ESCI 241 Meteorology Lesson 6 Humidity

Transcription

1 ESCI 41 Mtorology Lsson 6 Humiity Raing: MT Chatr 5 PARTIAL PRESSURE In a mixtur of gass, ach gas scis contributs to th total rssur. ο Th rssur xrt by a singl gas scis is known as th artial rssur for that scis. ο For a mixtur of ial gass, th artial rssur of any scis can b foun from th ial gas law ali to that scis only. For xaml, in air th artial rssurs of,, an woul b V = n V = n V = n RT; RT; RT; = R T = R T = R T. ο Th nsitis us in th abo quations ar artial nsitis. Th total rssur is qual to th sum of th artial rssurs, an th total nsity is qual to th sum of th artial nsitis. Th artial rssur of a scis is roortional to th numbr of mols of th scis. Th artial rssur of a scis can b foun by multilying th total rssur by th olum (or mol) fraction of th scis. For xaml, th artial rssur of is foun by multilying atmoshric rssur by 0.1 (1%). VAPR PRESSURE If you ha a substanc in liqui form, som of th molculs will sca into th aor has. Th artial rssur u to ths aor molculs is known as th aor rssur. Sinc th aor rssur u to watr molculs is roortional to th numbr of watr aor molculs in th atmoshr, aor rssur is on masur of humiity. W usually not aor rssur as. (From now on w will us th trm aor rssur to man th aor rssur u to watr). Absolut humiity is fin as th mass of watr aor r unit olum. It is mrly th nsity of th watr aor,

2 Vaor rssur is rlat to absolut humiity ia th ial gas law, = R T, whr R is th scific gas constant for watr aor (46 J-kg 1 -K 1 ). SATURATI VAPR PRESSURE Th aor molculs ar colliing with ach othr. Som may stick togthr brifly to form tiny watr rolts. Howr, ths tiny watr rolts ar also constantly braking aart. If nough aor molculs ar rsnt, thr may b nough collisions to form a stabl oulation of liqui watr rolts. This is call saturation, an th aor rssur at this oint is call th saturation aor rssur ( s ). ο ot: You oftn har this xrss in trms of th air not bing abl to hol any mor watr aor. This is rally oor trminology, bcaus it osn t mattr what othr gasss ar rsnt. Thr coul b only ur nitrogn, ur hlium, or n nothing ls rsnt. Th saturation aor rssur woul not chang! Th saturation aor rssur is a function of tmratur. It is gin by th Clausius-Clayron quation s = L 1 x R T0 1 T 0, whr 0 is th aor rssur at som known tmratur T 0, an L is th latnt hat of aorization. W tyically us T 0 = 73.15K, 0 = 611 Pa, an L = J-kg 1. Th saturation aor rssur raily incrass as tmratur incrass. This mans that at warmr tmraturs thr can b mor watr aor rsnt without raching saturation. ο This is why you har that warm air can hol mor watr than col air, but again, this is oor trminology bcaus it is not th air that is holing th watr aor!

3 SPECIFIC HUMIDITY AD MIXIG RATI Vaor rssur an absolut humiity ar not ry connint xrssions for humiity (at last for mtorologists). W fin som othr masurs of humiity. Mixing ratio: Th mass of watr aor r mass of ry air. This woul b imnsionlss (if xrss as kg/kg, or g/g). Howr, it is mor oftn xrss as grams of watr aor r kg of ry air, so th units of mixing ratio ar usually xrss as g/kg. Mixing ratio can b rlat to aor rssur ia whr ε = R /R. RT R r = = = = ε, R R T ο Th saturation mixing ratio, r s, is foun by using s in th formula. Scific humiity: Th mass of watr aor r mass of air. ο Scific humiity is ry clos to mixing ratio, as shown q = = + = 1+ sinc r << 1 (xrss as g/g or kg/kg). r = r, 1+ r ο In mtorology, mixing ratio is us mor oftn than scific humiity, an for most uross th two can b consir as quialnt. 3

4 DEW PIT TEMPERATURE Th saturation aor rssur is a function of tmratur, an crass with crasing tmratur. If you cool moist air, ntually th saturation aor rssur will qual th aor rssur, an saturation will b rach. Th tmratur at which th air must b cool at constant rssur in orr to rach saturation is call th w oint, or w oint tmratur. It is imortant to not that it is th saturation aor rssur, an not th actual aor rssur, that is changing as you cool th air! Th w oint tmratur can b foun from th Clausius-Clayron quation by using th actual aor rssur insta of th saturation aor rssur, an soling for T. This gis T 1 1 = ln. T0 L 0 R RELATIVE HUMIDITY Scific humiity, mixing ratio, aor rssur, an w oint rmain unchang if th air arcl is hat or cool at constant rssur. ο In othr wors, if I want to comar two air samls to fin which has mor watr aor, I can irctly comar thir mixing ratios, aor rssurs, scific humiitis, or w oints. Th on with th highr numbr will ha mor watr aor. ο I can comar th samls without worrying about whthr thy ar at th sam tmratur or not (howr, aor rssur will ha to b comar at th sam air rssur)! ο This is not tru of absolut humiity, which will chang as th air arcl is hat or cool. Rlati humiity, as its nam imlis, is a rlati masur of humiity. It is fin as th ratio of th aor rssur to th saturation aor rssur, RH 100%. s 4

5 In trms of mixing ratio, rlati humiity bcoms RH 100% s r = ε + r rs ε + r s = ( ε + rs ) r r ( ε + r) rs rs ο This mans w can us mixing ratio rathr than aor rssur to fin rlati humiity. Rlati humiity tlls us how clos an air arcl is to saturation. ο It os not irctly tll us how much watr aor is in th arcl! A arcl with highr rlati humiity may actually ha lss watr aor than anothr arcl with lowr rlati humiity!. KEY DIFFERECE BETWEE THE MEASURES F HUMIDITY Thr ar two ways to chang th rlati humiity, or absolut humiity of an air arcl: ο A or subtract watr aor. ο Chang th tmratur. Thr is only on way to chang mixing ratio, scific humiity, or w oint: ο A or subtract watr aor. HUMIDITY MEASUREMET Mtorologists commonly masur humiity by masuring th wt-bulb tmratur. ο Th wt-bulb tmratur is th lowst tmratur that can b achi by aorating watr into th air arcl at constant rssur (th aoration rquirs hat, which is suli by th air arcl). ο Wt-bulb tmratur is masur using a sychromtr. Th iffrnc btwn th air tmratur (ry-bulb tmratur) an th wtbulb tmratur is call th wt-bulb rssion. ο Th wt-bulb rssion is a rlati masur of th moistur contnt of th air. Dry air can b cool much furthr by aoration than moist air, so a 5

6 largr wt-bulb rssion mans lss humiity (for th sam ry-bulb tmratur). Th w-oint tmratur an rlati humiity ar foun by using sychromtric tabls, with ry-bulb tmratur an wt-bulb rssion as th innnt ariabls. VIRTUAL TEMPERATURE Moist air can b consir a mixtur of two ial gass (ry air an watr aor). Th ial gas law for moist air is = + = ( R + R )T. W can maniulat this in th following mannr R = RT 1 + = RT ( 1 q + q ε ) R R R = RT + = RT + R R If w fin a nw tmratur, T such that 6 ( 1 ) T = T q + q ε thn w can writ th ial gas law for moist air as T is call th irtual tmratur. = R T. For moist air w can us th ial gas law for ry air, only using th irtual tmratur in lac of th actual tmratur. Virtual tmratur is always gratr than or qual to th actual tmratur. ο Th aition of watr aor causs th air to bha as though it is warmr. This maks sns, bcaus moist air is lightr than ry air. Sinc ε = 0.6, w ha ( ) T = T + q. Virtual Tmratur Virtual tmratur can also b writtn in trms of mixing ratio as 1 + r ε T = T. 1 + r

7 Sinc mixing ratio an scific humiity ar so clos, w oftn writ irtual tmratur using mixing ratio as ( ) T T + r. In all of th rcing quations for irtual tmratur w must us th absolut (Klin) tmratur an th imnsionlss form of mixing ratio or scific humiity. ο Howr, thr is an aroximat formula for irtual tmratur in Clsius that uss th imnsional (g/kg) form of mixing ratio or scific humiity. This formula is T r T + 6 [ C] [ C] an is oftn us in orational mtorology (if you ar intrst, you can fin a riation of this formula at this link.) [ g kg] 7

8 EXERCISES 1. Show that th scific gas constant for watr aor, R, is 46 J-kg 1 -K 1. (R = J-mol 1 -K 1, an th molcular wight of watr is g/mol). Us th Clausius-Clayron quation to fin th saturation aor rssur at a. T = 1 C b. T = 10 C c. T = 0 C. T = 30 C 3. An air saml at stanar sa ll rssur, an with a olum of 1m 3 at 0 C, contains 7 grams of watr aor. a. What is th aor rssur? b. What is th rlati humiity? c. What is th absolut humiity?. What is th mixing ratio?. What is th scific humiity? f. What is th w-oint tmratur? 4. Th air arcl in qustion 3 is cool at constant rssur to 10 C. ow fin th aor rssur, rlati humiity, absolut humiity, mixing ratio, scific humiity, an w-oint tmratur. 5. a. What is th irtual tmratur of th air arcl in roblm 3? b. What is th nsity of th arcl in roblm 3? 8