2013-3-6 Chapter 12 Ideal Gas Mixture and Psychrometric Applications Learning Outcomes Describe ideal gas mixture composition in terms of mass fractions and mole fractions. Use the Dalton model to relate pressure,volume, and temperature and to calculate changes in U,H, and S for ideal gas mixtures Apply mass,energy,and entropy balances to systems involving ideal gas mixtures,including mixing processes. 1
2013-3-6 1 Chapter 12 Ideal Gas Mixture and Psychrometric Applications Learning Outcomes ►Describe ideal gas mixture composition in terms of mass fractions and mole fractions. ►Use the Dalton model to relate pressure, volume, and temperature and to calculate changes in U, H, and S for ideal gas mixtures. ►Apply mass, energy, and entropy balances to systems involving ideal gas mixtures, including mixing processes
2013-3-6 Learning Outcomes,cont. Demonstrate understanding of psychrometric terminology,including humidity ratio,relative humidity,mixture enthalpy,and dew point temperature. Use the psychrometric chart to represent common air-conditioning processes and to retrieve data. Apply mass,energy,and entropy balances to analyze air-conditioning processes and cooling towers. Describing Mixture Composition Consider a system consisting of a number of gases within a container of volume V.The te e perature and pressure of the gas mixture areand mixture can he des the numb by giving for each s m;or present ber of moles and molecular weightM e related by is in kmol when m;is in kg and M,is in kg/kmol. is in lbmol when m;is in (Eq.12.1) lb and M,is in Ib/lbmol. 2
2013-3-6 2 Learning Outcomes, cont. ►Demonstrate understanding of psychrometric terminology, including humidity ratio, relative humidity, mixture enthalpy, and dew point temperature. ►Use the psychrometric chart to represent common air-conditioning processes and to retrieve data. ►Apply mass, energy, and entropy balances to analyze air-conditioning processes and cooling towers. Describing Mixture Composition (Eq. 12.1) ►The mass mi , number of moles ni , and molecular weight Mi of component i are related by i i i M m n = ►Consider a system consisting of a number of gases within a container of volume V. The temperature and pressure of the gas mixture are T and p, respectively. ►The composition of the mixture can be described by giving the mass mi or the number of moles ni for each component present. ►ni is in kmol when mi is in kg and Mi is in kg/kmol. ►ni is in lbmol when mi is in lb and Mi is in lb/lbmol. Gas 1: n1, m1 Gas 2: n2, m2 Gas j: nj , mj Sum: n m …
2013-3-6 Describing Mixture Composition The mass fraction is the relative amount of each component in the mixture.The mass fractionf;of component i is n时= (Eq.12.3) m where m is the total mass of mixture The sum of the mass fractions of all components in a mixture equals unity. Describing Mixture Composition Alternatively,the mole fraction can be used to describe the relative amount of each component in the mixture.The 丹 mole fractiony;of component i is (Eq.12.6) where n is the total moles of mixture The sum of the mole fractions of all components in a mixture equals unity. The apparent (or average)molecular weight M of a mixture is determined as M=yM a mole-fraction average of the 1 component molecular weights: (Eq.12.9) 3
2013-3-6 3 Describing Mixture Composition ►The mass fraction is the relative amount of each component in the mixture. The mass fraction mfi of component i is (Eq. 12.3) m m mf i i = ►The sum of the mass fractions of all components in a mixture equals unity. where m is the total mass of mixture. Describing Mixture Composition ►Alternatively, the mole fraction can be used to describe the relative amount of each component in the mixture. The mole fraction yi of component i is n n y i i = (Eq. 12.6) i j i M ∑ yi M = = 1 (Eq. 12.9) ►The sum of the mole fractions of all components in a mixture equals unity. ►The apparent (or average) molecular weight M of a mixture is determined as a mole-fraction average of the component molecular weights: where n is the total moles of mixture
2013-3-6 Describing Mixture Composition Example:The molar analysis of a gas mixture is 50%N2,35%CO2,and 15%02.Determine (a)the apparent molecular weight of the mixture and (b)the analysis in terms of mass fractions. Solution: (a)The apparent molecular weight of the mixture is found using Eq.12.9 and molecular weights (rounded)from Table A-1 M=0.50(28)+0.35(44)+0.1532)=34.2kg/kmol Describing Mixture Composition ent,in kmol,is equal to its mole fraction,as shown in column (ii). Column(i)lists the respective molecular weights. Column (iv)gives the mass of each component,in kg per kmole of mixture,obtained using=nM,(Eq.12.1). hemasactionsnlsedaspercenagesncohecnatioial e values in column(iv)by the column 0.50 14 40.94 CO, 025 15.4 45.03 0.15 1404 4
2013-3-6 4 Describing Mixture Composition Example: The molar analysis of a gas mixture is 50% N2, 35% CO2, and 15% O2. Determine (a) the apparent molecular weight of the mixture and (b) the analysis in terms of mass fractions. (a) The apparent molecular weight of the mixture is found using Eq. 12.9 and molecular weights (rounded) from Table A-1 M = 0.50( ) 28 + 0.35(44)+ 0.15(32) = 34.2 kg/kmol Solution: Describing Mixture Composition ►Then, the amount ni of each component, in kmol, is equal to its mole fraction, as shown in column (ii). ►Column (iii) lists the respective molecular weights. ►Column (iv) gives the mass mi of each component, in kg per kmole of mixture, obtained using mi = ni Mi (Eq. 12.1). ►The mass fractions, listed as percentages in column (v), are obtained by dividing the values in column (iv) by the column total and multiplying by 100. (i) Component (ii) ni × (iii) Mi = (iv) mi (v) mfi % N2 0.50 × 28 = 14 40.94 CO2 0.35 × 44 = 15.4 45.03 O2 0.15 × 32 = 4.8 14.04 1.00 34.2 100 (b) Although the actual amount of mixture is not known, the calculations can be based on any convenient amount. We use 1 kmol of mixture
2013-3-6 Relatingp,K,and T for Ideal Gas Mixtures Many systems of practical interest involve mixtures where the overall mixture and each of its components can be modeled as ideal gases.For such mixtures the Dalton mixture model is commonly used. The overall mixture is considered an ideal gas P=IRT V (E4.12.10) The Dalton model also assumes each component behaves as an ideal gas as if it were alone at temperature T and volume V. Relating p,K,and T for Ideal Gas Mixtures Accordingly,with the Dalton model the individual components do not exert the mixture pressure p but rather a partial pressure denoted by Pi: (E4.12.11) V By combining Egs.12.10 and 12.11 the partial pressure P;can be determined alternatively from p,=yP(Eq.12.12) where the sum of the partial pressures equals the mixture pressure p=Ep (Eq.12.13) 5
2013-3-6 5 Relating p, V, and T for Ideal Gas Mixtures ►Many systems of practical interest involve mixtures where the overall mixture and each of its components can be modeled as ideal gases. For such mixtures the Dalton mixture model is commonly used. ►The overall mixture is considered an ideal gas V nRT p = (Eq. 12.10) ►The Dalton model also assumes each component behaves as an ideal gas as if it were alone at temperature T and volume V. Relating p, V, and T for Ideal Gas Mixtures ►Accordingly, with the Dalton model the individual components do not exert the mixture pressure p but rather a partial pressure denoted by pi : V n RT p i i = (Eq. 12.11) p y p i = i (Eq. 12.12) ►By combining Eqs. 12.10 and 12.11 the partial pressure pi can be determined alternatively from where the sum of the partial pressures equals the mixture pressure ∑ (Eq. 12.13) = = j i p pi 1
2013-3-6 Evaluating U,H,and S for Ideal Gas Mixtures For an ideal gas mixture,the values of U,H, and S are evaluated by adding the contribution of each component at the condition at which the component exists in the mixture. Evaluation of the specific interal energy or specific enthalpy of a mixture component i requires only a single intensive property:the mixture temperature,T. Evaluation of the specificentropy of a mixture component i requires two intensive properties. We will use the mixture temperature,T,and the partial pressure,p Evaluating U,H,and S for Ideal Gas Mixtures (Molar Basis) Accordingly,when working on a molar basis expressions for U,H,and S of a mixture consisting of several components are: U-4+a,++用属-之a(n 州=h+nA++nA-之nAn 2.6 6
2013-3-6 6 Evaluating U, H, and S for Ideal Gas Mixtures ►For an ideal gas mixture, the values of U, H, and S are evaluated by adding the contribution of each component at the condition at which the component exists in the mixture. ►Evaluation of the specific internal energy or specific enthalpy of a mixture component i requires only a single intensive property: the mixture temperature, T. ►Evaluation of the specific entropy of a mixture component i requires two intensive properties. We will use the mixture temperature, T, and the partial pressure, pi . Evaluating U, H, and S for Ideal Gas Mixtures (Molar Basis) ►Accordingly, when working on a molar basis expressions for U, H, and S of a mixture consisting of several components are:
2013-3-6 Evaluating U,H,and S for Ideal Gas Mixtures (Molar Basis) The mixture specific heats c,and c,are mole- fraction averages of the respective component specific heats. 6=2a 6-2 (Eq.12.23) (Eq.12.24) See Sec.12.4 for applications using these expressions for U,H,S,and the specific heats Evaluating U,H,and S for Ideal Gas Mixtures (Mass Basis) specific eoesnornS Table 12.2 R-A月，-yP ic..( 7
2013-3-6 7 Evaluating U, H, and S for Ideal Gas Mixtures (Molar Basis) ►See Sec. 12.4 for applications using these expressions for U, H, S, and the specific heats. ►The mixture specific heats and are molefraction averages of the respective component specific heats. vc p c (Eq. 12.23) (Eq. 12.24) Evaluating U, H, and S for Ideal Gas Mixtures (Mass Basis) ►When working on a mass basis the expressions for U, H, S, and specific heats of a mixture consisting of two components – a binary mixture – are: Table 12.2
2013-3-6 Engineering Applications of Ideal Gas Mixtures We encounter ideal gas mixtures in many important areas of application.Two of these are: 1.Systems involving chemical reactions and,in particular,combustion.For these applications we typically work on a molar basis.Combustion systems are considered in Chapter 13. 2.Systems for air-conditioning and other applications requiring close conro of water vapor in gas mixtures.For these applications we typically work on a mass basis.Systems of this type are considered in the second part of Chapter 12. Psychrometric Applications The remainder of this presentation centers on systems involving moist air.A condensed water phase may also be present in such systems. The term moist air refers to a mixture of dry air and water vapor in which the dry air is treated as a pure component. The Dalton model applies to moist air. By identifying gas 1 with dry air and gas 2 with water vapor,Table 12.2 gives moist air property relations on a mass basis. The study of systems involving moist air is known as psychrometrics. 8
2013-3-6 8 Engineering Applications of Ideal Gas Mixtures ►We encounter ideal gas mixtures in many important areas of application. Two of these are: 1. Systems involving chemical reactions and, in particular, combustion. For these applications we typically work on a molar basis. Combustion systems are considered in Chapter 13. 2. Systems for air-conditioning and other applications requiring close control of water vapor in gas mixtures. For these applications we typically work on a mass basis. Systems of this type are considered in the second part of Chapter 12. Psychrometric Applications ►The remainder of this presentation centers on systems involving moist air. A condensed water phase may also be present in such systems. ►The term moist air refers to a mixture of dry air and water vapor in which the dry air is treated as a pure component. ►The Dalton model applies to moist air. ►By identifying gas 1 with dry air and gas 2 with water vapor, Table 12.2 gives moist air property relations on a mass basis. ►The study of systems involving moist air is known as psychrometrics
2013-3-6 Moist Air Consider a closed system eratureT consisting of moist air occupying a volume /at mixture pressure p and mixture temperature T. In moist air the amount of water vapor present is much less than the amount of dry air: my <m lly <fla. -Boundary e t The Dalton model applies to the mixture of dry air and water vapor: Moist Air 1.The overall mixture and each component,dry air and water vapor,obey the ideal gas equation of state 2.Dry air and water vapor within the mixture are considered as if they each exist alone in volume /at the mixture temperature T while each exerts part of the mixture pressure 3.The partial pressures p and p,of dry air and water vapor are,respectively P=ypp,=八p (Eq.12.41b) vapo moist air expressions 9
2013-3-6 9 Moist Air ►Consider a closed system consisting of moist air occupying a volume V at mixture pressure p and mixture temperature T. ►The Dalton model applies to the mixture of dry air and water vapor: ►In moist air the amount of water vapor present is much less than the amount of dry air: mv << ma nv << na. Moist Air (Eq. 12.41b) 1. The overall mixture and each component, dry air and water vapor, obey the ideal gas equation of state. 2. Dry air and water vapor within the mixture are considered as if they each exist alone in volume V at the mixture temperature T while each exerts part of the mixture pressure. 3. The partial pressures pa and pv of dry air and water vapor are, respectively pa = ya p pv = yv p where ya and yv are the mole fractions of the dry air and water vapor, respectively. These moist air expressions conform to Eqs. (c) of Table 12.2
2013-3-6 Moist Air 4.The mixture pressure is the sum of the partial pressures of the dry air and the water vapor: P=P+Py 5.A typical state of water vapor in moist air is fixed using partial pressurep and the mixture temperature T. The water vapor is superheated at this state Moist Air 6.When p,corresponds to p at temperature T, the mixture is said to be saturated. 7.The ratio of p、and Pa is called the relative humidity,女. Pe)T.p (Eq.12.44 Relative humidity is usually expressed as a percent and ranges as 0一0≤≤100%- 10
2013-3-6 10 Mixture pressure, p , T Moist Air 4. The mixture pressure is the sum of the partial pressures of the dry air and the water vapor: p = pa + pv 5. A typical state of water vapor in moist air is fixed using partial pressure pv and the mixture temperature T. The water vapor is superheated at this state. Typical state of the water vapor in moist air Moist Air 6. When pv corresponds to pg at temperature T, the mixture is said to be saturated. T p p p , g v ⎟ ⎟ ⎠ ⎞ φ = (Eq. 12.44) Relative humidity is usually expressed as a percent and ranges as dry air only (pv = 0) 0 ≤ φ ≤ 100% saturated air (pv = pg) 7. The ratio of pv and pg is called the relative humidity, φ: