AB for hydrogen in steel is What is the molar flux of the hydrogen through the steel? Δx Wall. s kmole

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1 ignen 6 Soluion - Hydogen ga i oed a high peue in a ecangula conaine (--hick wall). Hydogen concenaion a he inide wall i kole / and eenially negligible on he ouide wall. The B fo hydogen in eel i.6 / ec ha i he ola flu of he hydogen hough he eel?. Δ all i o = Given daa: difuivi y.6, B kole Hydogen concenaion inide he ank (inide wall) i, kole o, Hydogen concenaion ouide he ank (ouide wall) all hickne. upion i) iffuion i only in one diecion i.e. diecion aco he wall heefoe he ye can be aued o ac a a lab ii) Seady ae wih no cheical eacion i.e. and R pply he above aupion o he equaion of coninuiy of pecie fo ecangula coodinae (Equaion -7 Gikey):

2 y y R eady ae o flu o flu o cheical eacion To obain: Theefoe i independen of i.e. i i a conan Modified Eq.-6 give: B + ( + B ) Since concenaion of coponen in he conaine wall i vey all,. Then bulk flow will be negligible. Eg. -6 give: B nd ince conan (concenaion ouide he all i negligible), hen: B B o i Subiuing he given daa: B o i.6. kole The ola flu of hydogen hough eel fo hi cae i:.6 kole.

3 -9 Benene a i open o he aophee in a cicula ank (6. in diaee). Vapo peue and pecific gaviy fo benene ae. a and.88. n ai fil of 5- hickne i above he benene. ha i he co of evapoaed benene pe (aue value of benene i $ pe gallon)? i fil Benene Given aa: Benene Tepeaue = Vapou peue of Benene =. a Specific gaviy =.88 i fil of hickne = 5 iaee of ank = 6. o of benene = $ pe gallon upion: iffuion of olecule (Benene) i only in one diecion i.e. in he diecion no flu in and y diecion Seady ae wih no cheical eacion i.e. and R In hi cae, he ye i a liquid (benene) evapoaing ino Ga B (ai) i.e. diffuion hough a agnan ga fil odel. pply he above aupion o he equaion of coninuiy of pecie fo ecangula coodinae (Equaion -7 Gikey): y y R eady ae o flu o y flu o cheical eacion

4 To obain: Theefoe i independen of i.e. i i a conan Modified Eg. -6 give: + B ( + B ) B = (Sagnan ai) Then eaanging give: ( ) B Equaion knowing Replace he above equaion ino equaion, we can deive he ola flu of olecule in e of ole facion : ( ) B Since, R and T ae conan, he can be facoed ou of he deivaive o obain: B ( ) Equaion The equaion obained above (equaion ) can be inegaed ove he following boun condiion:

5 = = = = ( ) B B B B ln B ( ) ln ( ( ) ) Leing (hickne) and eaanging he equaion above we obain: ( ) B ln ( ) ( ) Equaion The above equaion of flu (Equaion ) can be wien in e of ole facion fo he aionay olecule i.e. B a follow: B B ln Equaion 5 ( ) B he uface of benene liquid: The vapou peue of benene =. a heefoe:. a a =. and B uing all he benene i wep away by oving olecule of ai above he agnan ai fil i.e. he concenaion of benene above he ai fil i negligible, hen:

6 Since he diffuiviy of benene i no given, i can be calculaed fo he following equaion: B T M B B M B Fo -- in Gikey: Benene M k 97 o K i nd, B M B k B o K B B KT k k B o K To obain B, able -- can be ued uing: kt B Theefoe he diffuiviy i: B K B a.. B ow ha we have all he paaee needed o deeine he ola flu of benene, we can ubiue he above paaee ino he ola flu equaion deived ealie:

7 B ln ( ).999 B B g. ol.ec a ln a K (.5 ) ol. K Fo he ola flu, he aoun of benene in gol/ec can be deeined a follow: Z g. ol g. ol.ec 6. The aoun of benene evapoaed pe : = M.899 g. ol g 78. gol 88 g 6 h h. Gallon of benene evapoaed in one :. 6.7 gallon gallon Theefoe he o of benene evapoaed pe : o of benene evapoaed = gallon dola 7.5 dolla - Hydogen ga( 7 ; ba) i oed in a --diaee pheical ank (hick wall). Mola concenaion of hydogen a he inne and oue wall ae.5 kgole/ and. iffuiviy of hydogen in eel i. / ec. Find he iniial ae of hydogen lo hough he wall a well a he iniial ae of peue dop in he ank.

8 R i R o Given aa: Hydogen ga = olecule Seel = B olecule Tepeaue = 7 Iniial peue = ba oncenaion of hydogen inide ank =.5 kgole/ oncenaion of hydogen ouide wall = kgole/ iffuiviy B =. Spheical ank diaee = Tank wall hickne = upion: iffuion of olecule (hydogen ga) i only in one diecion i.e. in he diecion no flu in θ and diecion Seady ae wih no cheical eacion i.e. and R o bulk flow of fluid ince he concenaion of hydogen in he wall of he pheical ank i negligible. pply he above aupion o he equaion of coninuiy of pecie fo pheical coodinae (Equaion -8 Gikey): in in in R eady ae o flu o flu o cheical eacion

9 To obain: Theefoe i a conan Then, uing he odified Equaion -6 Gikey: Modified Eq. -6: B + ( + B ) In he wall,, o bulk flow. The equaion above educe o: B nd B Equaion Inegaing he above equaion (equaion above) ove he following boun condiion: = i = R i = o = R o B B Ro Ri i B Ro Ri o i

10 B R i o R o i Subiuing he given daa in he above equaion: kole kgole Theefoe he iniial ae of hydogen dop hough he wall of he pheical ank i: 7.5 kgole Fo eue dop V n n V Theefoe peue dop ae i: d V gole ec a 8. gole. K.5 K d.5 acal.5 7 Ba

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