UNIT 6 PROPERTIES OF MOIST AIR

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1 UNIT 6 PROPERTIES OF MOIST AIR Proertie of Moit Air Structure 6.1 Introduction Objectie 6.2 Working Subtnce in Air Conditioning Gibb-Dlton Lw Mole Frction of Comonent Ge Moleculr Weight nd G Contnt for Dry Air nd Wter Vour 6.3 Pychrometric Proertie Secific Humidity or Humidity Rtio Dew Point Temerture Degree of Sturtion Reltie Humidity Enthly of Moit Air 6.4 Humid Secific Het 6.5 Wet Bulb Temerture 6.6 Adibtic Sturtion nd Thermodynmic Wet Bulb Temerture 6.7 Pychrometric Chrt Sturtion Line Reltie Humidity Line Contnt Secific Volume Line Contnt Thermodynmic Wet Bulb Temerture Line Contnt Enthly Line 6.8 Summry 6.9 Anwer to SAQ 6.1 INTRODUCTION The rt of ir conditioning deeloed only grdully from the redeceor rt of cooling, clening, heting nd entilting. Towrd the ltter hlf of the 19 th century, the deeloment in the rt of humidifying ir went long with the rogre of textile indutry in Englnd. It i worth mentioning here the nme of A.R. Wolff who deigned ir-conditioning ytem for mny hundred building during hi life-time. But it i W.H.Crrier ( ) who i known the Fther of Air Conditioning. He engineered nd intlled the firt yer-round ir-conditioning ytem, roiding for the four mjor function of heting, cooling, humidifying nd dehumidifying. He mde ue of ir wher for controlling the dew oint of ir by heting or chilling recirculted wter. Crrier reented hi remrkble er Rtionl Pychrometric Formule in n ASME meeting. Crrier lo emloyed the centrifugl comreor for refrigertion in A fr ir conditioning for comfort i concerned, it got off the ground in motion-icture thetre in 1920 in Chicgo emloying CO 2 mchine nd in 1922 in Lo Angele emloying NH 3 comreor. In the following chter, ttention will henceforth be focued on the rt nd cience of ir conditioning which i the gretet ingle liction of 81

2 Refrigertion nd Air Conditioning refrigertion, in ddition to tht of heting nd entiltion. For thi uroe it i necery to tudy the roertie of the working ubtnce in ir conditioning, iz., moit ir. Objectie After tudying thi unit, you hould be ble to know the comoition of moit ir, know the roertie of moit ir, tudy of ychrometric chrt, nd know the terminology of ychrometric chrt. 6.2 WORKING SUBSTANCE IN AIR CONDITIONING An imortnt thing for the tudent of ir conditioning i to recite tht the working ubtnce under tudy, iz., moit ir, i mixture of two ge. One of thee i dry ir which itelf i mixture of number of ge nd the other i wter our which my exit in turted or uerheted tte. One might k whether moit ir cn be conidered ure ubtnce. But ure ubtnce i homogeneou nd inrible in chemicl comoition. Thu, homogeneou mixture of ge i ure ubtnce until it comonent do not chnge in he. Dry ir i good exmle of uch kind of ure ubtnce. Wter our i certinly ure ubtnce. But moit ir i not ure ubtnce in ny roce in which condention or eortion of moiture occur. In uch ce, regulr chrt he to be deeloed to decribe the thermodynmic roertie of the mixture under different condition nd comoition. It i, thu, een tht moit ir conit of two rt: one, comriing dry ir, conidered the fixed rt, nd the other, olely of wter our, conidered the rible rt. The dry ir rt i mixture of number of ermnent ge with roximte comoition gien in Tble 6.1. Both dry ir nd wter our cn be conidered erfect ge ince both exit in the tmohere t low reure. Hence, erfect g lw cn be lied to them indiidully. In ddition, Gibb-Dlton lw for non-rectie mixture of ge cn be lied to the dry ir rt only to obtin it roertie ingle ure ubtnce, before etblihing the roertie of moit ir Gibb-Dlton Lw Dlton Lw of Prtil Preure Conider homogeneou mixture of non-recting idel ge 1, 2, etc., t temerture T, reure nd occuying olume V hown in Figure 6.1 Let the number of mole of indiidul ge be n 1, n 2, etc.,nd their reectie me be m 1, m 2, etc. Then we he for totl number of mole n nd totl m m n = n 1 + n 2 +..= n i m = m 1 + m = m i

3 Proertie of Moit Air where i i the number of ech g. Figure 6.1: G Mixture In the Dlton model, ech g i conceied of exiting ertely t the temerture T nd totl olume V of the mixture hown in Figure 6.2. Figure 6.2: Illutrting Dlton Model If one were to meure the reure exerted by indiidul ge, they would be found to be 1, 2,.etc., iz., le thn the totl reure of the mixture. Thee re referred to rtil reure. Conidering mixture nd ech comonent g exiting ertely t T nd V, we he for binry g mixture: V Mixture V = n R T n = RT Comonent 1 V= n 1 R T P 2 V = n 2 R T V n 1 = 1 RT n 2 V 2 = RT V RT n 1 + n 2 = n gie = 1 2 ( ) = 1 2 Thu, for mixture of idel ge, the totl reure i equl to the um of the rtil reure. Thi i known the Dlton lw of rtil reure. = or = i i Mole Frction of Comonent Ge The rtio of rtil reure to totl reure, nd olume frction re equl to the mole frction of the g. V n ( Let ) 6.4 V n Let y1 83

4 Refrigertion nd Air Conditioning Moleculr M of Mixture Since m = m 1 + m 2, nd m = Mn, m 1 = M 1 n 1, m 2 = M 2 n 2, we he Mn = M 1 n 1 + M 2 n 2 Thu M = y 1 M 1 + y 2 M 2 or M = i y i M i 6.5 where M rereent the moleculr m of the mixture nd n 1 = m 1 /M 1, n 2 = m 2 /M 2, etc. imilrly, for the mixture, n = m/m. Gibb Theorem Gibb Theorem further enuncite tht the internl energy of mixture i equl to the um of internl energie of the indiidul comonent, tken ech t the temerture nd olume of the mixture. Thu, we he for the internl energy of the mixture. mu = m 1 u 1 + m 2 u It cn lo be hown tht the enthly nd ecific het of the mixture cn, imilrly, be written mh = m 1 h 1 + m 2 h mc = m 1 c 1 + m 2 c Moleculr Weight nd G Contnt for Dry Air nd Wter Vour From the reectie mole frction nd moleculr me of comonent ge, the moleculr m of the dry ir rt my be comuted. Since rt by olume rereent the mole frction. Uing the lue for mole frction from Tble 6.1: We he moleculr M of dry ir M M y (0.7803) + 32 (0.2099) (0.0094) + 44(0.0003) (0.0001) = Tble 6.1: Comoition of Dry Prt in Atmoheric Air Comonent Moleculr M Prt by Volume Prt by M N O Ar CO H Knowing tht the lue of the unierl g contnt i kj/kg mole K, the g contnt for the two rt of moit ir re follow: Dry ir M = R = kJ/kg. K

5 Wter our M = R = kJ/kg. K where ubcrit refer to wter our. Proertie of Moit Air 6.3 PSYCHROMETRIC PROPERTIES The roertie of moit ir re clled ychrometric roertie nd the ubject which del with the behiour of moit ir i known ychrometry. Moit ir i mixture of dry ir nd wter our. They form binry mixture. A mixture of two ubtnce require three roertie to comletely define it thermodynmic tte, unlike ure ubtnce which require only two. One of the three roertie cn be the comoition. Wter our i reent in the tmohere t ery low rtil reure. At thi low reure nd tmoheric temerture, the wter our behe erfect g. The rtil reure of dry ir i lo below one tmohere which my lo be conidered to behe ery much erfect g. The Gibb-Dlton lw of erfect g mixture cn be lied to the moit ir. Since the wter our rt i continuouly rible, ll clcultion in irconditioning rctice re bed on the dry ir rt. For clculting nd defining the ychrometric roertie, we my conider certin olume V of moit ir t reure nd temerture T, contining m kg of dry ir nd m kg of wter our hown in Figure 6.3. The ctul temerture t of moit ir i clled the dry bulb temerture (DBT). The totl reure which i equl to the brometric reure i contnt. Figure Secific Humidity or Humidity Rtio Secific or bolute humidity or humidity rtio or moiture content i defined the rtio of the m of wter our to the m of dry ir in gien olume of the mixture. It i denoted by the ymbol ω. m 6.10 m V V 85

6 Refrigertion nd Air Conditioning where the ubcrit nd refer to dry ir nd wter our reectiely. Now R R T PV m T M M R R T PV m T M M Subtituting for m nd m from thee exreion in Eq. ( 6.10),we obtin M M The unit of ω re kg of wter our er kg of dry ir. Alo, ince denote the ctul totl tmoheric reure, then from Dlton lw So tht = Conidering tht the totl tmoheric reure remin contnt t rticulr loclity, we cn ee tht ω = f ( ) iz., the ecific humidity i function of the rtil reure of wter our only Dew Point Temerture The norml thermodynmic tte 1 hown in the Figure 6.4 () of moit ir i conidered unturted ir. The wter our exiting t temerture T of the mixture nd rtil reure of the our in the mixture i normlly in uerheted tte. If mle of uch unturted moit ir contining uerheted wter our i cooled (t contnt reure),the mixture will eentully rech the turtion temerture t d of wter our correonding to it rtil reure, t which oint the firt dro of dew will be formed, i.e., the wter our in the mixture will trt condening. Thi temerture t d i clled the dew oint temerture (DPT). Figure 6.4() : Thermodynmic Stte of Wter Vour in Moit Air 86

7 Moiture cn be remoed from humid ir by bringing the ir in contct with cold urfce or cooling coil whoe temerture i below it dew oint temerture. During the roce of cooling, the rtil reure of wter our nd ecific humidity ω remin contnt until the our trt condening Degree of Sturtion Conider the wter our in the uer heted thermodynmic tte 1 in unturted moit ir rereenting the control olume V. the wter our exit t the dry bulb temerture T of the mixture nd rtil reure hown in the Figure 6.4 (b). Proertie of Moit Air Figure 6.4 (b) : An Imginry Iotherml Proce Showing the Chnge of Stte of Wter Vour Now conider tht more wter our i dded in thi control olume V t temerture T itelf. The rtil reure will go on increing with the ddition of wter our until it reche lue correonding to tte 2 in Figure 6.4 fter which it cnnot incree further i the turtion reure or mximum oible of wter t temerture T. the thermodynmic tte of wter our i now turted t oint 2. the ir contining moiture in uch tte i clled turted ir. In thi tte the ir i holding the mximum mount of wter our( the ecific humidity being ω, correonding to the rtil reure ) t temerture T of the mixture. The mximum oible ecific humidity, ω t temerture T i thu The rtio of the ctul ecific humidity ω to the ecific humidity ω of turted ir t temerture T i termed the degree of turtion denoted by the ymbol μ. Thu Thu the degree of turtion i meure of the ccity of ir to borb moiture Reltie Humidity The reltie humidity i defined the rtio of the mole frction of wter our in moit ir to mole frction of wter our in turted ir t the me 87

8 Refrigertion nd Air Conditioning 88 temerture nd reure. From erfect-g reltionhi nother exreion for i exiting ril reureof wter or turtion reureof ure wter t me temerture Alo, m 6.16 m V RT RT 6.17 V When i equl to, i equl to unity, nd the ir i turted nd i conidered to he 100 er cent RH. From Eq (6.14) nd (6.17), we cn write Alo we my write (1 ) Enthly of Moit Air According to Gibb lw, the enthly of mixture of erfect ge cn be obtined by the net ummtion of the enthlie of the reectie contituent. Therefore the enthly of the moit ir h i equl to the ummtion of the enthlie of dry ir nd of the wter our ocited with the ir. Hence, h=h + wh 6.22 Per kg of dry ir, where h i the enthly of the dry ir rt nd wh i the enthly of the wter our rt. The chnge in enthly of erfect g being conidered function of temerture only, the enthly of the dry ir rt boe dtum of 0 0 C i exreed : h =C t=1.005 t kj/kg (=0.24 t Btu/lbm where t i in 0 F) where C = kj/kg.k i the ecific het of dry ir, nd t i the dry-bulb temerture of ir in 0 C. Auming the reference tte enthly zero for turted liquid t 0 0 C, the enthly of wter our t oint A in the boe Figure cn be exreed : h = h A = C w t d + (h fg ) d + C (t t d ) kj/kg where C w = ecific het of liquid wter t d = dew oint temerture (h fg ) d = ltent het of oriztion t DPT C =ecific het of uerheted our

9 Tking the ecific het of liquid wter kj/kg K nd tht of wter our 1.88kJ/kg K, in the rnge 0 to 60 0 C, we he h = t d + (h fg ) d (t t d ) At low reure for n idel g, the enthly i function of temerture only. Thu in Figure 6.5 the enthlie t oint B nd C re lo the me the enthly t A. Accordingly, enthly of wter our t A, t DPT of t d nd DBT of t, cn be determined more coneniently by the following two method: () h A = h C = (h g ) t 6.26 (b) h A = h B = (h fg ) 0 o C + C ( t 0) 6.27 Proertie of Moit Air Figure 6.5: Elution of Enthly of Wter Vour Prt Uing econd exreion nd tking the ltent het of oriztion of wter t 0 0 C 2501 k/kgk, we obtin the emiricl exreion for the enthly of the wter our rt h = t kj/kg And combining Eq 6.23 nd 6.24, we he the enthly of moit ir 6.28 h =1.005t + ω( t) kj/kg d HUMID SPECIFIC HEAT The enthly of moit ir cn lo be written h=(c + ωc ) t + ω(h fg ) 0 o C = C t + ω(h fg ) 0 o C 6.30 where C = C + ωc = ( ω) kj/ (kg d..) (K) i termed the humid ecific het. It i the ecific het of moit ir (1 + ω) kg er kg of dry ir. 6.5 WET BULB TEMPERATURE (WBT) A ychrometer comrie of dry bulb thermometer nd wet bulb thermometer. The dry bulb thermometer i directly exoed to the ir nd meure the ctul temerture of ir nd i clled dry bulb temerture. When the thermometer bulb i urrounded by wet cloth exoed to the ir. The temerture which i meured by the wick-coered bulb of uch thermometer 89

10 Refrigertion nd Air Conditioning indicte the temerture of liquid wter in the wick nd i clled the wet bulb temerture. It i denoted by the ymbol t'. The difference between the dry bulb nd wet bulb temerture i clled wet bulb dereion (WBD). WBD = (t t' ) If the mbient ir i turted, i.e. the RH i 100 er cent, then there will be no eortion of wter on the bulb nd hence WBT nd DBT will be equl. The WBT i n indirect meure of the dryne of ir. 6.6 ADIABATIC SATURATION AND THERMODYNAMIC WET BULB TEMPERATURE The thermodynmic wet bulb temerture or dibtic turtion temerture i the temerture t which the ir cn be brought to turtion tte, dibticlly, by the eortion of wter into the flowing ir. The equiment ued for the dibtic turtion of ir, in it imlet form, conit of n inulted chmber contining dequte quntity of wter. There i lo n rrngement for extr wter (known mke-u wter) to flow into the chmber from it to, hown in Figure Figure 6.6: Adibtic Sturtion of Air Let the unturted ir enter the chmber t ection 1. A the ir e through the chmber oer long heet of wter, the wter eorte which i crried with the flowing trem of ir, nd the ecific humidity of the ir incree. The mke u wter i dded to the chmber t thi temerture to mke the wter leel contnt. Both the ir nd wter re cooled the eortion tke lce. Thi roce continue until the energy trnferred from the ir to the wter i equl to the energy required to orie the wter. When tedy condition re reched, the ir flowing t ection 2 i turted with wter our. The temerture of the turted ir t ection 2 i known thermodynmic wet bulb temerture or dibtic turtion temerture. The dibtic turtion roce cn be rereented on T- digrm hown by the cure 1-2 in Figure 6.7. During the dibtic turtion roce, the rtil reure of our incree, lthough the totl reure of the ir-our mixture remin contnt. The unturted ir initilly t dry bulb temerture t d1 i cooled dibticlly to dry bulb temerture t d2 which i equl to the dibtic turtion temerture t w. It my be noted tht the dibtic turtion temerture i tken equl to the wet bulb temerture for ll rcticl uroe.

11 Proertie of Moit Air Figure 6.7: T-S Digrm for Adibtic Sturtion Proce Let h 1 = Enthly of unturted ir t ection 1, W 1 = Secific humidity of ir t ection 1, h 2, W 2 = Correonding lue of turted ir t ection 2, nd h fw = Senible het of wter t dibtic turtion temerture. Blncing the enthlie of ir t inlet nd outlet (i.e. t ection 1 nd 2), h 1 + (W 2 W 1 ) h fw = h 2 h 1 - W 1 h fw = h 2 W 2 h fw The term (h 2 W 2 h fw ) i known igm het nd remin contnt during the dibtic roce We know tht h 1 = h 1 + W 1 h 1 where h 2 = h 2 + W 2 h 2 h 1 = Enthly of 1 kg of dry ir t dry bulb temerture t dl, h 1 h 2 h 2 = Enthly of uerheted our t t er kg of our, = Enthly of 1 kg of ir t wet bulb temerture t w, nd = Enthly of turted our t wet bulb temerture t w er kg of our. Now the eqution (6.33) my be written : (h 1 + W 1 h 1 ) - W 1 h fw = (h 2 + W 2 h 2 ) - W 2 h W 1 (h 1 - h fw ) = W 2 (h 2 - h fw ) + h 2 - h 1 W W 1 = 2 h 2 h h 1 fw h h fw 2 h 6.7 PSYCHROMETRIC CHART All dt eentil for the comlete thermodynmic nd ychrometric nlyi of ir-conditioning rocee cn be ummried in ychrometric chrt. At reent, mny form of ychrometric chrt re in ue. The chrt which i mot commonly ued i the ω-t chrt, i.e. chrt which h ecific humidity or wter our reure long the ordinte nd the dry bulb temerture long the bci. The chrt i normlly contructed for tndrd tmoheric reure of 760 mm Hg or br, correonding to the reure t the men e leel. A tyicl lyout of thi chrt i hown in Figure

12 Refrigertion nd Air Conditioning Figure 6.8 : Contnt Proerty Line on Pychrometric Chrt Sturtion Line The turtion line rereent the tte of turted ir t different temerture. A n exmle of fixing uch tte on the chrt, conider n tmohere A t 20 o C nd turtion hown in Figure 6.9. From the tem tble t 20 o C, wter our reure Figure 6.9: Sturted Air t 20 o C = = mm Hg =2342 N/m 2 Prtil reure of dry ir = = = N/m2 Secific humidity t 20 o C turtion ω = (2342) = = kg w../kg d.. knowing t nd ω, oint cn be lotted. In imilr mnner, turtion tte t other temerture cn lo be lotted to drw the turtion line on the ychrometric chrt Reltie Humidity Line The reltie humidity i defined the rtio of the mole frction of wter our in moit ir to mole frction of wter our in turted ir t the me temerture nd reure. From erfect-g reltionhi nother exreion for i exiting ril reureof wter or turtion reureof ure wter t me temerture The reltie humidity line re cured line nd follow the turtion cure. 92

13 Generlly, thee line re drwn with lue 10%, 20%, 30% etc.nd u to 100%.The turtion cure rereent 100% reltie humidity. The lue of reltie humidity line re generlly gien long the line themele hown in Figure Proertie of Moit Air Figure 6.10: Reltie Humidity Line The line on ychrometric chrt for ny other deired lue of RH cn he contructed follow. Tking 50 er cent RH n exmle, the oint on the 20 C line correonding to thi RH mut be t the interection C (Figure 6.11) with the line rereenting our reure of At thi oint = = 1171 N/m 2 Figure 6.11: Drwing 50 ercent RH Line = = N/m2 ω = 0.622(1171) = kg w.. /kg d Likewie, oint for other temerture cn be lotted to contruct the comlete 50 er cent RH line. It my be noted tht ω = 0 line lo correond to zero er cent RH Contnt Secific Volume Line The contnt ecific olume line re obliquely inclined tright line nd uniformly ced hown in Figure Thee line re drwn u to the turtion cure. To etblih oint on line of contnt ecific olume, 0.90 m 3 /kg for exmle, From the erfect-g eqution, the ecific olume i 93

14 Refrigertion nd Air Conditioning R T m 3 /kg dry ir R T t ubtitute 0.90 for, the brometric reure for t, nd t rbitrry lue of T ole for. the ir of nd t lue then decribe the line of contnt. Figure 6.12: Secific Volume Line Contnt Thermodynmic Wet Bulb Temerture Line The wet bulb temerture line re inclined tright line nd non-uniformly ced hown in Figure 6.13 ny oint on the turtion cure, the dry bulb nd wet bulb temerture re equl. 94 Figure 6.13: Wet Bulb Temerture Line The lue of wet bulb temerture re generlly gien long the turtion cure of the chrt hown in the Figure Contnt Enthly Line The enthly (or totl het) line re inclined tright line nd uniformly ced hown in Figure Thee line re rllel to the wet bulb temerture line, nd re drwn u to the turtion cure. Some of thee line coincide with the wet bulb temerture line lo.

15 Proertie of Moit Air SAQ 1 Figure 6.14: Contnt Enthly Line The lue of totl enthly re gien on cle boe the turtion cure hown in the Figure () (b) (c) (d) Wht i the working ubtnce in ir conditioning? Would you cll it ure ubtnce? How do you clculte it moleculr m? Ditinguih between ecific humidity nd reltie humidity correlte degree of turtion with ecific nd reltie humidity. Differentite between ecific het of our nd humid ecific het. Wht i dibtic turtion roce? Show it on T-S digrm nd ychometric chrt. 6.8 SUMMARY The liction of ir-conditioning for the indutril uroe h oened new er in the ir-conditioning indutry. The ir-conditioning i commonly ued now-dy for the reertion of food, in utomobile nd rilwy, jute nd cloth indutrie nd mny other. Air-conditioning i field of work which neer tgnte. Indin tmoheric condition re ried in different rt of the country. No doubt, ir-conditioning will become neceity for Indin in coming few decde with the rid indutril deeloment nd with the economic growth of the country. 6.9 ANSWERS TO SAQ Refer the relent receding text in the unit or other ueful book on the toic lited in the ection Further Reding to get the nwer of the SAQ. 95

Mon 2:04:28 PM. Introduction

Mon 2:04:28 PM. Introduction Mon 2:04:28 PM Slide Nr. 0 of 18 Slide Introduction Air in the tmohere normlly contin ome wter vor (or moiture) nd i referred to tmoheric ir. By contrt, ir tht contin no wter vor i clled dry ir. It i often