h c t t a = p,a =1.01 kJ/kg；For water vapor, the specific heat at constant pressure , 1.86 kJ/(kg K) p v c = and the latent heat of vaporization at 0℃ is r = 2501 kJ/kg. Thus, the enthalpy of the water vapor at the temperature t is, , 2501 1.86 v p v h r c t t = + = + Therefore, the total enthalpy of moist air per unit mass dry air is h =1.01t + 0.001d(2501 +1.86t) kJ/(kg dry air) (7-10) 【Example 7-1】10 000 m3 atmospheric air is at B = 0.1 MPa, t = 30 ℃ and = 60% . Determine the dew point temperature d t , the humidity ratio d , the density and the specific volume v , the total enthalpy H and the mass m of the moist air. 【Solution】⑴ The dew point temperature d t From the steam table, we can obtain that the saturation pressure of water vapor corresponding to t = 30 ℃ is 4 242 s p = Pa. Then the vapor pressure can be calculated by 0.6 4 242 2 545 v s p p = = = Pa From the steam table, we can obtain that the saturation temperature of water vapor corresponding to 2 545 v p = Pa is 21.5 ℃, which is the dew point temperature of the moist air. That is 21.5 d t = ℃ (2) The humidity ratio 5 2 545 622 622 =16.24 g /(kg dry air) 10 2 545 v v p d B p = = − − (3) The density and the specific volume v of the moist air The density of the moist air is determined as following
05 0.001315-=1.139kg T0.287×303 And the specific volume v of the moist air is 1+0.00ld 1+0.001×16.24 1.139 (4)The enthalpy of the moist air In terms of eq (7-10), h=1.01t+0.001d×(2501+1.861) =1.01×30+0.001×1624×(2501+1.86×30) =71. 8 kJ/kg dry air) When V=10 000 m, the mass of dry air is mn=P2=00-255×100106kg RT 287×303 So, the total enthalpy of the moist air is H=mh=11206×718 =804590kJ (5)The mass of the moist air m=m2(1+0.001d)=11206×(1+0.01624)=11388kg 【 Example7-2】A5m×sm×3 m room contains air at25°andl00 kPa with relative humidity of 75%. Determine (l) the dew point temperature of the moist air, (2)the partial pressure of the dry air, (3) the humidity ratio, (4)the enthalpy of air per unit mass of dry air, and (5)the masses of the dry air and (Solution I Assumptions: The dry air and the water vapor in the room are ideal gases Properties: The constant-pressure specific heat of air at room temperature is c,=1.005 kJ/(kg. K). For water at 25C, we know P,=3. 1687 kPa, and h, =2 546.29 kJ/kg (From table A-I in the (1) Determine the dew-point temperature of the moist ai The vapor pressure of the moist air is: p=P,=0.75x3 1687 kPa=2 376Pa As t=t(p,), from steam table, we can get the dew point temperature ta=20.12 C (2) The partial pressure of the dry air can be determined by Pa=P-P,=(100-2.376)kPa=97624kP (3)The humidity ratio of the air is determined from eq (7-5) 2376 100000-2376 15.14 g/kg dry air) (4)The enthalpy of air per unit mass of dry air can be calculated by using eq. (7-10) h=cnM+0.001·d·(2501+1.86) 1.005×25+0.01514×2547.5 63.69 kJ/(kg dry air) 112
112 100 2 545 3 0.001 315 0.001 315 1.139 kg/m 0.287 303 303 v a p p R T T = − = − = And the specific volume v of the moist air is 3 1 0.001 1 0.001 16.24 = 0.892 m /kg 1.139 d v + = + = (4) The enthalpy of the moist air In terms of eq.(7-10), 1.01 0.001 (2 501 1.86 ) =1.01 30+0.001 16.24 (2 501+1.86 30) =71.8 kJ/(kg dry air) h t d t = + + When 3 V =10 000 m , the mass of dry air is 5 (10 2 545) 10 000 11 206 kg 287 303 a a a p V m R T − = = = So, the total enthalpy of the moist air is 11 206 71.8 =804 590 kJ H m h = = a (5) The mass of the moist air m m d = + = + = a (1 0.001 ) 11 206 (1 0.016 24) 11 388 kg 【Example 7-2】A 5 m×5 m×3 m room contains air at 25 °C and 100 kPa with relative humidity of 75%. Determine (1) the dew point temperature of the moist air, (2) the partial pressure of the dry air, (3) the humidity ratio, (4) the enthalpy of air per unit mass of dry air, and (5) the masses of the dry air and water vapor in the room. 【Solution】 Assumptions: The dry air and the water vapor in the room are ideal gases. Properties: The constant-pressure specific heat of air at room temperature is 1.005 kJ/(kg K) p c = . For water at 25 °C, we know 3.168 7 kPa s p = ，and 2 546.29 kJ/kg v h = (From table A–1 in the appendix). ⑴ Determine the dew-point temperature of the moist air The vapor pressure of the moist air is: 0.75 3.168 7 kPa 2 376 Pa v s p p = = = As d s ( ) v t t p = ，from steam table, we can get the dew point temperature d t = 20.12 ℃ (2) The partial pressure of the dry air can be determined by (100 2.376) kPa 97.624 kPa a v p p p = − = − = (3) The humidity ratio of the air is determined from eq.(7-5) 2 376 622 622 15.14 g/(kg dry air) 100 000 2 376 v v p d p p = = = − − (4) The enthalpy of air per unit mass of dry air can be calculated by using eq. (7-10), 0.001 (2501 1.86 ) p h c t d t = + + =1.005×25+0.015 14 ×2 547.5 =63.69 kJ/(kg dry air)