ESCI 341 Atmospheric Thermodynamics Lesson 16 Pseudoadiabatic Processes Dr. DeCaria

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1 ESCI 34 Atmohi hmoynami on 6 Puoaiabati Po D DCaia fn: Man, A an FE obitaill, 97: A omaion of th uialnt otntial tmatu an th tati ngy, J Atmo Si, 7, Btt, AK, 974: Futh ommnt on A omaion of th uialnt otntial tmatu an th tati ngy, J Atmo Si, 3, Bunt, D, 934: Phyial an Dynamial Mtoology, Cambig Uniity P, 4 SPECIFIC HEA OF MOIS AI Wat ao i a tiatomi molul, bnt at an angl of 9 h ifi hat of wat ao annot b foun by though a iml ul uh a 7/ (hi i bau tmining th ngy aoiat with th ibational mo i not a taightfowa alulation) h hat aaiti fo wat ao a naly oubl tho fo y ai, a hown blow Dy Ai Wat Vao (J-kg -K ) 77 4 (J-kg -K ) 5 85 h ifi hat of a mixtu of ial ga i gin by m Fo a mixtu of y ai an wat ao thi bom m i i i Sin i o mall, w an oftn nglt th ontibution of th wat ao to th ifi hat, an jut u th ifi hat of th y ai, m (a imila agumnt ali fo m) HEMODYNAMIC EQUAION FO A MOIS AI PACE W will oni a moit ai al that onit of th omonnt: Dy ai of ma m

2 Wat ao with ma m iui wat with ma ml h total ntoy of th ai al i S S S wh th ubit,, an l f to y ai, wat ao, an liui wat h ntoy of th y ai i gin by S S S m ln n Fo th ntoy of th wat ao, w oul wit a imila xion, but inta it i mo onnint to aliz that in ntoy i a tat aiabl, an thfo on t n on th ath takn btwn two tat, w an aum that th ntoy of wat ao at tmatu i ual to th ntoy of liui wat at tmatu lu th latnt hat of aoization ii by, S S m ln wh i th ifi hat of liui wat h ntoy of th liui wat i l l m Sl S m ln h total ntoy of th ai al i thfo m S S S Sl m ln n mln ml ln whih in iffntial fom i S m m m m n l l h ifi ntoy of th moit ai i foun by iiing by th ma of moit ai, m, to gt m m m m Uing th following intiti ml m n m m m,

3 m m m m m m m w gt that l, () wh i th wat ao mixing atio (ma of wat ao ma of y ai) an l i th liui wat mixing atio (ma of liui wat ma of y ai) Euation () i th thmoynami uation fo moit ai ungoing ibl o If w aum ou ai al i an iolat ytm, thn fo ibl o = So, th uation that gon an iolat moit ai al ungoing ibl o i Fo onnin w will wit uation (3) a l (3) wh (4) l Euation (4) i wittn in tm of th atial u of y ai It woul b ni to ha th uation wittn in tm of th total u W an o thi by xaning th iffntial in uation (4) to gt o w ha 3 an uing th Clauiu-Clayon uation w an how that

4 4 W alo know that o if w aum th al i atuat w an ubtitut thi fo in th lat tm an aang to gt W an alo wit o w n u with (5) On futh moifiation w an mak to uation (5) i to multily it though by to gt, an howing that o that uation (5) i aoximatly wittn a (6) Not that uation (4) an (6) a ntially th am uation hy a both wittn blow (4) (6)

5 h only ignifiant iffn btwn th two uation i that (4) ali to any iolat, moit ai al, wha uation (6) aum that th ai al i alo atuat PSEUDOADIABAIC POCESSES A uoaiabati o i an iibl o in whih a atuat ai al i lift, allowing th la of latnt hat though onnation o oition, but no oth iabati hating i allow In a uoaiabati o w aum that any liui wat i immiatly mo fom th ai al, o that i = Puoaiabati o a imotant bau w oftn aoximat moit ontion a a uoaiabati o h a al ky aamt o fatu of uoaiabati o that w n to fin an xlo h a: Euialnt otntial tmatu Puoaiabati la at Moit tati ngy EQUIVAEN POENIA EMPEAUE h uialnt otntial tmatu () i fin a th tmatu that th ai woul ha if th ai al w lift y aiabatially to th ll of onnation, thn uo-aiabatially to a y low u uh that all th wat ao w onn an mo fom th al, an thn mo aiabatially to a u of mb h uialnt otntial tmatu an b i fom uation (4), whih i ln ln (7) ( w aum that = ) All of th iffntial in uation (7) a xat iffntial, an thfo w an intgat uation (7) btwn two thmoynami tat an not woy about th ath of th intgation 5

6 Fo th fit noint w hoo th onnation ll, whih i th ll whn th ai al fit bom atuat u to aiabati lifting At th onnation ll w ha wh i th onnation tmatu, i th atial u of th y ai at th onnation ll, an i th oiginal mixing atio of th ai al h oth noint i at a u of mb an a mixing atio of zo hu mb Intgating uation (7) btwn th noint gi x (8) Euialnt otntial tmatu i on in ibl, uoaiabati motion PSEUDOADIABAIC APSE AE o fin th la at of a iing, atuat ai al w will tat with uation (6) h iation i ai if w wit th lat tm in tm of atuation ifi humiity inta of atuation mixing atio W oul jut aoximat, but to b a littl mo xat w will u th lation to gt that hu, uation (6) bom Uing th fat that (9) 6

7 7 uation (9) an b wittn a, an uing th Clauiu-Clayon uation w gt Diiing though by z thi bom z z, an aft ubtituting fo /z fom th hyotati uation, w n u with g z Puoaiabati a at () If w mak th aoximation that, thn th uoaiabati la at an b wittn a whih illutat th following imotant oint: = whn th al i y ( = ) MOIS SAIC ENEGY Stating with uation (6), an auming that = w ha (6) Subtituting fom th hyotati uation gi

8 o gz, gz E h uantity E = + gz + i on un uoaiabati motion in a hyotati atmoh, an i all th moit tati ngy (oma it with th y tati ngy fom on 7) 8

9 EXECISES A aml of moit ai at a u of mb an tmatu of 3C ha a nity of 3 kg/m 3 a What i th itual tmatu of th ai aml? b What i th ifi humiity of th ai aml? What i th mixing atio of th ai aml? If th lati humiity i 96%, what i th atuation mixing atio? What i th ao u of th ai aml? f What i th atuation ao u of th ai aml? g What i th abolut humiity of th ai aml? h If th ai aml w hat at ontant u, il tho mau of humiity that woul main ontant:,,,,, H Stating with fill in all t to how that th uoaiabati la at i g 9

Solutions to Supplementary Problems

Solutions to Supplementary Problems Solution to Supplmntay Poblm Chapt Solution. Fomula (.4): g d G + g : E ping th void atio: G d 2.7 9.8 0.56 (56%) 7 mg Fomula (.6): S Fomula (.40): g d E ping at contnt: S m G 0.56 0.5 0. (%) 2.7 + m E