Introduction to Humidity Basic Principles on Physics of Water Vapor

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1 Introucton to Humty Basc Prncpls on Physcs of Watr Vapor Prfac Ths Applcaton Not gs a short ntroucton to physcs of humty an th most mportant formula. It puts rlaton btn th most mportant ntts an pros som physcal framork. Snsron s a manufacturr of humty an tmpratur snsors s SHTxx prouct ln. Startng from rlat humty an tmpratur, ths Applcaton Not hlps to calculat most physcal alus scrbng atr apor. 1 Basc Consratons Humty scrbs th quantty of atr apor n a gas lk ar. Thr ar many ffrnt ays to xprss humty,.g. rlat humty, absolut humty, pont tmpratur or mxng rato. In th follong, th orgn of atr apor n ar s scuss an th most frquntly us fntons for humty ar scrb. 1.1 Th Orgn of Watr Vapor Consr a clos chambr th lqu atr as shon n Fgur 1. Th arag kntc nrgy, an thus th mpuls of th atr partcls n th lqu atr, s gorn by tmpratur. Som partcls ha hghr nrgy than th arag an can scap from th lqu so call aporaton abo lqu. Snc th gasous partcls bounc aroun th clos chambr som of thm ll ht th surfac of th lqu atr an may b trapp thr agan. Aftr som tm, thr ll b qulbrum hr th numbr of atr partcls lang th surfac of th lqu atr s qual to th numbr rjonng t. If ths qulbrum s ach, th numbr of gasous atr partcls rmans statstcally constant. lqu atr gasous atr Fgur 1 Clos chambr th lqu atr an gasous atr partcls (apor). In qulbrum, th numbr of atr partcls lang th surfac of th lqu atr s qual to th numbr rjonng t. Th gasous atr partcls xrt a prssur to th all. 1. Saturat Vapor Prssur an Snc th gasous atr partcls ht th all of th clos chambr n Fgur 1, a prssur ( stans for aporaton an s us for partal atr prssur only) s xrt to th all. In qulbrum, ths prssur s call saturat apor prssur abo atr or abo c, hch can b xprss by th Clapyron rlaton: T L, (1) TV hr L s th latnt hat, T th absolut tmpratur n Kln, an ΔV th olum chang of th phas transton. Snc th spcfc olum of th lqu s much smallr than that of th gas an assumng th apor gas to b al (pv = nrt), quaton (1) can b approxmat by th Clausus-Clapyron quaton T L, () R T hr R s th atr apor gas constant. Solng ffrntal quaton () las to th follong quaton for th saturat apor prssur knon as th Magnus formula β t ( t) α xp (3) λ t hr t s th tmpratur n C an th paramtrs α, β, an λ ar gn n Tabl 1. Conton T rang ( C) α (hpa) β λ ( C) Abo atr Abo c Tabl 1 Magnus Paramtrs for quaton (3). Th saturat apor prssur abo atr s plott n Fgur. Th corrsponng saturat apor prssur abo c (t) s calculat accorng to quaton (3) usng th corrsponng paramtrs from Tabl 1. Btn tmpraturs of -45 C an 6 C, quaton (3) has an uncrtanty of lss than ±.6% at 95% confnc ll. If mor accuracy s rqur, quatons for saturat apor.snsron.com Vrson. August 9 1/6

2 Applcaton Not: Physcs of Humty prssur oftn la to mplct functons that can only b sol numrcally. Th raton of most formula n th nxt sctons s bas on quaton (3). Saturaton Vapor Prssur (hpa) Tmpratur ( C) Fgur Saturat Vapour Prssur (t) 1.3 Watr Vapor Enhancmnt Factor In ar, atonal gass or gas mxturs ar prsnt. In ths cas, th total baromtrc prssur s th sum of th partal prssurs p p p p. (4) ntrogn oxygn othrs Snc th ffrnt gas partcls n ar ntract, a prssur pnnt corrcton may b rqur to ajust th atr apor prssur. Th ral actual apor saturaton prssur abo atr or c s gn by ' f or f ' (5) hr th atr apor nhancmnt factor f s gn by 6 1 f ( p) p.74 (6) p an th baromtrc prssur p can rang from 3kPa to 11kPa. At normal baromtrc prssur, t can b assum that f = 1. At 6bar, th nhancmnt factor s 1.. Trms of Humty.1 Rlat Humty an Rlat humty abo atr or abo c s mostly us for masurmnt purposs. It s fn as th rato of th partal apor prssur n ar to th saturat apor prssur at a gn tmpratur t, (t) t 1% (7) t an abo c t 1%. (8) t Thrfor, th rlat humty n th clos chambr of Fgur 1 s xactly 1%RH hn qulbrum s ach. Th alu of rlat humty s ry snst to tmpratur. Not, that at rlat humty of about 9%RH at ambnt tmpratur a tmpratur aton of Δt = 1 C rsults n a chang of up to Δ 5%RH. Calculaton of rlat humty at ffrnt tmpratur: Consr a quantty of ar th a constant numbr of gas an atr molculs th rlat humty 1 at tmpratur t 1. If, at constant prssur, th tmpratur s chang from t 1 to t, th corrsponng rlat humty gts β t1 xp λ t1 1. (1) β t xp λ t It s assum that no connsaton or cng occurs urng or aftr th tmpratur chang from t 1 to t. Conrson from rlat humty masur abo atr to rlat humty masur abo c : β t xp λ t. (11) β t xp λ t Most humty snsors ar calbrat rlat to (t), n blo C (supr cool atr) accorng to Worl Mtorologcal Organzaton (WMO). For conrson to alus rlat to (t) quaton (11) shoul b us.. D Pont Tmpratur t Consr a quantty of ar th constant numbr of atr partcls (.. no connsaton or aporaton) at a crtan tmpratur t an rlat humty < 1%. Th pont tmpratur t s fn as th tmpratur to hch ths quantty of ar must b cool on such that, at constant prssur, connsaton occurs ( = 1%). It can b r by usng quaton (1) th 1 = 1% an t 1 = t an thn rsol t to t : t β t ln λ t t λ 1%,. (1) β t β ln 1% λ t For calculatng frost tmpratur t f, hr c s sublmat out of saturat ar, th sam formula s.snsron.com Vrson. August 9 /6

3 Applcaton Not: Physcs of Humty appl th rplac by an Magnus coffcnts α, β an λ fn abo c (s Tabl 1)..3 Absolut Humty Absolut humty s fn by th mass of atr apor m HO pr hum ar olum V an can b xprss as mh O. (13) V Applyng th al gas la to partal atr prssur, V = nrt, hr V s th olum, n th numbr of atr partcls n mol, R = J mol 1 K 1 th unrsal gas constant an T th absolut tmpratur, an applyng th molar ght of atr M HO = 18.g/mol th follong quaton rsults V mh M n 18. n 18. O H O. (14) RT Combnng quaton (13) an quaton (14), on rs mh O V RT T (15) th T n Kln, n Pa an n g/m 3. Absolut humty n g/m 3 th n hpa an t n C s gn by 16.7 (16) 73.15C t or by substtutng from quaton (3) β t α xp 1% λ t (17) 73.15C t.4 Mxng Rato r Mxng Rato s th rato of th mass of atr apor an th mass of ry ar. sng th molar mass of ry ar an atr apor M 9. g mol -1 ryar M 18. g mol -1 H O on rs M 18. H O R T r. 6 M p ryar p (18) 9. R T n g/g th th total baromtrc prssur p. Mxng rato r n (g kg 1 ) s xprss n trms of rlat humty an tmpratur usng quaton (3): β t α xp 6 1% λ t r 6 p β t p α xp 1% λ t.5 Hat Inx HI. (19) Hat Inx ncats ho th human boy fls tmpratur. If rlat humty s lo human boy cools tslf by prspraton, sspatng hat from th boy. At hghr rlat humty th aporaton rat from th human skn s lor. In that cas, th boy cannot sspat hat as asly as t s th cas n ry ar. Th hat nx s bas on subjct masurmnts an s only manngful abo 5 C an %RH. Th most popular fnton of th Hat Inx s th on of th Natonal Wathr Src an Wathr Forcast Offc of th Natonal Ocanc an Atmosphrc Amnstraton (NOAA). Th Hat Inx n C s gn by HI c c 1t c 1 c t c 1 t 1 c c t 11 t th th follong coffcnts: c t c c c c c c c c c c -.13 Tabl Coffcnts for Hat Inx formula () Fgur 3 splays th Hat Inx as a functon of rlat humty an tmpratur. Tmpratur ( C) Rlat Humty (%RH) Fgur 3 Hat Inx n C. Valus blo C: no scomfort, C: som scomfort, 45 C: grat scomfort, abo 45 C: angrous, abo 54 C: hat strok mmnnt..snsron.com Vrson. August 9 3/6

4 Applcaton Not: Physcs of Humty 3 Proprts of Hum Ar 3.1 Spcfc Enthalpy Spcfc nthalpy h n kj/kg s th sum of nrgs n to arm up 1kg ry ar from C to t, aporatng apor ns most ar an armng up th apor from C to t: h c t l c t r (1) pa p th th hat capacty of ar c pa = 1.5 kj/(kg K), th hat capacty of atr apor c p = kj/(kg K) an th latnt hat of atr apor l = 51 kj/kg. r s th mxng rato ntrouc by quaton (18). 3. Dnsty of Hum Ar Th nsty rato btn ry an hum ar s gn by ρh α β t 18. xp 1 1 () ρar 1% p λ t 9. hr ρ h s th nsty of hum ar, ρ ar th nsty of ry ar an p th baromtrc prssur n Pa. Th paramtrs α, β an λ ar gn n Tabl 1. Analyzng th quaton t bcoms clar that hum ar has a lor nsty than ry ar. 3.3 Hat Capacty of Hum Ar Hat capacty of hum ar can b xprss as ρh CPh α β t 33.6 xp 1 1 (3) ρar CPar p λ t 9.1 th hat capacty of hum ar C Ph an ry ar C Par. Th quaton rals that th hat capacty of hum ar s hghr than that of ry ar. 4 Applcatons 4.1 Psychromtrc Chart - Mollr Dagram Psychromtrc charts or Mollr agrams splay aqupotntal curs of nthalpy, rlatng rlat humty on charts of mxng rato an tmpratur. Thy hlp to nagat n systms hr humty an tmpratur play an mportant rol.g. n a tumbl ryr. A typcal Mollr agram s shon n Fgur 4. Aqupotntal curs of nthalpy (blu lns) ar r from quaton (1) hl th curs of qual rlat humty (grn lns) ar r from quaton (19). As an xampl lt us consr a tumbl ryr for launry ryng: In a frst stp a quantty of ar th fx mxng rato s hat up outs th tumblr rum rprsnt as a horzontal path on th chart to th rght. In a scon stp th sam quantty of ar s la to th rum hr th ar absorbs atr apor from th t launry th path on th chart gos along a blu nrgy aqu-potntal ln as no nrgy s a at that stp. Entually th t ar s xtract from th rum an cool on to th ntal tmpratur th path gos to th rght th fx mxng rato untl t hts pont tmpratur an thn follos th 1%RH ln. For a tmpratur cycl btn 1 C an C, nrgy of kj pr kg ar s consum an up to 8g atr pr kg ar an ryng cycl may b conns. Mxng Rato (gho/kgar) kJ/kg 6kJ/kg 5kJ/kg kj/kg kj/kg kj/kg 1kJ/kg kj/kg 8kJ/kg 9kJ/kg 1kJ/kg 1% 8% 6% % % % Tmpratur ( C) Fgur 4 Mollr Dagram: Blu lns ar of qual nthalpy, r lns not qual rlat humty. 4. Wt- an Dry-Bulb Tmpratur A t- an ry-bulb hygromtr s shon n Fgur 5. C Ar flo C Fgur 5 Sktch of a t bulb hygromtr or psychromtr. Th t bulb thrmomtr masurs lor tmpratur than th ry bulb u to aporaton at ts bulb aporaton that at ts s pns on th local rlat humty % 5% %.snsron.com Vrson. August 9 4/6

5 Applcaton Not: Physcs of Humty To thrmomtrs, of hch on of thm s s nclos n a porous mum hch s mantan t by a t sock or ck masur tmpraturs t DB (ry bulb tmpratur) an t WB (t bulb tmpratur). As th t sock aporats atr ts tmpratur s ruc an as th aporaton s strongr n ry ar than n t ar, th tmpratur ffrnc s a masur for rlat humty. Ths t an ry bulb hygromtr s also call psychromtr psychros mans col n Grk languag. Humty can b calculat by usng th psychromtr quaton t B p t t (5) DB DB WB hr p s th total baromtrc prssur n hpa an B th psychromtr coffcnt that ars btn B = C 1 an B = C 1 pnng on th ntlaton of th psychromtr. Inual alus ar assgn by calbraton of th psychromtr. Rlat humty can b calculat by substtutng quaton (5) th quatons (3) an quaton (7) β tdb α xp B p tdb twb λ t1 tdb, twb 1%. β tdb α xp λ tdb (6) Rsolng quaton (6) on t WB allos for xprssng t bulb tmpratur n functon of rlat humty an tmpratur t: 5 Glossary Th follong Tabl gs symbols accorng to VDI/VDE 3514 stanar. Symbol Physcal Valu nt Rlat humty %RH Rlat humty abo atr %RH Rlat humty abo c %RH p Baromtrc prssur hpa pntrogn Partal ntrogn prssur (analogu for othr gass, xcpt atr) hpa Partal atr prssur hpa Saturat apor prssur abo atr hpa Saturat apor prssur abo atr n ral gas mxtur hpa Saturat apor prssur abo c hpa Saturat apor prssur abo c n ral gas mxtur hpa t,t Tmpratur C, K t D pont tmpratur C tf Frost tmpratur C r Mxng rato g/kg Absolut humty g/m 3 h Spcfc nthalpy J/kg α β t t WB t xp 1. (7) B p λ t 1%.snsron.com Vrson. August 9 5/6

6 Applcaton Not: Physcs of Humty Rson Hstory Dat Vrson Pag(s) Changs May Intal rlas July Complt n rlas Copyrght 9, SENSIRION. CMOSns s a tramark of Snsron All rghts rsr Haquartr an Sals Offcs Haquartr SENSIRION AG Phon: Laubsrutstr. 5 Fax: CH-871 Stafa ZH nfo@snsron.com Stzrlan Sals Offc SA: SENSIRION Inc. Phon: Tonsgat R., Sut 4 Fax: Wstlak Vllag, CA mchal.karst@snsron.com SA Sals Offc Japan: SENSIRION JAPAN Co. Lt. Phon: Postal Co: Fax: Shnagaa Staton Blg. 7F, nfo@snsron.co.jp 4-3-5, Takanaa, Mnato-ku Tokyo, Japan Sals Offc Kora: SENSIRION KOREA Co. Lt. Phon: ~7 #1414, Anyang Constructon Tor B/D, Fax: , Bsan-ong, Anyang-cty nfo@snsron.co.kr Gyongg-Pronc South Kora Sals Offc Chna: Snsron Chna Co. Lt. phon: Room 411, Man Tor fax: Jn Zhong Huan Busnss Bulng, nfo@snsron.com.cn Futan Dstrct, Shnzhn,.snsron.com.cn Postal Co PR Chna Fn your local rprsntat at: Vrson. August 9 6/6

Relate p and T at equilibrium between two phases. An open system where a new phase may form or a new component can be added

Relate p and T at equilibrium between two phases. An open system where a new phase may form or a new component can be added 4.3, 4.4 Phas Equlbrum Dtrmn th slops of th f lns Rlat p and at qulbrum btwn two phass ts consdr th Gbbs functon dg η + V Appls to a homognous systm An opn systm whr a nw phas may form or a nw componnt