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A method for measuring the dielectric constant of liquids Dunell, Basil A. 1946

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A)* H 5 A METHOD FOR MEASURING THE DIELECTRIC CONSTANT OF LIQUIDS A Thes i s submit ted i n p a r t i a l f u l f i l m e n t of the requirements f o r the degree o f Mas ter of A p p l i e d Science at the U n i v e r s i t y of B r i t i s h Columbia . B a s i l A . D u n e l l , B i A . S c . The U n i v e r s i t y o f B r i t i s h Columbia J u l y , 1946. Acknowle dgement s I am most p l eased to acknowledge the guidance of D r . W. F . Seyer , whose a s s i s t a n c e and sugges t ions have always been ve ry h e l p f u l and encouraging* I am a l s o g r a t e f u l to Mr* E . P r i c e o f the P h y s i c s Department, who has been ve ry generous w i t h sugges-t i o n s and w i t h adv ice on h i g h frequency c i r c u i t s . M r . F . C . Alexander o f the U n i v e r s i t y o f P i t t s b u r g sent us a drawing o f the t e s t c e l l and has r e c e n t l y been v e r y k i n d i n o f f e r i n g f u r t h e r a s s i s t a n c e w i t h the work* Table of Contents Aoxnowle dgem en t s Object of Research;-Purity of Materials Equipment for and Method of Measuring the Dielectric Constant Test Cell Constant temperature oven High frequency circuit 7 Calibration of Equipment 9 Experimental Difficulties 14 Accuracy of the Method 22 Precision of the tuning condenser 22 Orientation of the centre eleotrode 23 Anomalous dispersion 24 Accuracy obtainable for £ 25 Accuracy obtainable for de/dlT 2& Corrections for Change in Dimensions of the Test Cell with Temperature 2\ Results 2^ A Correction for Evaporation ^' Bibliography 35 (iii) I . Object o f the Besearch Work done on the isomers o f decahydronaphthalene i n t h i s l a b o r a t o r y d u r i n g the l a s t few years has i n d i c a t e d tha t there i s a s i n g u l a r i t y i n some o f the p h y s i c a l p rop -e r t i e s o f the c i s isomer near 50°G. The ob jec t o f t h i s researoh i s to measure the d i e l e c t r i c constant o f pure c i s - and t rans-decahydronaphthalene and to observe whe-the r any s i n g u l a r i t y e x i s t s i n the ourve showing the v a r i a t i o n o f the d i e l e c t r i c cons tant o f the o i s - i s o m e r w i t h temperature. I I . M a t e r i a l s Used &» 01s Decahydronaphthalene R e c t i f i c a t i o n o f a mix tu re o f the isomers at about 9 mm. abso lu te p ressure i n a Stedman Column (1) e f f e c t e d a s epa ra t ion i n t o q u i t e pure c i s - d e o a l i n and t r ans -deoa-l i n . The pures t f r a c t i o n s o f each isomer had a p u r i t y ( l ) A n g l e y , P o t k i n s , Rush - B a c h e l o r ' s T h e s i s , 1942. 2 . o f about 99.5 - 9 9 . 8 $ . The pures t f r a c t i o n o f c i s d e o a l i n was f u r t h e r p u r i -f i e d by r e c r y s t a l l i z a t i o n i n a d r y - i c e ba th , f o l l o w i n g the method used by Seyer and Walker ( 2 ) . A f t e r success -i v e r e c r y s t a l l i z a t i o n s a product was obta ined whose f r e e z i n g p o i n t was constant at - 4 3 . 1 5 ° C , as measured by a Leeds and Northrup p l a t i n u m / ; r e s i s t a n c e thermometer. T h i s sample o f c i s d e c a l i n i s cons ide red to be as pure a sample as can be o b t a i n e d . B . Trans Decahydronaphthalene Success ive r e c r y s t a l l i z a t i o n s o f the pures t f r a c t i o n o f t r ans d e c a l i n y i e l d e d a product w i t h a constant f r e e z -i n g p o i n t o f - 3 0 . 6 4 ° C . 0 . Benzene "Merck thiophene f ree benzene" was t e s t ed f o r t h i o -phene by shak ing a sample o f the benzene w i t h a few cc o f G . P . cone. H2SO4. S ince no darken ing o f the a c i d l a y e r was observed , i t was assumed tha t no thiophene was p r e s e n t . About 500 c c . o f t h i s benzene was c r y s t a l l i z e d i n an ioe ba th u n t i l a l l but some 50 cc o f benzene had s o l i d i f i e d . T h i s r e s idue was r e j e c t e d . A f t e r the f o u r t h r e c r y s t a l l i z a t i o n , the product had a constant f r e e z i n g p o i n t o f 5 . 3 7 ° 0 as measured by a Leeds and Northrup p l a t i num r e s i s t a n c e thermometer. (2) Seyer and Walker. J . A . C . S . 60 2125, (1938) 3 . I I I . Equipment f o r and Method o f Measur ing D i e l e c t r i c Constant An e x c e l l e n t d i s c u s s i o n o f the methods o f measuring d i e l e c t r i c constant can he found i n G. P . Smyth's mono-graph " D i e l e c t r i c Constant and M o l e c u l a r S t r u c t u r e " . The method and equipment used i n t h i s r e sea rch i s essen-t i a l l y tha t desc r ibed by Alexander ( 3 ) . A t e s t c e l l i s c o n s t r u c t e d , and i t s c a p a c i t y determined by c a l i b r a t i o n w i t h a l i q u i d o f known d i e l e o t r i e constant as the d i e l e c -t r i c . I t s c a p a c i t y i s aga in determined when the l i q u i d o f unknown d i e l e o t r i e cons tant i s the d i e l e c t r i c , and . from t h i s c a p a c i t y the d i e l e c t r i c constant o f the t e s t l i q u i d i s c a l c u l a t e d . The t e s t o e l l ^ i n p a r a l l e l w i t h three v a r i a b l e condensers and an inductance , formsthe tuned p l a t e c i r c u i t o f a vacuum tube o s c i l l a t o r ; and a c r y s t a l o s c i l l a t o r i n p a r a l l e l w i t h a r e s i s t o r forms the tuned g r i d o i r c u i t . The vacuum tube used i s one o f type 6E5, an " e l e o t r o n r ay" tube , which serves both as an o s c i l l a t o r and as a means o f d e t e c t i n g when the c r y s t a l o s c i l l a t o r "snaps i n " ; tha t i s , when the p l a t e o i r c u i t i s tuned to o s c i l l a t e to the c h a r a c t e r i s t i c frequency o f the c r y s t a l . (3) F . C. Alexander , " D i e l e c t r i c Constant M e t e r " , E l e c t r o n i c s . 18, #4, p 116 ( A p r i l 1945) 4 . A . Test C e l l . The two meta l p a r t s o f the t e s t c e l l were machined from s t a i n l e s s s t e e l a c c o r d i n g to the s p e c i f i c a t i o n s shown i n f i g . 2 , and a s m a l l sapphi re mounted i n a l i t t l e b rass ho lde r was screwed i n t o the end o f the cent re e l e c -t rode to o r i e n t the middle e l e c t r o d e i n the cup o f the t e s t c e l l . A c c o r d i n g to Alexander ( 4 ) , such a c e n t e r i n g dev ice inc reases the r e p r o d u c i b i l i t y o f r e s u l t s from 1% e r r o r wi thout the sapphire to 0 .3$ e r r o r w i t h the sap»f p h i r e . The p o i n t o f the sapphire f i t s i n t o a s m a l l ho le d r i l l e d i n the bottom o f the cup o f the t e s t c e l l . The cen t re e l e c t r o d e was f i x e d i n i t s p o r o e l a i n ho lde r i n the f o l l o w i n g manner. The e l e c t r o d e was centered i n the ou te r pa r t o f the c e l l and three or four asbes tos-paper washers were put between the top o f the e l e c t r o d e and the under s ide o f the p o r c e l a i n ho lde r i n o rder to make the (4) l o c o l t e l e c t r o d e bear aga ins t i t s b o l d e r when centered and touch ing the bottom o f the w e l l i n the outer p a r t o f the c e l l . F i n a l l y , a nut was screwed down l i g h t l y over the threaded p r o j e c t i o n - shown i n f i g , : . 3 . With the c e l l thus assembled and h e l d f i r m l y toge ther by hand i n an upsidedown p o s i t i o n , some "Chicago China Handle Cement", a qu ick d r y i n g cement resembl ing p l a s t e r o f P a r i s , was worked i n t o the space between the e l e c t r o d e and the s ide o f the h o l d e r . A f t e r the cement had set h a r d , two or three asbestos washers and a brass washer were put over the top o f the ho lde r and the assembly was made secure by t i g h t e n i n g down the nu ts which screwed onto the threaded contac t p r o j e c t i n g up through the h o l d e r from the cent re e l e c t r o d e . L a t e r i t was found tha t l i q u i d s put i n the c e l l evaporated so r a p i d l y tha t even d e c a l i n would evaporate enough to cause c o n s i d e r a b l e change i n the c a p a c i t y o f the t e s t c e l l a f t e r two o r three days o f cont inuous o p e r a t i o n . A f i b r e c o l l a r was t h e r e f o r e made to f i t around the t h i n p o r t i o n o f the cent re e l e c t r o d e and to cover the annular space c o n t a i n i n g the d i e l e c t r i c . S i n c e Cenco L a b e l V a r n i s h was found to be r e s i s t a n t to the a c -t i o n o f benzene and d e c a l i n , a coat o f t h i s v a r n i s h was used as a cement to f i x the f i b r e c o l l a r to the cent re e l e c t r o d e . A coat o f v a r n i s h a l s o prevented the cement .-A. Tlj^izdecf projg.cti.ori^fronn centre electrode Cobber bus r-bar _C. fed fibre insulator ... . P- Shoulder of test cell E. Fibre cap for reducing evaporation F. Fan 6. tfi^h frequency lead, grounded Side H. H.r. lead. J. Auxiliary heating Coil K. Fibre insulator -EIG. 3. Hssemhly.^of lest Ce.lL in Oven. 6. i n the ho lde r from becoming so f t from the a c t i o n of water , benzene, or d e c a l i n , and prevented any p a r t i c l e s o f cement f a l l i n g i n t o l i q u i d i n the t e s t c e l l . B . Constant-Temperature Oven A constant temperature oven f o r the t e s t c e l l was made from a sheet meta l box 4" x 4" x 6* h i g h . The bottom of the box was r e i n f o r c e d by a 1/8" brass p l a t e , and one s ide by a t h i n n e r copper p l a t e . A s m a l l f i b r e b l o c k was mounted on t h i s s i d e to support the copper bus bar which made contact w i t h the centre e l e c t r o d e of the t e s t c e l l . The box was covered by one l a y e r of as -bestos paper over which 45 to 50 feet of Chromel A #22 guage r e s i s t a n c e wi re were wound, g i v i n g a 45 ohm h e a t i n g c o i l . The oven was i n s u l a t e d on the bottom and s ides w i t h 1 1/2" of rock wool i n s u l a t i o n . In order to o b t a i n c lose temperature c o n t r o l , a sma l l s o i l o f Chromel r e s i s -tance wire was put i n s i d e the oven. The power input to the main h e a t i n g c o i l was c o n t r o l l e d by a v a r i a c ; and the input to the secondary c o i l i n s i d e the oven cou ld be changed by means o f a v a r i a b l e r e s i s t a n c e i n s e r i e s w i t h i t . The temperature c o n t r o l u n i t was an American I n s t r u -ment Company " M e t a s t a t i c " mercury t h e r m a l - r e g u l a t o r used w i t h an Amineo mercury r e l a y , which c o n t r o l l e d the input to the secondary h e a t i n g c o i l o n l y . 7. The a i r i n the even was c i r c u l a t e d by a s m a l l fan d r i v e n by a v a r i a b l e speed s t i r r i n g motor . Two h o l e s were d r i l l e d and tapped i n the bottom o f the t e s t c e l l , so tha t i t cou ld be screwed onto a b rass p l a t e about 2 l / 2 t t square. Holes were then d r i l l e d and tapped, i n t h i s p l a t e and i n the base p l a t e a t the bottom o f the oven. T h i s a l l owed the o e l l t o be screwed f i r m l y to the bottom o f the oven, the screws making good e l e c -t r i c a l contac t between oven and t e s t c e l l ; and the c e l l cou ld be e a s i l y removed from the oven f o r washing, f i l -l i n g o r r e p a i r s . In a d d i t i o n to s e r v i n g as an oven, the sheet meta l box, which was grounded, ac ted as an e l e c -t r i c a l s h i e l d f o r the t e s t c e l l , .0. Remainder o f E l e c t r i c a l C i r c u i t The remainder o f the c i r c u i t shown i n f i g . 1 was assembled i n a box s h i e l d e d e l e c t r i c a l l y by sheet m e t a l . c i r c u i t rough ly to the o s c i l l a t i n g frequency o f the c r y s t a l . Gg was a sma l l v a r i a b l e condenser which a l lowed the c a l i b r a t e d d i a l o f condenser C3 to be se t a c c u r a t e l y a t any d e s i r e d r ead ing when the t e s t c e l l con ta ined o n l y a i r as the d i e l e c t r i c , Gg was a v a r i a b l e condenser w i t h s e m i c i r c u l a r p l a t e s , such tha t i t s c a p a c i t y v a r i e d ve ry n e a r l y l i n e a r l y w i t h the number o f degrees through which the moveable p l a t e s were turned w i t h respec t to the f i x e d p l a t e s . A d i a l c a l i b r a t e d from 0 to 100 through 180° was mounted w i t h Cg so that when the d i a l read z e r o , c a p a c i t y Gg was a mazimum^and when the d i a l read 100, c a p a c i t y Gg was a minimum, the t o t a l v a r i a t i o n i n eapa-the t e s t o e l l w i t h temperature o r w i t h change o f d i e l e c -t r i o a l t e r e d the frequency o f o s c i l l a t i o n o f the p l a t e c i r c u i t from tha t of the quar tz c r y s t a l , t h i s condenser was used to re- tune the c i r c u i t to the frequency o f the c r y s t a l . The inductance i n the p l a t e c i r c u i t c o n s i s t e d o f 30 tu rns o f co t t on i n s u l a t e d copper wi re wound on a 1 1/2 inoh diameter form. The quar tz c r y s t a l was a Y-out type o f about 2 mega-c y c l e s f requency. As noted p r e v i o u s l y , a 6E5 type tube ac ted both as an o s c i l l a t o r and a de t ec to r to i n d i c a t e when the p l a t e c i r c u i t was tuned to the frequency o f the c r y s t a l * The power f o r the p l a t e c i r c u i t was s u p p l i e d by two 45 v o l t , #385 Eveready d ry c e l l s * The f i l amen t c i r c u i t was heated by a number o f 1*5 v o l t , #6, d ry c e l l s . I t was found tha t o p e r a t i n g the f i l ament o i r c u i t c o n t i n u o u s l y g r e a t l y decreased the vo l tage d e l i v e r e d by the dry c e l l s w i t h i n a shor t t i m e . Since v a r i a t i o n i n f i l amen t vo l t age was one f a c t o r c o n t r i b u t i n g to e r r a t i c When v a r i a t i o n s i n the c a p a c i t y o f 9* r e s u l t s , t h i s vo l t age was kept constant a t E v o l t s by oonneot ing i n p a r a l l e l 2 o r 3 s e r i e s - s e t s o f 4 c e l l s and p l a c i n g a sma l l v a r i a b l e rheos ta t i n the f i l amen t c i r c u i t * S t i l l l a t e r , t h e f i l amen t was run from a 6 v o l t l e ad s t o r -age c e l l * Dur ing some o f the f i r s t obse rva t ions made, i t was found that v a r i a t i o n i n room temperature caused apparent v a r i a t i o n i n the c a p a c i t y o f the t e s t c e l l even though the c e l l was kept a t constant temperature i n the oven. The main p o r t i o n o f the r . f . c i r c u i t was, t h e r e f o r e , en-c l o s e d i n a 5 - p l y box which acfeed as thermal i n s u l a t i o n , and the box was kept a t the constant temperature o f 30°G by a sma l l chromel r e s i s t a n c e wi re h e a t i n g c o i l a c t i n g i n con junc t ion w i t h a mercury thermal r e g u l a t o r and a r e l a y * The a i r i n t h i s constant temperature ba th was c i r c u l a t e d by a fan operated by a v a r i a b l e speed s t i r r i n g motor . The l eads between the t e s t c e l l and the r e s t o f the c i r c u i t were f i x e d i n p o s i t i o n as r i g i d l y as p o s s i b l e and were e l e c t r i c a l l y s h i e l d e d . They were run through s m a l l pyrex t ub ing and s h i e l d e d , one by copper t u b i n g and the other by s i l v e r f o i l * The l e a d which was not grounded had to be more r i g i d l y f i x e d than the o t h e r . C a l i b r a t i o n o f Equipment To determine over what range o f d i a l r ead ings the v a r i a t i o n i n c a p a c i t y Cg was l i n e a r , the c a p a c i t y o f con-10. denser Cg was measured, f o r v a r i o u s d i a l r e ad ings , by a Boonton Radio Corpo ra t i on Q-Meter, Type 160-A. The c a p a c i t y d i a l on the Q-Meter was c a l i b r a t e d from 30 to 4 5 0 ^ « ^ 8 a n d was used w i t h a v e r n i e r d i a l c a l i b r a t e d over a range o f 6^yif in t en ths o f b l ^ / u ^ • Changes i n c a p a c i t y cou ld be es t imated to O.Ol^uf. The condenser was c a l i -b ra ted a f t e r i t had been mounted i n the s h i e l d e d box. S ince a sharp resonant peak was not ob ta ined i n the c i r -c u i t used f o r the c a l i b r a t i o n , s e v e r a l c a l i b r a t i o n s were made and a weighted average o f the d i f f e r e n c e s i n capa-c i t y between success ive d i a l r ead ings was s t ruck as shown i n t a b l e I . The p l o t o f these r e s u l t s i n f i g . 5 shows that the c a p a c i t y o f the t un ing oondenser Gg v a r i e s l i n e a r l y between 15 and 85 on the d i a l . For t h i s reason^ the d i a l was set a t 15.0 when the t e s t c e l l had minimum c a p a c i t y ; i . e . , when i t conta ined a i r as d i e l e c t r i c * / Before c o n s i d e r i n g how the t e s t c e l l was c a l i b r a t e d , i t w i l l not be out o f p l a c e to mention the d i f f e r e n c e be-tween d i e l e c t r i c constant and opoo i f l o i n d u c t i v e c a p a c i t y . From Coulomb's law we can de f ine e l e c t r i c a l i n t e n -s i t y as the fo rce exer ted by charge ^.fon u n i t charge o r ^ ~ TT " ^ r where it = constant o f p r o p o r t i o n a l i t y . Table I D i a l Reading C a p a c i t y Increments Weighted A v g . A i A 2 ^ 3 ^ 4 0 0 0 0 0 0 0 3 0.30 0.15 0.15 0.15 0.10 0.13 5 0.20 0.30 0.20 0.35 0.33 0 .30 8 0 .90 0.65 0.65 O.65 0.60 0.64 10 0 .40 0.50 0 .40 0 .40 0.35 0 .40 15 1.10 1.35 1.60 1.50 1.45 1.50 20 1*40 1.35 1.30 1*27 1.32 1.32 30 2.60 2.55 2.60 2.48 2 .45 2.49 40 2.60 2 .50 2 ,40 2 .40 2.48 2.48 30 2 .30 2.50 2.75 2 .45 2 .40 2.44 60 2..40 2.25 2 ,40 2 .40 2.47 2*3? 70 2*60 2.50 2.55 2.52 2.45 2*52 80 2.60 2.75 2.50 2.63 2.63 2.62 85 1*15 1*10 1.25 1.25 1.25 1.25 90 1*15 1.20 1.15 1.15 1.15 1.15 93 0.60 0.65 0.55 0.53 0.45 0.55 95 0.30 0.15 0.35 0.27 0.30 0.30 97 0.25 0.30 0.35 0 .40 0.35 0.35 LOO 0.25 0.25 0.20 0.25 0.30 0.25 29 -— — - - — - -- -- — — - - — — --- --- - - -— Zo — — it \ %— 1 j i I — \ — k \ ' i 1 > 1 y Fit 7, c 15 i Col lb raff Oi fc z 7 curve 7 r t uninq Q • v. /, 0 z 4 r r ? 2 z r 2 c 7 s •o c Z. C cJ t>l ELECT k?!C c ONSTR f n ( J 4 o m. dim t i ?<2£ c r 6c 2 fi 11. E l e c t r o s t a t i c s a l s o de f ines e l e c t r i c a l d isplacement as Then i n t e n s i t y and displacement are r e l a t e d by the f a c t o r JUL; thus J ) =/tt E y U i s the i n d u c t i v e c a p a c i t y or the p e r m i t t i v i t y o f the medium. Vacuum has an i n d u c t i v e c a p a c i t y ofyUy. Cons ider two charged p l a t e s which form a condenser . L e t q he the charge on each p l a t e . Wi th vacuum as d i -e l e c t r i c we have q a CQ^O where C 0 i s the c a p a c i t y and V 0 i s the p o t e n t i a l d i f f e r e n c e between the p l a t e s when vacu-um i s d i e l e c t r i c . W i t h some substance as d i e l e c t r i c q r C ^ S ince q does not change when we change the d i e l e c t r i c C 0 V 0 a CxVx Experiment shows Cx c 0 or C i n € , C 0 where 6 , i s c a l l e d the d i e l e c t r i c cons tan t . Then c . v „ - e . c „ v , How the p o t e n t i a l d i f f e r e n c e between p l a t e s A and B i s v- - f ( r . a r ; A When vacuum i s the d i e l e c t r i c V o ^ - f ? E f . <*T) = - f ^ - X - d s 0 0 5 0 = X f i d s C o s G Z 4 - J A / t a ere 9 is -Hie acn^ le befween E and cts 12 . When any substance i s d i e l e c t r i c 6 - i t * * " 6 A»so y t - Vo I n the egs system o f e . s . u n i t s 1 aucl i n d u c t i v e c a p a c i t y and d i e l e c t r i c constant are the same numer ica l ly< In o ther systems o f u n i t s , however, $ 1 and £ ^ • Fo r any system, however, the d i e l e c t r i c constant o f any one substance i s the same* From the r e l a t i o n €tyU, /j/(oit can be seen t ha t f o r vacuum as d i e l e c t r i c ; i . e . w h e n ^ , £ s 1*0000. Now a i r has a d i e l e c t r i c constant o f 1.00059 a t 0°G which i s i n d i s t i n g u i s h a b l e from tha t o f vacuum w i t h the apparatus used . Henoe to c a l i b r a t e the t e s t c e l l , condenser Cg was set t o read 15 (page 7J when the t e s t c e l l con ta ined o n l y a i r as d i e l e c t r i c and the c i r c u i t was tuned w i t h Cg. The t e s t c e l l was then f i l l e d to the shoulder ( f i g , 3} w i t h benzene, the c i r o u i t tuned w i t h condenser Cg, and the new d i a l r e a d i n g observed . Then 15.0 on the d i a l corresponds to a d i e l e c t r i c constant o f l.OOO^and the d i a l r e ad ing f o r benzene corresponds to the d i e l e c t r i c constant o f benzene (2.283 at 20°0 (5) ) . (5) F . G. A lexande r , p o p . c i t . 1 3 . 1 I f C>0 i s the c a p a c i t y o f the t e s t c e l l when a i r i s d i e l e c t r i c , and i f i s i t s c a p a c i t y when a t e s t l i q u i d i s d i e l e c t r i c , the the d i e l e c t r i c constant o f the l i q u i d i s £ s C 2 : / C » 0 L e t C x - C 0 r which i s the c a p a c i t y change made i n the t u n i n g condenser . S u b s t i t u t i n g f o r C x we get £ c D - c 0 = c C o Thus i t i s shown that d i e l e c t r i c constant v a r i e s l i n e -a r l y w i t h the change i n c a p a c i t y o f the condenser C g , and between 15 and 85 on the G 3 d i a l , d i a l r e a d i n g and d i e l e e t r i o cons tant are l i n e a r l y r e l a t e d . The thermometer used to take the temperature o f the constant temperature oven was c a l i b r a t e d from -10°C to 110°C i n t e n t h s . The i c e and steam p o i n t s were cheeked and a c o r r e c t i o n f o r the i naccu racy o f the o r i g i n a l c a l l b r a t i o n was a p p l i e d to a l l temperature read ings i n a d d i -t i o n to a c o r r e c t i o n f o r stem exposure . The stem expo-sure c o r r e c t i o n i s g iven by the formula t * 0.000165 ( t - t s ) ( 0 ) t s observed temperature t s = temperature o f exposed p o r t i o n o f stem Q z no . o f degrees on the s ca l e over which the mercury i s exposed* 14 . Exper imen ta l D i f f i c u l t i e s I t was cons idered d e s i r a b l e to observe the c a p a c i t y o f the empty c e l l at v a r i o u s temperatures before measur-i n g the d i e l e c t r i c constant o f d e c a l i n over a range o f temperatures . The temperature o f the c e l l was r a i s e d to 50°G and c a p a c i t y read ings were taken p e r i o d i c a l l y over a 10 1/2 hour p e r i o d , d u r i n g which the temperature o f the r e s t o f the e l e c t r i c a l c i r c u i t was kept a t 3 0 ° C ± 1 ° . The vo l t age a p p l i e d ac ross the f i l amen t o f the 6E5 was ob-served when each r ead ing was t a k e n . The apparent capa-c i t y o f the t e s t c e l l was found to decrease w i t h t ime , as shown i n f i g . 6. When these measurements were made 3 the f i l amen t o f the 6E6 was s u p p l i e d by 3 o r 4 dry c e l l s i n s e r i e s . S ince the c u r r e n t , 0 .3 amp.^taken from the c e l l s was very heavy, i t was necessary to add another c e l l to the s e r i e s from time to t ime ; and l a r g e sudden v a r i a t i o n s i n f i l amen t v o l t a g e occur red d u r i n g the course o f these o b s e r v a t i o n s . These have a l s o been p l o t t e d aga in s t time i n f i g . 6 and i t can be r e a d i l y seen tha t a r e l a t i o n e x i s t s between the f i l amen t v o l t a g e and the measured c a p a c i t y o f the t e s t c e l l * T h i s r e l a t i o n , how-ever , appears to be superimposed upon a cont inuous d r i f t toward dec reas ing c a p a c i t y w i t h t i m e . S ince i t was sug-gested tha t change i n p l a t e vo l t age might account f o r t h i s d r i f t , a c a p a c i t y and r e s i s t a n c e were put i n the FIG fc> > how i / / V •s ? c 1rrfi r n t Catpacit / < h 'St i -e t ~e\ai /nr~> 1 / } J in - -o-o — ~— T 1 T — 1 \ • ... — — <• 1 " 1 -! 1 • • s :^ 1 "S ~~ 1 1 •• E — TT — / 1 V • . ok 5 d! i < SIO n C r V ML 2 <?/ ca£\ it r 0 f c<c em lest eel / J — i * r — — 1 H Z C 7 A t ) i s\ (h 15 . p l a t e c i r c u i t , as shown i n f i g . 7, to e l i m i n a t e any change i n the c a p a c i t y o f the vo l t age source , and the p l a t e vo l t age was decreased by 22 v o l t s . F i g . 7 T h i s vo l t age change produced a change o f c a p a c i t y o f —0'0oo35^v9V v o l t , which i s an i n s i g n i f i c a n t e r r o r . A t the same time the e f f e o t o f changing f i l amen t vo l t age was cheoked, and i t was found tha t a change o f 1.5 v o l t s on the f i l amen t had no e f f e c t on the measured oapao i ty e i t h e r immedia te ly or w i t h i n 15 minu tes . S t i l l l a t e r measurements showed a change i n c a p a c i t y w i t h f i l amen t vo l t age s i m i l a r to tha t shown i n f i g . 6. To determine whether t h i s observed change was caused merely by change i n the c a p a c i t y i n the f i l amen t c i r c u i t when another dry c e l l was added, an o l d c e l l whose p o t e n t i a l was o n l y 0 .2 v o l t s was put i n s e r i e s w i t h the o ther dry c e l l s i n the f i l amen t c i r c u i t . The r e s u l t i n g change i n the apparent c a p a c i t y o f the t e s t c e l l was o n l y 0 . 0 2 ^ 6 ^ . I t was the re fo re assumed tha t the vo l t age ac ro s s the f i l a m e n t , 16. and not the oapao i ty o f the f i l amen t c i r c u i t determined the v a r i a t i o n i n d i a l r e a d i n g s . S ince on two o c c a s i o n s , once over a 6 1/2 hour p e r i o d and once over a 4 1/2 hour p e r i o d , the c a p a c i t y was found to he constant when the t e s t c e l l was a t room temperature, i t was cons ide red p o s s i b l e tha t s m a l l quan-t i t i e s o f grease or ammonium c h l o r i d e might be d i s t i l -l i n g out from the c e l l a t the e l eva t ed temperature . The c e l l was, t h e r e f o r e , .scrubbed out w i t h soap and wate r , r i n s e d w i t h d i s t i l l e d water and baked a t about 70 G C f o r a few h o u r s . For a few days a f t e r t h a t , the measured c a p a c i t y o f the t e s t c e l l remained constant w i t h t ime at any one temperature . L a t e r , the measured c a p a c i t y o f the c e l l aga in decreased w i t h time at 50°G; but even a f t e r washing the c e l l * f i r s t w i t h soap, then w i t h c o l d water f o r 4 hours , then r i n s i n g i t out w i t h tw ice d i s -t i l l e d a l c o h o l , and f i n a l l y w i t h twice d i s t i l l e d e t h e r , the d r i f t w i t h time was not e l i m i n a t e d . With the f i l amen t vo l tage main ta ined a t 5*0 v , the c e l l was t e s t e d f o r d r i f t when i t con ta ined t r ans d e c a l i n as d i e l e c t r i c * The measured c a p a c i t y o f the c e l l v a r i e d qu i t e i n c o n s i s t e n t l y ; a t room temperature both d r i f t t o -ward decreas ing c a p a c i t y and unreasonably l a r g e f l u c t u -a t i o n s o f c apao i ty were observed , ( f i g , 8 ) . 17. To determine whether t h i s u n d e s i r a b l e behaviour was caused by the t e s t c e l l o r by the remainder o f the c i r c u i t , the t e s t c e l l was removed and d i a l r ead ings were taken p e r i o d i c a l l y . The c i r c u i t was kept a t 30°G and f o r the f i r s t few hours the f i l amen t vo l t age was 5.0 v . As shown i n f i g . 9, d r i f t cont inued a t much the same r a t e as before (compare w i t h f i g s . 6 and 8 ) . S ince the r a t e d f i l amen t vo l t age f o r a 6E5 tube i s 6.3 v o l t s , i t was thought p o s s i b l e tha t o p e r a t i n g the tube at 5 v o l t s made i t s e n s i t i v e to ve ry s m a l l changes i n f i l a -ment vo l t age and that a change i n the c h a r a c t e r i s t i c s o f the tube was r e s p o n s i b l e f o r the observed d r i f t . For t h i s reason the f i l amen t vo l t age was i nc rea sed to 6.1 v o l t s , the f i l amen t now be ing heated from a l e a d s torage c e l l . F i g u r e 9 shows tha t the c a p a c i t y d r i f t p e r s i s t e d a f t e r the v o l t a g e had been changed. Al though the h i g h frequency c i r o u i t i s s e n s i t i v e to temperature change, the d r i f t toward lower c a p a c i t y i s not acoounted f o r by sma l l f l u c t u a t i o n s i n the temper-s' a ture o f the c i r c u i t s ince such temperature f l u c t u a t i o n s should produce cor responding inc reases and decreases i n the measured c a p a c i t y o f the system* The r e l a t i o n be -tween the temperature tof the c i r c u i t and the d i a l r ead -i n g i s i l l u s t r a t e d i n f i g u r e s 10, 11 , 12 and 13 . Al though the r e l a t i o n s h i p i s sometimes i r r e g u l a r , the graphs CHANGE IN DIAL READIES (divisions) CHRNGE //V DIRL READING X I t ts I 0 I V 9 0 0 •c r*. Q i 3 0 4-4-•• s-•H k 0 — —-0 a-/c ! 1 — MS — • TT / — -— -— -H — — — — -— . . .. °\ \ \ g j T m h \ 1 i o I / >•» / c o 4 c \ 1 4— 3 1 [0 1 1 • 1 1 L c • 1 1 j c L 3 r p —*• VJ / <T XT c n 1 > 1 J "si < 4 >> 5 si g i , \ -a-^.i ET 5 • 8 1 1 — *5 i cS -" 1 _ 1^1 ^ f i m i Eg i 5 Or 1 3 -11  <L 3 S S 1^ 1  § _ fftttt < CD Co CIRCUIT 7£MPERf\Tbf?E 18, i n d i c a t e tha t a f t e r cons ide rab l e time l a g the d i a l r ead -i n g i nc r ea se s as the temperature o f the c i r c u i t inoreases^ and tha t the average r a t e o f inc rease i s 0 .5 d i a l d i v i -s i o n per degreeyuhich represen t s an i nc rea se i n the mea-sured o a p a c i t y o f the c e l l o f 0 . 1 1 ^ n £ , o r an inorease o f 0.012 i n the d i e l e c t r i c constant o f any l i q u i d i n the t e s t c e l l . I t should be emphasized, however, tha t the d r i f t toward lower c a p a c i t y i s not accounted f o r by even qu i t e l a r g e f l u c t u a t i o n s i n the temperature o f the c i r -o u i t , A new 3502 K i l o c y c l e Pedersen Radio Company c r y s t a l was bought and i n s t a l l e d i n the c i r c u i t . S ince i t s temperature c o e f f i c i e n t was a t most 2 o y c l e s per mega* c y c l e per degree c e n t i g r a d e , i t was p robab ly A T - c u t . With the t e s t c e l l s t i l l out o f the c i r c u i t and the f i l a -ment vo l t age a t 6 v o l t s , the performance o f the apparatus was aga in t e s t ed by t a k i n g d i a l r ead ings two or three t imes each hour . The r e s u l t s are p l o t t e d i n f i g u r e s 10 and 1 1 . A c o n t i n u a l d r i f t i n oapao i ty i n one d i r e c t i o n was no longer observed , but t h i s d r i f t was r e p l a c e d by p e r i o d i c changes i n oapac i ty i n e i t h e r d i r e c t i o n . Some, but not a l l , o f t h i s change can be a t t r i b u t e d to v a r i -a t i o n i n the temperature o f the c i r c u i t . S ince i t might have been the tube tha t was caus ing the t r o u b l e , a new 6E5 was put i n the c i r c u i t and the 19. behaviour o f the apparatus observed as b e f o r e . Dur ing these obse rva t i ons the temperature was kept a t 30.3 ± 0 . 1 ° 0 . The r e s u l t s , which are p l o t t e d i n f i g . 12 show (a) the change i n tubes d i d not change the o p e r a t i n g c h a r a c t e r i s t i c s o f the appara tus . (b) m a i n t a i n i n g the c i r o u i t a t a temperature con-s tan t w i t h i n 0 .2°C does not e l i m i n a t e the p e r i -o d i c v a r i a t i o n s i n o a p a c i t y a l s o observed p r e v i o u s l y . S ince there was a p o s s i b i l i t y tha t a r e l a t i o n s h i p might e x i s t between humid i ty and the d i a l r e a d i n g , the humid i ty was observed over an 11 hour p e r i o d du r ing which d i a l r ead ings were be ing t a k e n . The r e s u l t s , p l o t t e d i n f i g . 12, i n d i c a t e tha t no such r e l a t i o n e x i s t s . I n s p e c t i o n o f the data p l o t t e d i n f i g . 9 shows, i n the l i g h t o f subsequent da ta , tha t the v a r i a t i o n i n d i a l r e ad ing d u r i n g the p e r i o d when f i l amen t vo l t age was a t 6.1 v o l t s and the o l d c r y s t a l was i n the o i r c u i t was not l a r g e r than v a r i a t i o n s observed a f t e r the new c r y s t a l had been put i n the c i r c u i t . To t e s t , then , whether the change o f c r y s t a l o r change o f vo l t age had produced the more constant d i a l r e ad ings , the o l d c r y s t a l was re turned tp the c i r c u i t and the apparatus run w i t h 6.8 v o l t s a c -r o s s the f i l ament of the 6E5 and w i t h the c e l l s t i l l out o f the c i r c u i t • The r e s u l t s , p l o t t e d i n f i g . 13, resemble 20. the r e s u l t s ob ta ined w i t h the new c r y s t a l * As a f u r t h e r check, the f i l amen t vo l t age was lowered to 5*0 v o l t s and read ings taken over s i x hou r s . T h i s o p e r a t i n g c o n d i t i o n seems l e s s s t a b l e than the one i n which the f i l amen t I s run a t or above i t s r a t e d vo l tage* D u r i n g most o f the t e s t s , the o r y s t a l was kept os -c i l l a t i n g c o n t i n u o u s l y ; and the ques t ion arose as to whether the mechanica l s t r a i n so produced caused f a t i g u e i n the o r y s t a l which was r e s p o n s i b l e f o r v a r i a t i o n i n i t s resonant f requency,and consequent v a r i a t i o n i n d i a l r e a d i n g . The data p l o t t e d i n f i g u r e s 11 and 12 was taken w i t h the o r y s t a l o s c i l l a t i n g o n l y l o n g enough to determine each d i a l r e a d i n g . S ince v a r i a t i o n s o f the same magnitude as had been-found p r e v i o u s l y s t i l l o c c u r -r e d , i t was concluded that c r y s t a l f a t i g u e due to c o n t i n -uous o s c i l l a t i o n d i d not account f o r the poor r e s u l t s * In summary, then , we have the f o l l o w i n g r e s u l t s * 1. The temperature o f the c i r c u i t should be c o n t r o l l e d to w i t h i n ± 0 . 1 ° G to keep the measured c a p a c i t i e s i n -dependent o f c i r o u i t temperature* 2 . The c o n t i n u a l d r i f t toward lower c a p a c i t y , observed d u r i n g the f i r s t t e s t s , i s not e n t i r e l y c h a r a c t e r i s t i c o f the apparatus wi thout the t e s t c e l l . A l though f i g u r e 9 was a t f i r s t thought to i n d i c a t e tha t the d r i f t p r e s i s t e d when the o l d Y-out c r y s t a l was i n the 21 . o i r c u i t , f i g u r e 13 shows tha t the d r i f t i s not as p r e -s i s t e n t as tha t o r i g i n a l l y observed ( f i g ; 6 ) . The new AT-cu t c r y s t a l appears , however, to be s l i g h t l y more s t ab l e than the o t h e r . Why the d r i f t d i d not r e t u r n when the t e s t c e l l was put back i n the c i r c u i t i s not e x p l a i n e d . (These data are p l o t t e d i n f i g u r e 14.) 3 . Around four v o l t s , change i n f i l ament vo l t age has a pronounced e f f eo t on the measured o a p a c i t y o f the t e s t c e l l . Most s a t i s f a c t o r y o p e r a t i o n i s p robab ly ob ta ined by hav ing 6.3 v o l t s , or a l i t t l e more, ac ross the f i l a m e n t . 4i A l though B e n d e r (6; s t a t e s tha t e r r a t i c o p e r a t i o n may be expected i n humid weather, no d i r e c t connec t ion was observed between h u m i d i t y and d i a l reading* S ince the humid i ty i s almost always h i g h i n Vancouver, i t i s suggested tha t B e n d e r »s recommendation o f r i n -the s i n g / t u n i n g condenser p l a t e s In abso lu te a l c o h o l be t r i e d i n any f u r t h e r r e s e a r c h . Al though a f i b r e cap had been made to f i t over the annular opening o f the t e s t c e l l to reduce evapora t ion ';. l o s s from the c e l l , i t was found t h a t evapo ra t i on s t i l l cont inued at an exces s ive r a t e . At 22°C, w i t h the fan i n the oven o p e r a t i n g , and w i t h benzene i n the c e l l , f^ul B e n d e r . J . Chem. E d u c a t i o n , 23, #4, p . 179, A p r i l 1946. 22. evapora t ion l o s s e s caused a decrease i n the c a p a c i t y o f the o e l l o f 0 .00l5 / t j / u ^ p e r minute; and when the fan was not r unn ing , the r a t e o f decrease was O.OOOl j^u / -pe r minu te . At h i g h e r temperatures , l o s s o f d e o a l i n by evapora t ion i s an e r r o r o f s i m i l a r magnitude; ah e r r o r which makes the de t e rmina t ion o f d e y £ / T q u i t e u n f e a s i b l e . V I , Aocuraoy o f the Method 1* P r e c i s i o n of Tuning Condenser S ince the t u n i n g c a p a c i t o r was a good q u a l i t y con-denser w i t h s e m i c i r c u l a r p l a t e s , one would expect ohange i n c a p a c i t y to be l i n e a r over most o f the o a p a c i t y range . The abso lu te va lues o f c a p a c i t y measured by the 0-meter , which was used to check the t u n i n g condenser f o r l i n e -a r i t y , are not impor tan t ; but d i f f e r e n c e s i n c a p a c i t y should be a c c u r a t e l y measured. I n d i v i d u a l v a l u e s o f oapac i t y on the 0,-meter d i a l are accura te to ± o r ± l f 0 , whichever i s the g r e a t e r . I n cheoking the t u n i n g oondenser, the range between 30^Myttf and 60 /Uyu£on the 0,-meter was used . Hence, i f the 0,-meter was c a l i b r a t e d aga ins t a s tandard c a p a c i t y a t lO^ylt-f- i n t e r v a l s i n t h i s range, a p o s s i b l e e r r o r of 20% may e x i s t i n the measure-ment o f a oapac i t y d i f f e r e n c e . Al though t h i s e r r o r i s p o s s i b l e ^ i t i s not cons ide red p r o b a b l e . I t was found tha t c a p a c i t y read ings on the 0,-meter wander as the instrument con t inues i n o p e r a t i o n , even 23. a f t e r a few hour s . The r a t e o f wandering i s of the order o f O . l ^ j ^ p e r hour , and f o r t h i s reason the 0,-meter i t s e l f i s u n s u i t a b l e f o r measuring d ^ / d T w h e n the oapac i t y of the t e s t c e l l i s s m a l l . T h i s wandering would not a f f e c t the c a l i b r a t i o n o f the t u n i n g condenser because o n l y the d i f f e r e n c e between s u c c e s s i v e 0-meter r e a d i n g s , which were taken every minute or two, are important i n t h i s c a l i b r a t i o n . 2. O r i e n t a t i o n of the Centre E l e c t r o d e S ince a s m a l l change i n the p o s i t i o n of the centre e l ec t rode produces an app rec i ab l e ohange i n the oapac i ty of the t e s t c e l l , i t i s Important to^ be ab l e t o r e p r o -duce, as a c c u r a t e l y as p o s s i b l e , the s e t t i n g o f t h i s e l e c t r o d e . I t was found e a s i e r to o r i e n t the e l e c t r o d e when the f i b r e cap, used to cut down evapo ra t i on , was not i n the c e l l . D i a l r e ad ings were t aken f o r a s e r i e s o f d i f f e r e n t s e t t i n g s of the middle e l e c t r o d e . These are shown i n Table I I toge ther w i t h the average d e v i -a t i o n in t roduced i n t o the va lue s o f 6 . The probable e r r o r i n the d i e l e c t r i c constant of d e c a l i n ( £ d e c a l i n — 2.15) w i l l be v e r y c l o s e to 0.845 (Avg . d e v i a t i o n f o r benzenej whereTt i s the number o f o b s e r v a t i o n s . That i s , the probable e r r o r i n 6 i e o a ^ ^ n caused by o r i e n t a t i o n o f the Table I I (a) F i b r e Cap Absent C e l l empty C e l l f i l l e d to shoulder w i t h Benzene C e l l f i l l e d to the top w i t h Benzene 15.0 65.O 15.2 64.8 14.7 65.0 15.0 64.8 15.1 64.7 Mean 15*0 64.9 Avg* d e v i a t i o n Capao i ty*of t e s t c e l l empty Capao i ty^o f t e s t c e l l w i t h benzene A v g . d e v i a t i o n i n £ f o r a i r A v g . d e v i a t i o n i n B f a r benzene (b) F i b r e Cap Presen t 67*0 67.3 67.2 67.O 67*0  67.I 0*1 d i v i s i o n = 0.023^1^ 9.8 ,U/*f 22.4 jUjuf 0.2% o.a.% C e l l empty •15*0 14.5 14.0 15.0 14.3 14.7 14.8 Mean 14.6 Avg* d e v i a t i o n 0.3 d i v . A v g . d e v i a t i o n i n 6 0.7' C e l l f i l l e d to shoulder w i t h Benzene 65.5 65.3 64.2 65.I 65.4 65.I O.56 d i v . 0.4?. A C a p a c i t y of tha t pa r t of the c e l l which w i l l be or i s f i l l e d w i t h l i q u i d . 24. middle e l e c t r o d e i s not more than 0.21*. e v e n when the f i b r e c o l l a r i s i n the c e l l * 3. Anomalous Dispers ion(7) When h i g h f requenc ies are used i n the measurement of d i e l e c t r i c cons tan t , the phenomenon of anomalous d i s p e r s i o n may be encountered; i . e . , the d i e l e c t r i c oon-higher s tant becomes smal le r a t high- f requencies* The pheno-menon i s conf ined to p o l a r l i q u i d s ^ a n d commences a t a frequency whose r e c i p r o c a l i s equal to the r e l a x a t i o n t ime o f the d i p o l a r m o l e c u l e s . The r e l a x a t i o n t ime i s g iven by where 7j s v i s c o s i t y a s mo lecu la r r a d i u s k s Bol tzmann 1 s constant T s abso lu te temperature Al though d e c a l i n has been found to have zero moment(8), i t i s conce ivab le tha t the unsymmetr ica l c i s form has a sma l l d i p o l e moment, and hence tha t anomalous d i s p e r s i o n might be encountered i n measuring S f o r d e c a l i n . The c r i t i c a l frequency at which the phenomenon commences may be shown to be much h ighe r than 3502 k . c , the ma x i -,(7) C .P .Smyth , D i e l e c t r i c Constant and M o l e c u l a r S t r u c t u r e , Chemical C a t a l o g C o . , 1931, P*p. 34-38 (8)Estermann, Z . p h y s i k . Chem., (B) 1, 161 (1928); 2, 287 (1928) . 25. mum frequency used . Thus^ i f we s u b s t i t u t e 7j « 0.0338 p o i s e (9) a = 6 x 10" 8 cm (10) k s I.38 x l O " 1 ^ erg/degree i n t o T r 293°K = 4Jr-?7a we get X * 2.29 x 10"*^ sec . f o r c i s d e c a l i n at 20°C. Hence the c r i t i c a l frequenoy i s o f the order o f 400 megacycles . 4 . The Aoouraoy o f € I f the d i e l e c t r i c constant o f a l i q u i d i s d e s i r e d at one temperature o n l y , t h i s method and apparatus p r o -v i d e s an easy and accura te method of making the measure-ment* I f the measurement oan be made before the l o s s of l i q u i d from the c e l l by evapora t ion i s a p p r e c i a b l e , then the main e r r o r i s the v a r i a t i o n i n oapac i t y w i t h t ime , inheren t i n the apparatus as i t stands at present* The maximum v a r i a t i o n found l a t t e r l y i s about 0*25yuyn£» a substance whose d i e l e c t r i c constant i s 2, t h i s v a r i a -t i o n represen ts a maximum e r r o r o f 1.3% i n the determined va lue o f € . (9) Seyer and L e s l i e , J . A . C . S . , 64, 1914 (1942) . (10) Smyth, o p . c i t . , p . 38, quotes the mo lecu l a r r a d i u s of n i t robenzene as approx. 3 x 10~° cm. An approx imat ion f o r the mo lecu l a r r a d i u s o f d e c a l i n i s , then , 6 x 10~Qom* 26. 5. Aoouraoy of Aooord ing t o the C l a u s i u s - M o s o t t i equa t ion , the molecu la r p o l a r i z a t i o n P i s g iven by e+2 where £, s d i e l e c t r i c constant M s moleou la r weight p a d e n s i t y Now i f the d i p o l e moment of a substance i s ze ro , P j£^*(T) , and hence f o r d e c a l i n we may w r i t e , assuming i t to he n o n - p o l a r , a_ I ~ > A — J_ c r r l e + 2 / H ar = df dr dr 6 — 2.15 f o r d e c a l i n s -0.000734 f o r o i s d e c a l i n (,11) C I T p s 0.8967 at 20°C f o r o i s (11) T h e n d ^ T = -0 .0013 pe r degree 0 f o r o i s d e c a l i n . I f £ be measured at 10 degree i n t e r v a l s , and i f the maximum e r r o r i n the d i f f e r e n c e between two succes s ive va lues o f £ be 40%, then the maximum a l l o w a b l e e r r o r i n e i t h e r measurement i s ± 0.003, or+0 .14?.. The d i f f i c u l t i e s o f o a p a c i t y v a r i a t i o n w i t h time and o f evapora t ion make aoouraoy of tha t order q u i t e u n a t t a i n a b l e . ( l l ) S e y e r and Davenport, J . A . C . S . , 65, 2426 (1941) 27. V I I . C o r r e c t i o n s f o r Changes i n Dimensions of the C e l l w i t h where 1 « l e n g t h o f c y l i n d e r formed by two c o a x i a l c y l i n d e r s i s g i v e n by o-24lG The oapao i ty o f a condenser r i s r a d i u s o f ou te r c y l i n d e r FJG.I7. T2 s r a d i u s o f i nne r c y l i n d e r U s i n g the dimensions g i v e n i n f i g u r e 2, the oapao i ty of the p a r t o f the t e s t c e l l i n d i c a t e d by the shading i n f i g . 17 can be c a l c u l a t e d as 8.07426 s t a t - f a r a d s at 20°C. Talcing the c o e f f i o i e n t of l i n e a r expansion of 18-8 s ta in-l e s s s t e e l as Ot_s 18.0 x 1G~^  pe r degree C , We c a l o u -l a t e tha t the c a p a c i t y o f the same p a r t of the c e l l i s 8.08874 s t a t - f a r a d s at 120°C. Then the i n c r e a s e i n the oapaoi ty of the empty c e l l i s 0.0018$ per degree C . Observa t ions showed tha t the measured oapao i ty of the t e s t c e l l i n c r e a s e d , on the average, at the r a t e o f 0*0087 iiitf.per degree C , o r 0.087% pe r degree. Then p robab ly 1/4 of t h i s inc rease occurs i n a p a r t of the c e l l where a t e s t l i q u i d can r e p l a c e a i r as d i e l e c t r i c , and the r e s t where the a i r i s not rep laced* When the c e l l i s f i l l e d w i t h d e c a l i n , a c o r r e c t i o n must be sub-t r a c t e d from the observed d i a l r e a d i n g , f o r a l l readings 28. t aken above 20 °C, to compensate f o r the change i n the c a p a c i t y of the c e l l which i s caused by a change i n the dimensions o f the c e l l r a t h e r than by a change i n the d i e l e c t r i c constant o f the t e s t l i q u i d . Expressed i n d i a l d i v i s i o n s , the c o r r e c t i o n i s - (k-Zjfaief)* | ( 0 . 0 3 S ) ] where t = temperature i n degrees C . 2.15 ^ € f o r d e c a l i n 0.038 d i a l d i v i s i o n s per degree correspond to O.OO87jxjxfper degree. The c o r r e c t i o n reduces to - ( t -20 ) (0 .049) The inc rease i n the annu la r volume i n d i c a t e d by the shaded area i n f i g . 17 i s g i v e n by 3<XSV pe r degree C . where o( sz ooeff* o f l i n e a r expansion o f s t e e l - 18.0 x 1 0 ~ 6 V a the annular volume s 0.0814 c u . i n . at 20°C The i n c r e a s e i n the volume o f t e s t l i q u i d i n the c e l l i s g i v e n by T 'V per degree C where 7* a ooe f f . o f volume expansion o f the t e s t l i q u i d = 81*8 x 10"- 5 f o r c i s d e c a l i n * V s 0.0814 c u . i n . at 20°C 29. * V t = ( n - i r t ) V . also ft = p + fc ^ Hence T - - # = + ^ f 7 ( ° ° ° ° - < 3 4 ) a t ^ Then the excess volume o f c i s d e c a l i n , occupying the -5 space above the shoulder o f the c e l l , i s 6.2 x 10 c u . i n . f o r each degree r i s e i n temperature . From t h i s one may c a l c u l a t e tha t the l i q u i d r i s e s through 0*14$ o f the he igh t from shoulder to top o f the c e l l w i t h each degree r i s e i n temperature. From Table I I i t i s seen tha t when the c e l l con ta ins benzene, f i l l i n g to the shoulder and f i l l i n g to the top i n v o l v e s a d i f f e r e n c e i n d i a l r e a d i n g of 2,2 d i v i s i o n s , o r a d i f f e r e n c e i n o a p a c i t y o f 0 . 5 1 ^A£ Then when the c e l l i s f i l l e d to the shoulder a t 20°C w i t h c i s d e c a l i n , each degree r i s e i n temperature i nc reases the c a p a c i t y o f the c e l l by (0 .0014)(2 .15) (0 .51) = 0.00067«irf (2728) ™ due to the expansion o f the l i q u i d . T h i s d i s c u s s i o n has , o f course , ignored l o s s o f l i q u i d by e v a p o r a t i o n . T i l l . R e s u l t s Al though the two major d i f f i c u l t i e s o f v a r i a t i o n of c a p a c i t y w i t h time and l o s s of l i q u i d from the c e l l by evapora t ion had not been o lea red up , one run was made z s : = * w i t h each o f c i s and t r ans d e c a l i n to conclude t h i s f i r s t year o f i n v e s t i g a t i o n . The t u n i n g condensers were set so tha t the d i a l r e ad ing was 15.0 when the t e s t o e l l was 30 . empty. The c e l l was then f i l l e d w i t h 1.40 oo o f benzene a t 20°C and d i a l r ead ings were taken q u i c k l y before much benzene oould evapora te . Two success ive d i a l r e ad ings , a d i f f e r e n t sample o f benzene be ing used f o r each o f these r e a d i n g s , showed 6 5 . 5 . S ince t h i s checks w e l l w i t h the d i f f e r e n c e between d i a l read ings f o r a i r and benzene shown i n Table I I p a r t ( b ) , 65*5 was cons idered to c o r -respond to £ r 2 .282 , the d i e l e c t r i c constant o f benzene a t 20°C . The benzene was removed from the t e s t c e l l , the c e l l c leaned out w i t h e t h e r , and then f i l l e d w i t h 1.38 oo* o f t r ans d e c a l i n . The temperature o f the oven and c e l l was r a i s e d from 20° to 8 5 0 C i n 12 hours so tha t evapora t ion l o s s e s would be as s m a l l as p o s s i b l e . Even then,about 0 .3 cc was l o s t by e v a p o r a t i o n . The f o l l o w i n g day the c e l l was oleaned out and f i l l e d w i t h c i s d e c a l i n to the shou lde r . The temperature was r a i s e d from 20° to 90°0 i n 7 1/2 hour s . Loss by evapora t ion was some 0.25 c o . Dur ing a l l these measurements the f i b r e cap was on the c e l l to reduce e v a p o r a t i o n . Other o p e r a t i n g data are frequency 3502 k c . f i l amen t v o l t a g e 6.4 v o l t s c i r c u i t temperature 3 0 . 0 ° G ± 0 . 2 ° R e s u l t s a re shown i n Table I I I 31. A C o r r e c t i o n f o r evapora t ion Since the vapour o f the t e s t l i q u i d i n the c e l l must d i f f u s e through the s m a l l spaces between the f i b r e cap and the c e l l i n o rder to escape, the problem o f l o s s o f l i q u i d from the c e l l may perhaps be t r e a t e d by the k i n e t i c theory o f i n t e r d i f f u s i o n o f gases . Le t us assume tha t on one s i d e o f the f i b r e cap the t e s t l i q u i d and i t s vapour are i n e q u i l i b r i u m a t temper-a ture Tj g i v i n g a vapour pressure p ; and that on the o ther s ide the c o n c e n t r a t i o n o f vapour i n the a i r i s n e g l i g i b l e , s i n c e the fan i n the oven i s o p e r a t i n g . The number o f molecules o f vapour d i f f u s i n g ac ross u n i t a rea a t the upper face o f the f i b r e d i s o i n u n i t t ime i s g iven by where t ~ time D - d i f f u s i o n - constant "7"-/d2 • d i s t ance r a t e o f change o f c o n c e n t r a t i o n o f vapour i n the d i r e c t i o n o f d i f f u s i o n . Loeb (12) g ives where F Q =. mole f r a c t i o n o f gas A at the c ross s e c t i o n where dK/d t i s be ing measured. TJ s avg . speed L - « mean f ree pa th (12) Loeb, K i n e t i c Theory o f Gases. 2nd e d . , p . 264* McGraw-H i l l , N . Y . 3 2 . A t p o i n t "CL" we are c o n s i d e r i n g that F Q = 0 , gas A b e i n g the vapour o f the t e s t l i q u i d . Hence ^ oc C A L A cbv d t A A d z Now d-rv/dz oc df>/d2 oc )p where MA i s the mo lecu l a r weight o f A . A l s o L - . ! But p M 4 ^ 7 i 7 n c a whereTttC? i s a cons tan t Hence L OC L P a n d d N o c p T J _ b = ^ - , , 1 Let us compare the r a t e s o f l o s s o f benzene and d e c a l i n a t 20°C. ( d N \ ^ J U r * -^ d t J c ( o a i 8 o c J ^ — L - T T h e n Now evapora t ion o f benzene at 20°Q caused a l o w e r i n g o f d i a l r e a d i n g of 0.065 d i v i s i o n s pe r minute when the fan was o p e r a t i n g , hence the p r e d i c t e d l o w e r i n g f o r d e c a l i n at 20°G would be ^ ( ^ ^ ^ ^ Q H f c B ^ f 0 ° 0.0115 d i v i s i o n s per minu te . 3 3 . D e t a i l s o f c o r r e c t i o n s f o r temperature change and l o s s o f l i q u i d are shown i n Tables IV.and V . The ohange i n d i -e l e c t r i c constant w i t h temperature , so determined, i s shown In f i g u r e s 15 and 16. No o l a i m i s made f o r the r e l i a b i l i t y o f the r e s u l t s . Two i n t e r e s t i n g c o i n c i d e n c e s should be p o i n t e d ou t , however. (a) The value o f de/dT f o r t r ans beyond 55°G i s not f a r from the t h e o r e t i c a l l y c a l c u l a t e d v a l u e . (b) The sharp d i s c o n t i n u i t y i n the curve f o r c i s near 51°G occurs a t a temperature o lose to the p o i n t a t which phenomena have been observed i n o ther p h y s i c a l p r o p e r t i e s o f the c i s isomer* The p o s i t i v e va lues ob ta ined f o r de/dT below 50°G are c o n t r a r y to theory (page 2G>) and set a l l these r e s u l t s on a ve ry unsteady f o u n d a t i o n . Table I I I TRAITS DECALIN Time Temperature Reading 0:00 21*6 59.4 0:45 25.0 59.3 1:45 29.6 59.6 2:45 34*8 59.8 5:40 40.2 60*3 4:45 43.8 59*9 5:35 49.5 59.8 6:45 55.1 59.5 7:40 60*4 58.8 8:40 64.6 58.O 9:45 . 68.9 57.3 10:35 70.8 56.3 11:10 75-7 55.4 11:35 83.2 55*1 CIS DECALIN Time Temperature Reading 0:00 21.1 61*0 0:45 25.2 60.5 1:15 29.8 60.8 1:45 35.2 61.1 2:10 40.2 61.1 2:30 45*0 6I.3 3:10 50.7 61.6 3:18 51.8 61.9 3:23 52.2 61.9 3:29 52.8 62.2 3:39 53.8 62.3 3:50 54.7 62*4 4:15 58.6 62.2 5:05 67.5 61.1 6:15 82.6 5 8.0 6:40 90.1 57.3 1. 2. 3. 4. 5. 7. 6. 8. 9 Time I n t - Temp Uncorrec ted C o r r e c t i o n Rate o f T o t a l change Change o f Cor rec ted e r v a l Reading. f o r change change i n o f d i a l r e ad - d i a l r e a d - r ead ing 6 i n c e l l w i t h d i a l r e a d - i n g from l o s s i n g i n temp. i n g w i t h o f l i q u i d i n t e r v a l l o s s o f l i q -u i d from c e l l 0 21,6 59.3 o 0 0 59.3 2.140 105 29.6 59.6 0.5 0.0116 1.2 1.22 60.3 2.168 60 34.8 59.8 0.7 0.0117 I- 9 0.70 61.0 2.182 55 40.2 60.3 1.0 0.0118 2.5 0.65 61.8 2.202 65 43.8 59.9 1.2 0.0119 3.3 0.77 62.0 2.206 50 49.8 59.8 1.5 0.0120 3.9 0.60 62.2 2.210 JO 55.1 59.3 1.7 0.0121 4.8 0.85 62.6 2.220 55 60.4 58.8 2.0 0.0122 5*5 0.67 62.3 2.212 60 64.6 58.0 2.2 0.0123 6.2 0.74 62.0 2.206 65 68.9 57.3 2.4 0.0124 7.0 0.80 61.9 2.204 50 70.8 56.3 2.5 0.0124 7.6 0.62 61.4 2.219 557 75.7 55.4 2.7 0.0125 8.4 0.44 61.1 2.184 15 83.2 55.1 3.1 0.0126 8.7 0.31 60.7 2.176 TABLE I V . C o r r e c t i o n s f o r t r a n s - d e c a l i n 1. 2. 3. Time I n t - Temp. Uncorrec ted e r v a l Reading 4. 5. C o r r e c t i o n Rate o f f o r change change i n i n c e l l w i t h d i a l r e a d -temp, i n g w i t h l o s s o f l i q -u i d from c e l l T 7. T o t a l change o f d i a l r e ad -i n g from l o s s o f l i q u i d 6. Change o f d i a l read-i n g i n i n t e r v a l 8. Cor rec t ed r e a d i n g 9« 0 45 50 30 25 20 40 8 5 6 10 11 25 50 45 70 25 21.1 25.2 29.8; 35.2 40.2 45.0 50.7 51.8 52.2 52.8 53.8 54.7 58.6 .5 4.8 2.6 9o.l 6l.o 0 0 0 61.0 2.182 60.5 0.2 0.0116 0.5 0.52 60.8 2.178 60.8 0.5 0.0117 0.8 0.35 61.1 2.184 61.1 0.7 0.0117 1.2 0.35 61.6 2.196 61.1 1.0 0.0118 1.5 0.29 61.6 2.196 61.3 1.2 0.0119 1.7 6124 61.8 2.202 61.6 1.5 0.0120 2.2 0.48 62.3 2.212 61.9 1.6 0.0121 2.3 0.1 62.6 2.220 61.9 . 1.6 0.0121 2.4 0.1 62.7 2.224 62.2 1.6 0.0121 2.5 0.1 63.1 2.232 62.2 1*7 0.0121 2.6 0.1 63.2 2.234 62.4 1.7 0.0121 2.7 0.1 63.4 2.238 62.2 1.9 0.0122 3,0 0.3 63*3 2.236 61.1 23 0.0123 3.6 0.61 62.4 2.214 60.1 2.7 0 0124 4.2 Q.>6 61.6 2.196 58.0 3.0 0.0126 5.1 0.88 60.1 2.166 57.3 3.4 0.0128 5.4 0.32 59.3 2.140 TABLE V . C o r r e c t i o n s f o r c i s - d e c a l i n 34. Method of C a l c u l a t i o n : Column 4 =» ( C o l . 1 - 20)(0 ,49) (page 2 « ) Column 5 • 0.0115 ^ A v g , t e m p ^ d u r i n g i n t e r v a l in°K (page 32 ) Column 6 s ( C o l . 5 ) ( C o l , 1) Column 8 s C o l * 5 - C o l * 4 + C o l . 7 Column 9 i s ob ta ined from f i g . 5* B i b l i o g r a p h y Alexander , F . C . , E l e e t r o n i o s , 18 ^ #4, p* 116, ( A p r i l 1945) . Ang ley , P o t k i n s , and Rush, Bache lo r*s T h e s i s , 1942. Bender* P . , J* Chem. E d . , 23* #4, p . 179 ( A p r i l 1946; Estermann, J . , p h y s i k . Chem., (Bj 1, 161 ( I 9 2 8 J ; zt 287 c.1928;. Frank , H". H . , I n t r o d u c t i o n to E l e o t r i o i t y and Opt ics* M c G r a w - H i l l , Iff. Y* ,1940 . Leob, L . B . j K i n e t i c Theory of Gases, 2nd e d . , McGraw-H i l l ^ N . Y . , 1934* Seyer and Davenport , J . A . C . S . , 63 . 2426, (1941J . Seyer and L e s l i e * J . A . C . S . , 64* 1914, (1942 ; . Seyer and Walker , J . A . C . S . , 6 0 , 2125, ( 1 9 3 8 ; . Smyth, C . P . , D i e l e o t r i o Constant and M o l e o u l a r  S t r u c t u r e , Chemical C a t a l o g C o . , 1931. 

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