Series Evaluation of the Isotherm D ata of C 02 between 0 and 150 C. and up to 3000atm.*

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Dwnlae frm http://rspa.ryalscietypublishing.rg/ n June 26, 2018 348 H. Jeffreys reference t th e prbability th a t a system will apprach a steay state.

1 Dwnlae frm n June 26, H. Jeffreys reference t th e prbability th a t a system will apprach a steay state. Sme efects in th e current treatm ents f th e prblem s are pinte ut, an an alternative iscussin is given. R e f e r e n c e s Campbell, N. R hysics: the Elem ents. Camb. Univ. ress. Fwler, R. H Statistical Mechanics, 2n e. Camb. Univ. ress. Jeans, Sir J. H Dynamical Thery f Gases, 3r e. Camb. Univ. ress. Jeffreys, H Scientific Inference. Camb. U niv. ress rc. Ry. Sc. A, 138, rc. Ry. Sc. A, 140, rc. Camb. hil. Sc. 32, Keynes, J. M Treatise n rbability. Lnn: Macmillan. Sterne, T. E rc. N at. Aca. Sci., Wash., 2 0, Stuent 1908 Bimetrika, 6. Wishart, J. an Bartlett, M. S rc. Camb. hil. Sc Series Evaluatin f the Istherm D ata f C 02 between 0 an 150 C. an up t 30atm.* B y A. M ic h e l s a n M r s C. M ic h e l s (< Cmmunicate by F.A. Revise 27 F ebruary 1937) The usual m eth f expressing th e results f istherm m easurem ents is in a series in term s either f th e pressure r th e ensity. Frm the value f th e first cefficients f th e pwers f p an, theretical cnclusins have been raw n (Fwler 1929, p. 211 etc.). A series evaluatin f an istherm is als f great help in fining th e pressure a t a given ensity r the ensity a t a given pressure. A n a tte m p t was therefre m ae t represent the istherm a ta f C 0 2 given in previus publicatins (Michels, A. an C. 1935; Michels, A. an C. an W uters 1935) by a series equatin. Gerver (1934, p. 71) ^ as alreay shwn th a t the expansin in a pseri f high ensities an the evaluatin was therefre carrie ut in a series. I t will be shwn in th e present paper th a t fr the ensities uner cnsieratin the series als es n t give an ieal representatin f the experim ental results. * 49th publicatin f the van er Waals Fun.

Dwnlae frm http://rspa.ryalscietypublishing.

2 Dwnlae frm n June 26, 2018 Istherm Measurements A first trial was mae t represent the experimental ata in a series pv = A B C2 D4 in which is expresse in Am agat units. Fllwing a suggestin f Kamerlingh nnes, the pwers, except the first ne, were mitte. The values taken fr A are thse given in a previus publicatin (Michels, A. an C. 1935). I t was als thught t be f avantage t take the values fr B calculate frm the lw-pressure istherms (Michels, A. an C. 1935), as B can be interprete as the graient f the istherms fr 0 an it is therefre clear th a t the best value can prbably be calculate frm the ata a t the lwest ensities. I t appeare, hwever, th a t the series s btaine i nt fit very well with the experim ental figures. As an example the ifferences between the experimental values f pv fr the 50 istherm an thse calculate frm the series are pltte against ensity, in the first curve f fig. 1. The pints lie n a smth curve, shwing th a t the lack f agreement is nt ue t inaccuracy f the measurements, but th a t it is impssible t represent the measure pints by a series f this type. Several mre attem pts were mae t imprve the crrelatin between the calculate an bserve values f pv. 2 The suggestin th a t the pwers except the first ne shul be mitte, was given up an the thir pwer ae t the series, t give C2 Z3 D # F 8. The agreement was better, but nt yet sufficient, as can be seen frm curve 2. 3 A trial was mae t fit the experim ental ata with a series f the first type, but this tim e the suggestin th a t B shul be taken frm the lwpressure istherms was given up. Fr clearness f expressin the new value f B is intruce as B /?, where B is the l value. Curve 3 sh except fr the lw ensities, the eviatin is less than with the first series, but still greater than the experim ental accuracy. 4 The best results were btaine by cmbining the meths f the tw previus paragraphs an applying the series pv = A (B fi) C* Z3 D* EG The agreement btaine can be seen frm curve 5. 5 Finally, a series was trie f the type where the thir pwer was mitte an a tenth pwer ae. The results given in curve 4 shw th at

$rg/ n June 26, 2018 / A -7 T K \ / \ * b Ufa 1 \ > X - 1 _i_ i i r \ J pv= AB C2D4 E6 F8 10-1 0 20 10-1 0 / / i r / 'hll * -j» i / i 1 /!$

3 350 A. Michels an C. Michels the ifference between experim ental an calculate values has again increase. ) ) Dwnlae frm n June 26, 2018 / A -7 T K \ / \ * b Ufa 1 \ > X - 1 _i_ i i r \ J pv= AB C2D4 E6 F / / i r / 'hll * -j» i / i 1 /!. it i \ " i x / ' p \ N, / i l t I \ X - H \ 1%l / / A J \ / \ / is< >. / n y i X f \ / V. A pv- A B C2Z8 D4 E F8 pv= A IB0lC2 D4E6 F8 10 1/ < ' i \ / 1 / N 1 \ J i / \ / \ Y u K / \ \ " 7 IY i \ / n V / -20 V / A. J y\ r~r x / X ' V 4 y ~n < ' \ / T /i i l 'Xi F ig. 1 pv= AIB/HC2 D4 E6 F8 H10 pv~ AIB/9lC2Z3 D4E6 F8 The cnclusin seems therefre allwe th a t the istherm ata btaine a t the higher ensities cannt be expresse w ith an rinary pwer series. The reasn can be seen frm the values f each f the term s f the series. int 33 gives fr instance: = Z? = 2*07278 = 1*196 D4= -6*77216 ( ytf) = -3*27320 E= 8*11718 C2 = 3*55171 F= - 2*04027 These figures shw th a t fr th e higher ensities th e series is n t cnvergent.

4 Dwnlae frm n June 26, 2018 Istherm Measurements 351 I t is therefre bvius th a t uner these circumstances it will be angerus t raw cnclusins frm the value f the cefficients f the series evaluatin. In the series evaluatin f his results n nitrgen, Gerver (1934) fun th at the values-fr B calculate frm the istherm ata in the high pressure range, were nt the same as thse frm the lw pressure istherms f tt, Michels an W uters (1934). He ascribe this t an im purity present in the gas use. I t nw seems mre prbable hwever th a t the ivergence is ue t the reasn given abve. The series evaluatin, hwever, is still f im prtance fr the calculatin f p at a given ensity uner the cnitin th a t the eviatin curve between experimental an calculate values is knwn. Therefre the series evaluatin f type 4, pv = A (B fi) C2 Zs D # has been carrie ut fr the tem peratures between 40 an 150 C. Fr the tem peratures belw 40 C., it was impssible t fit the experiments with ne series. Tw series were therefre calculate, ne fr the range f the gas ensities an ne fr the range f the liqui ensities. Use was mae f the ensities f the saturate vapur an f the liqui uner vapur pressure (i.e. pv a t critical ensity) as publishe by Michels, A., Blaisse an Michels, C. (1937). The cefficients fr the ifferent series are given in Table I. The eviatins betw een th e experim ental values f p v an thse calculate frm the series evaluatin are shwn in Table II. The values fr the cefficients f the series between 40 an 150 C. are pltte as functins f tem perature in figs. 2 an 3. As can be seen, they all lay n smth curves. This facilitates interplatin a t ther tem peratures. I t may be rem arke th a t in the previus publicatin, where the results f the series evaluatin fr the lw pressure ata were evaluate, nly the values f B an nt thse f the ther cefficients fitte n smth curves (Michels, A. an C. 1935)- The a ta given abve, tgether w ith the values lr publishe previusly, allw the calculatin f pv a t any interm eia ensity an they als pen the pssibility f cmparing the istherm results publishe w ith thse f ther authrs. Calculatin shwe th a t the average eviatin frm A m agat s istherms up t 10 atm.* is abut %, althugh ccasinally eviatins as high as 1 \% ccur. * 66Internatinal Critical Tables, 3, 11.

$Michels H Hi w EH <N rh X 6* Q r H X Kl <M 1^40 ph I > ph 4 0 4 0 S ph l <M <M <M W* w v#> CI HH \J1 <M <M ^ <M ^ j *.$

5 Dwnlae frm n June 26, A. Michels an C. Michels H Hi w EH <N rh X 6* Q r H X Kl <M 1^40 ph I > ph S ph l <M <M <M W* w v#> CI HH \J1 <M <M ^ <M ^ j *.«/ /*s wv W» j <-4J XJ1 H Q (M CS l > <M ph ph GS S 4 0 Th <N 40 <M c s S 4 0 l > (M ^ 0 0 H I cb cb 40 H 4 0 S ph S S I I q c c s c J3 ^ l (N 1C l <M (M ^ «H I> ^ X (N (N p H H I I C l H ^ ^ T i l ^ c h f l J x c h ib i c ph c b ^ (N I r I l 1> H I I I H H rh X p H X 8 H ^ <M <M CM (N i l 0 0 rh Tfl (M i c c i 1> 0 0 CM s 6 A i> c I I I I t > i > c c l > Tfi Q ^ H I> H 1> Tji H ^ (N S S S I I 0 5 (N <M 0 0 ph t> h (M CM ^ S ph t> ph 4 0 I <M S c s ph T* 4 0 I> cb s s -rt< Q 40 H H C c l h S X ShlhhHH ^«5(M^Hi Hl>(MiHh S ^ H h - C C S ( N i ( N C ^ S I C C S S lbib^xh^cbcbcbcbibib I I I I I I I I I I I 0(NH^I>^l(N I C C C SC (N C C (N I INIIWh ^^^ShHi N 40 S!> S ph <m <m hcsic ^ i h h h ph ph ph ph ph ph ph ph ph ph ph l (N l> h M l> W5 H ^ If5 h ph N h H <S csxbcsibibcsphcm ^ ^ r> S (N l ph ph <M <M 'I

6 Dwnlae frm n June 26, 2018 Istherm Measurements 353 K5 ijl CDJCC^C^S^jHeqjHjSJStjjHS MU5 6 l I I I i I I 1 I I i I i i 7177 WNlC C(M?0(N5^C^N>0'rtlC1>QW^Xt>,(N l> X X 7i i 7 i i 77i 7777 I 7 I7 Q C D ^ t,* C H H l X W W H H H H f l 5 0 ^ C W l i 0 ^ l > rhphr-h<n'-h r I <N<M<M<NH H WWN H <M<MH H I ^ IQ H I h i I I I I I I I H I I I I h i I I I I I H I h I I l l 7777i77777 NNGHHH^Q^^ X (M (N (N (M l w I>-Q I I I I I I I Ni«Tji«l»(8MH ih I II I t»i>nmn 0 H WW^l N I I I I I I I Mh-#N M «h I I I I I I MHt»HNNNlM II I III I i777777^ ^ ^ih^<mc5t^ W I I -I--- I---I- 1-1 ^ ^ ^ I I t>hh<nq*aa*^h H i H I --1 _l_ t'* rh XHWN I I I ^I>«H H H 50 H (N(M^^ H N fh I I I I I 50 ph rh r~h ^HrH I I I rhr-h(m I I II rh H 50 *> 'thrh 50 rh H rh rh Tf! th TjH 50 ',5h Tf- t ^ ^ ^ W ^ H ^» G S J G S W y H H H ( N ^ ^

Dwnlae frm http://rspa.ryalscietypublishing.rg/ n June 26, 2018 354 A. Michels an C.

7 Dwnlae frm n June 26, A. Michels an C. Michels The istherms, publishe by Nijhff, Michels an Gerver (1930), up t 18 atm. give an average eviatin f 0*2 % an a maximum f 0-35 %. 1 z.is ib-w0).13 Keesm (1903) publishe istherm s in th e neighburh f the critical

Dwnlae frm http://rspa.ryalscietypublishing.rg/ n June 26, 2018 Istherm Measurements 355 pint.

8 Dwnlae frm n June 26, 2018 Istherm Measurements 355 pint. His values iffer frm the authrs at ensities belw 3 A n the average 0-3 %, but at ensities run 4 A abut 4 %. F.i23 E.I 20.0 I 5.0 F ig. 3 Beattie an Brigeman (1928) have publishe a new equatin f state fr fluis with which we have cmpare ur bservatins in Table III. The equatin fr ensities up t 112 fits the experiments with an accuracy f 0-7 %.

Dwnlae frm http://rspa.ryalscietypublishing.rg/ n June 26, 2018 356 A. Michels an C.

9 Dwnlae frm n June 26, A. Michels an C. Michels EH fc> p H H fc ic ic ic fh C5 rh 1C l> *-h 1> 1C Til rhl> q q G ic I> T* c C5 ^ l> l Th 1> ic T* 1C G H T* 1C rh rh!> h 1C ^ 9 9 Th l> 1C T*i 1C rh 1C l> ic H M W WH ic I> rh Tt* Q I> ^ T* ic Hi 1C 1C rh rh Tti Tfi 6 JZ5 MH G l> c ^ 6 6 fc> G> H fc cb c TtH 1C ic ic ^ rh ic 1C rh > I> T* Tti l> Xjl cs M h m i> ic T*i H c c ic H Eh W fc M H<1 H p ic l> t H 1C 1C i rh 1C IC ic rh 1C t> f l> 1C ^ c ic ic H M > t> l> t> t> c ic I i 5 rh h C5 Tti 6 6 c ic c H i ^ H ic «H«W & <1 eg 3 3 ps JC ic t> G <M ic rh rh I> ic G rh I> ic ic c 6 rh 1C Q rh 1C H IT'* rh ^ rh rh 1C ic ^ Tfl ^ rh rh l> I> 1C H " H rh rh rh I> ic ic Hi CC rh rh 1C H Hi t* ^ rh rh p pp H U5 ^»6 ~ C<J II ^ %» ft ^ ii» ^ ^ ft l> Eh ^ ftl * «? ^ s l 6. II Q &«Q?> a, ft ft

10 Dwnlae frm n June 26, 2018 Istherm Measurements 357 I t may be pssible t fin cefficients which allw representatin f the experimental ata up t the critical ensity, with an estimate accuracy f 10 % (Beattie, Halck, ffenberger, 1935); fr still higher ensities there is little hpe f any agreement. The series evaluatin as evelpe in ur paper fits the results better than the equatin. Uner thse circumstances it es nt seem justifie t recalculate the cefficients f the equatin ver a higher ensity range. S u m m a r y I t is cmmn practice t represent istherm ata by a series expressin either with pwers f the pressure r f the ensity, e'.g. either pv = A Bp... r pv = A B C2... reviusly it has been shwn th at fr istherm ata abve 5 atm. the first series is nt aequate. The present paper shws th at als the secn series cannt represent accurately the istherm ata f C02 up till 30 atm. as publishe by the authrs. The series representatin is, hwever, still f value fr interplatin purpses, if eviatin curves between experimental ata an series are knwn. The istherm ata have therefre been expane in series f the type pv = A B C2 Z* The value f a cefficient epens n the ensity regin fr which the series is applie, the number f cefficients, etc. an it is therefre angerus t raw t rigi physical cnclusins frm the numerical values. With the help f the series the results publishe have been cmpare with thse publishe by ther authrs. R e f e r e n c e s Beattie, J. A. an Brigeman,. C rc. Amer. Aca. Sci. 63, 229. Beattie, J. A., Halck, C. an ffenberger, N J. Chem. hys. 3, 93. Fwler, R. H Statistical Mechanics. Camb. Univ. ress. Gerver, A Dissertatin, Amsteram. Keesm, W. H Cmmun. hys. Lab. Leien, N. 88. Michels, A. an Michels, C rc. Ry. Sc. A, 153, 201. Michels, A., Blaisse, B. an Michels, C rc. Ry. Sc. A, 160, 358. Michels, A., Michels, C. an Wuters, H rc. Ry. Sc. A, 153, 214. Nijhff, G.., Michels, A. an Gerver, A rc. Aca. Sci. Amst. 33, 72. tt, J., Michels, A. an Wuters, H hys. Z. 35, 97. Vl. CLX A. 2 B

(Communicated at the meeting of January )

(Communicated at the meeting of January ) Physics. - Establishment f an Abslute Scale fr the herm-electric Frce. By G. BOR ELlUS. W. H. KEESOM. C. H. JOHANSSON and J. O. LND E. Supplement N0. 69b t the Cmmunicatins frm the Physical Labratry at