School of Chemical & Biological Engineering, Konkuk University

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1 Shool of Cheil & Biologil Engineeing, Konkuk Univesity

2 Letue 3 he vn de Wls eqution he piniple of oesponding sttes Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-

3 Johnnes Dideik vn de Wls, Duth physiist (1837~193) Nobel pize fo physis, He is fous fo his wok on the eqution fo gses nd liquids whih desibes the eltion between the pessue, volue, nd tepetue of fluids (gses nd liquids). In 1873 he obtined his doto's degee t Leiden Univesity fo thesis entitled On the ontinuity of the gs nd liquid stte. In this thesis he deived the vn de Wls eqution. Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-3

4 Johnnes Dideik vn de Wls, Duth physiist (1837~193) Nobel pize fo physis, His thesis gve odel in whih the liquid nd the gs phse of substne ege into eh othe in ontinuous nne. It shows tht the two phses e of the se ntue. In deiving his eqution, he ssued not only the existene of oleules (whih in physis ws disputed t the tie), but lso tht they e of finite size nd ttt eh othe. Sine he ws one of the fist to postulte n inteoleul foe, howeve udienty, suh foe is now soeties lled vn de Wls foe. Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-4

5 Johnnes Dideik vn de Wls, Duth physiist (1837~193) Nobel pize fo physis, he seond get disovey of vn de Wls ws published in 1880: he Lw of Coesponding Sttes. his lw shows, tht fte sling tepetue, pessue, nd volue by thei espetive itil vlues, genel fo of the eqution of stte is obtined whih is pplible to ll substnes. Fo his wok he won the 1910 Nobel Pize in physis Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-5

6 vn de Wls eq. is n ppoxite eqution fo el gs. Rel gs: thetilly oplited but physilly siple. Model building fo el gses by thinking sientifilly. R b nr n p p nb Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-6

7 Due to the non-zeo volue (o epulsion) of the oleules theselves, - nb nr nr p p nb Assuing the oleules e hd sphees, the losest distne between two oleules of dius is. he oleul volue: oleule 4 3 So the volue exluded is 8 oleule oleule he volue exluded pe oleule is 4 oleule. b 4 oleule N A Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch Ex) b = d 3 /ol fo H hydogen = 4416 Å 3 = (16.4Å) 3

8 Pessue depends on both the fequeny of ollisions with the wlls nd the foe of eh ollision. Both the fequeny of ollisions nd thei foe e edued by the tttive foes. he stength of tttive foe is popotionl to the ol onenttion (n/) of oleules. Beuse both the fequeny nd the foe of the ollisions e edued by the tttive foe, the pessue is edued in popotion to (n/). p nr nb p nr nb n Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-8

9 p nr nb n Expeientl isothe Idel gs eq. n de Wls eq. Wow! It s diffeent! Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-9

10 Below the, isothes of the vn de Wls eqution osillte. he osilltions, the vn de Wls loops, e unelisti, they suggest tht n inese of pessue esults in n inese of volue. he loops should be epled by hoizontl lines (Mxwell onstution). Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-10

11 Mxwell Equl Ae Rule (Mxwell Constution) he ed line in the isothe of the vn de Wls eqution is not unelisti. he loop should be epled by hoizontl lines so tht the loop defines equl es bove nd below the line. Why should the es be equl? Wok done on syste in going fo to b should equl wok elesed on going fo to b. (in sttistil ehnis) Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-11

12 p R b Pefet gs isothes e obtined t high nd lge. he vn de Wls loops, whee liquids nd gses oexist, ou when both the tttion nd epulsion tes hve siil gnitudes. Fo <, the lulted isothes osillte. At, the isothe hs flt inflexion. Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-1

13 At the inflexion point, both the 1 st nd nd deivtives e zeo. R p b dp d d p d R R b b At the itil point (= inflexion point), the solutions of these thee equtions e: 8 3b P 7b 7Rb Plese deive the solutions fo youself! If we know the vlues of itil onstnts, the vlues of nd b n be deteined by these eltions Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-13

14 Let s think bout opession fto t the itil point. Citil opession fto (Z ) Z p RZ At itil point, p R Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch p 3b 7b 8 R 7Rb Citil opession fto (Z ) is pedited to be 3/8 ~ fo ll gses. 3 8 R Plese see ble 1.5 to ope to the vlues fo vious gses. he disepny is esonbly sll. Z Ah!!!

15 he itil onstnts e hteisti popeties of gses. he P, nd sles n be e-sled to set up eltive sles by using P, nd s ydstiks. Let s intodue the diensionless edued vibles of gs by dividing the tul vible by the oesponding itil onstnt: p p p vn de Wls fist tied this poedue, hoped tht el gses t the se nd would exet the se P. His hope ws lgely fulfilled! Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-15

16 At 0 o C 1. 1 he piniple of oesponding sttes: el gses t the se nd exet the se P. Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-16

17 he piniple is only n ppoxition. It woks best fo gses oposed of spheil oleules. It fils when the oleules e non-spheil o pol. Why? Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-17

18 he vn de Wls eqution give hint! p p p p R b R b b R 8 7Rb 3 7 3b b b p 7b 7b 3 1 9b p p p 3b P 7b 8 by dividing by. 7b p Rb Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-18

19 p his edued eqution hs the se fo s the oiginl, but the oeffiient nd b, whih diffe fo gs to gs, hve disppeed. heefoe, if the isothes e plotted with P nd, then the se uves e obtined whteve the gs. Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-19

20 Reding: pge 8 ~ 33 Poble set Disussion questions 1.6 Exeises 1.1(b), 1.7(b), 1.17(b), 1.0(b), 1.(b) Due dte: M. 16 (befoe the letue) Disussion Setion M. 16, 19:00 ~ 0:00 ( 별 3) Mke photoopy of you epot. Pof. Yo-Sep Min Physil Cheisty I, Sping 009 Ch. 1-0