V i = component volume of component i. T282. c Dr. Md. Zahurul Haq (BUET) Gas Mixture ME 203 (2017) 6 / 22. Moist Air T284

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1 Ideal Gas ixtures Properties of Homogeeous ixtures & Pyschrometry Dr. d. Zahurul Haq Professor Departmet of echaical Egieerig Bagladesh Uiversity of Egieerig & Techology (BUET) Dhaka-000, Bagladesh E 203: Egieerig Thermodyamics m = m + m 2 + m 3 + +m k = k i= m i mf i m i m : k i= mf i = = k = k i= i Y i i : k i= Y i = m i = mass of compoet i m = total mass of mixture i = umber of moles of compoet i = total umber of moles i mixture mf i = mass fractio of compoet i Y i = mole fractio of compoet i = molecular mass of compoet i = apparet molecular mass of mixture i c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) / 22 m i = i = m = m+m2+ +m k : m = = k k = k i= Y i = k ( i ) i= i Dry air (ole basis): 78.08±N 2, 20.95±O 2, 0.93±Ar, 0.03±CO 2: = (28.02) (32) (39.94) (44) = kg/kmol Apparet gas costat, R = Ru Dry air: R = 8.34 = kj/kg K = m = m k i= i mf i = m i m = i m = ( ) k mi = ) k mi /m = ( ) k mfi i= i=( i= = ( ) k mfi i= i = i / i / = Y Yi i mf i = Y i : mf i = Y i ( ) = Y Yi i : Y i = mfi = mf mfi i/ / c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 2 / 22 Coversio: ass Fractio ole Fractio = k i= ( ) Yii Y i = mfi = mf i/ mfi / Y i mf i mf i i H O CO = mfi/ = = 2.5 kg/kmol. = ( ki= mfi ) mf i = Y i = Y i Yi i Y i Y i mf i H O CO = Y i = 2.5 kg/kmol. c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 3 / 22 c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 4 / 22

2 P-v-T Behaviour of Gas ixtures Dalto s Law of Additive Pressures The pressure of a gas mixture is equal to the sum of the pressures each gas would exert if it existed aloe at the mixture temperature ad volume. P = P + P 2 + +P k = k i= P i(t,v) P i = partial pressure of compoet i. Amagat s Law of Additive Volumes The volume of a gas mixture is equal to the sum of the volumes each gas would occupy if it existed aloe at the mixture temperature ad pressure. V = V + V 2 + +V k = k i= V i(t,p) V i = compoet volume of compoet i. T282 T28 P = P A + P B = P i(t,v) P V = V A + V B = ir ut/v R ut/v = i = Y i : Y i i = P i P = V i V V i (T,P) V = ir ut/p R ut/p = i = Y i (Ideal gas) c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 5 / 22 c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 6 / 22 Gibbs-Dalto s Law I a mixture of ideal gases each compoet of the mixture acts as if it were aloe i the systet the volume V ad the temperature T of the mixture. U = U + U 2 + +U k = k i= U i U = u = u + 2 u k u k = k i= i u i u specific iteral eergy o mole basis. = u = U = Y u + Y 2 u 2 + +Y k u k = k i= Y i u i U = mu = m u + m 2 u 2 + +m k u k = k i= m iu i = u = U m = mf u + mf 2 u 2 + +mf k u k = k i= mf iu i u specific iteral eergy o mass basis. u = Y i u i : h = Y i h i : s = Y i s i : g = Y i g i u = mf i u i : h = mf i h i : s = mf i s i : g = mf i g i c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 7 / 22 oist Air T284 Atmospheric air cotais several gaseous compoets icludig water vapour ad cotamiats such as dust ad pollutats. Dry air refers oly to the gaseous compoets whe all water vapour ad cotamiats have bee removed. oist air refers to a mixture of dry air ad water vapour i which the dry air is treated as if it were a pure compoet. P = P a + P v = a + v m = + m v Y a = a : Y v = v P a = Y a P : P v = Y v P c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 8 / 22

3 Dew-poit Temperature, T dp Relative Humidity, φ ad oisture Cotet, ω Relative humidity, φ Pv P g : P g = P sat (T) ]T,P oisture cotet, ω mv ω = mv = PvVv/RuT P = v P v av a/r ut a P a Pv P a : 8.0/28.95 = ω = Pv P a = Pv P P v = φpg P φp g T286 T287 Whe the temperature of a cold drik is below the T dp of the surroudig air, it sweats. T dp = T sat (P v ) Costat-pressure coolig of moist air ad the dew-poit temperature o the T-s diagram of water. T285 c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 9 / 22 [Borgakke.2]: Cosider 00 m 3 of a air-water vapour mixture at 0. Pa, 35 o C, ad 70% relative humidity. Calculate the humidity ratio, dew poit, mass of air, ad mass of vapour. P v = φp g = 0.70(5.628)= 3.94 kpa T dp = T sat (P v ) = 28.6 o C P a = P P v = = kpa ω = kg/kg da = P a V/R a T = )/( )= 08.6 kg m v = ω = (08.6)= 2.77 kg [Borgakke.3]: Calculate the amout of water vapour codesed if the mixture of Example.2 is cooled to 5 o C i a costat-pressure process. T 2 < T dp : so codesatio occurs ad φ 2 =.0 P v2 = P g (T 2 ) = kpa P a2 = = kpa ω 2 = /99.28= kg/ kg da; ω = kg/kg da m w2 water codesatio, m v = m v2 + m w2 mw2 = mv mv2 ma m w2 = (ω ω 2 ) = 2.72 kg If heated to 35 o C, φ = 5% (very dry) c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) / 22 c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 0 / 22 oist Air Ethalpy, h T283 H = H a + H v = h a + m v H v h H = h a + mv h v = h a +ωh v h v h g (T) := h = h a +ωh g h a = c pa T =.005T [kj/kg da] h w = c pw T = 4.867T [kj/kg water] h g = T [kj/kg water vapour] T i o C. c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 2 / 22

4 [Borgakke.5]: Coolig ad dehumidificatio i a coolig coil of a AC: Adiabatic Saturatio Process T295 ass balace: = 2 = : m v = m v2 + m w2 Eergy balace: Q cv + m i h i = m e h e φ = Pv P g : ω = φpg P φp g h a =.005T : h v = h g = T : h w = 4.86T : h = h a +ωh v Q cv = (h a2 +ω 2 h v2 ) (h a +ω h v )+(ω ω 2 )h w2 = (h 2 h )+(ω ω 2 )h w2 = 4.64 kj/kg da T288 h v (T) h g (T), h v (T as ) h g (T as ), ω = m v /, ω = m v/m a h a (T)+m v h g (T)+(m v m v)h w (T as ) = h a (T as )+m vh g (T as ) ω = ha(tas) ha(t)+ω [h g(t as) h f (T as)] h g(t) h f (T as) : ω = pg(tas) P P g(t as) c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 3 / 22 c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 4 / 22 Wet Bulb Temperature, T wb ad Psychrometer T309 Adiabatic saturatio process provides a mea to measure humidity cotet of moist air, ad the process ca be approximated by usig a wet-bulb thermometer. Wet-bulb temperature, T wb is read fro wet-bulb thermometer, which is a ordiary liquid-i-glass thermometer whose bulb is eclosed by a wick moisteed with water. Dry-bulb temperature, T db refers simply to the temperature that would be measured by a thermometer placed i the mixture. Ofte a wet-bulb thermometer is mouted together with a dry-bulb thermometer to form a istrumet called a psychrometer. c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 5 / 22 Example: T db = 25 o C & T wb = 20 o C: P g (T) = P sat (T) : P g (T db ) = 3.69 kpa, P g (T wb ) = kpa φ =.0, ω = φ2pg(twb) P φ 2P g(t wb) ω = h a (T wb ) h a (T db ) =.005(T wb T db ) : h w (T wb ) = 4.86T wb h g (T db ) = kj/kg, h g (T wb ) = kj/kg ω = ha(twb) ha(tdb)+ω [h g(t wb) h w(t wb)] h g(t db) h f(t wb) ω = φpg(tdb) P φp g(t db) φ = = h = h a (T d b)+ωh g (T db ) = kj/kgda P v = φp g (T db ) = kpa T dp = T sat (P v ) = 7.6 o C Note That: By default, P = kpa. Psychrometric charts are prepared for atmospheric pressure. c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 6 / 22

5 Psychrometric Chart T29 T292 T290 c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 7 / 22 Psychrometric Processes c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 8 / 22 Adiabatic ixig of Two oist Air Streams T294 c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 9 / 22 T289 Dry air : + 2 = 3 ω ma+ω2 ma2 Water vapour : m v + m v2 = m v3 := ω 3 = + 2 (h a +ω h v )+ 2 (h a2 +ω 2 h v2 ) = 3 (h a3 +ω 3 h v3 ) = h + 2 h 2 = 3 h 3 := h 3 = h ma+h2 ma2 + 2 c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 20 / 22

6 [ora 2.4]: Usig psychrometric chart, solve the problem: T = ρ a (AV) = (AV) v a 2 = ρ a2 (AV) 2 = (AV)2 v a2 ω 3 = ω ma+ω2 ma2 + 2 #$%&7'9 0 = 3.0 kg/s = 6.06 kg/s = kg/kg da " 0! 0! Psychrometric chart: v a = 0.79 m 3 /kg v a2 = m 3 /kg ω 2 = kg/kg da Psychometric chart: state 3 will be o the lie joiig ad 2. T 3 = 9 o C Air at 0. Pa, 30 o C ad 80% RH is compressed isothermally to.0 Pa. Estimate the psychrometric coditio of the compressed air. : P = 0.Pa, φ = 0.8 ω = kg/kg da 2 :If ω = ω 2 = φdpv2 P φ 2p v2 φ 2 = 7.88 >.0 So water codesatio occurs, ad φ 2 = 00% ω 2 = φdpv2 P φ 2p v2 = = kg/kg da w = (ω ω 2 ) = 0.09 kg/kg da (codesatio) c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 2 / 22 c Dr. d. Zahurul Haq (BUET) Gas ixture E 203 (207) 22 / 22