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The thermal conductivity of Cis and Trans Decahydronaphthalene Schoening, M. A. 1949

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THE THERMAL CONDUCTIVITY OF CIS AND TRANS  DECAHYDRONAPHTHALENE by M.A. Schoening, B.A.Sc. T h e s i s submitted i n p a r t i a l f u l f i l l m e n t o f the requirements f o r the degree of MASTER OF APPLIED SCIENCE i n CHEMICAL ENG-INEERING-THE UNIVERSITY OF BRITISH COLUMBIA September, 1949 ABSTRACT THE THERMAL CONDUCTIVITY  OF CIS AND TRANS DECAHYDRONAPHTHALENE M.A. Schoening A convenient method f o r measuring the thermal con d u c t i v i t y of l i q u i d s i s t h a t i n t r o d u c e d by Bridgman i n 1923. In t h i s procedure the l i q u i d i s h e l d i n the annular space between two c o n c e n t r i c c y l i n d e r s . By s u p p l y i n g heat at & d e f i n i t e l y known r a t e to the i n n e r c y l i n d e r and measuring the temperature drop across the l i q u i d , the thermal c o n d u c t i v i t y o f the l i q u i d may be determined. Because the l i q u i d f i l m i s o n l y 0.04 cms. i n t h i c k n e s s and the temperature drop across the f i l m does not exceed one degree, c o n v e c t i o n w i t h i n g the l i q u i d i s prevented. The temperature drop across the f i l m i s measured by means o f d i f f e r e n t i a l thermocouple Bridgman's c e l l has the advantage over o t h e r thermal c o n d u c t i v i t y apparatuses In t h a t i t r e q u i r e s o n l y a ve r y small volume of l i q u i d f o r the measurement. In t h i s i n v e s t i g a t i o n the thermal c o n d u c t i v i t i e s of c i s - and trans-decahydronaphthalene were measured. When the r e s u l t s were compared with those o f L e v e l t o n and P e r r i s , who determined the same q u a n t i t i e s by the method of Bates, i t was found t h a t lower v a l u e s had been o b t a i n e d f o r both the thermal c o n d u c t i v i t i e s and the temperature c o e f f i c i e n t s . The d i f f e r e n c e i n the c o n d u c t i v i t y may be e x p l a i n e d i n p a r t by the s u r f a c e f i l m d i s c o v e r e d by Bates. In Bridgman's apparatus no allowance i s made f o r t h i s f i l m and the measured temperature drop r e p r e s e n t s the average temperature g r a d i e n t from one boundary o f the l i q u i d to the o t h e r . Unless t h i s s u r f a c e f i l m changes c o n s i d e r a b l y w i t h temperature i t would o f f e r no e x p l a n a t i o n f o r the v e r y d e f i n i t e d i f f e r e n c e found i n the temperature c o e f f i c -i e n t s . Attempts to e x p l a i n the divergence of r e s u l t s on the b a s i s o f p u r i t y o f m a t e r i a l s meet wi t h l i t t l e success because of a l a c k of necessary d a t a . An attempt has been made to design a s i m p l i f i e d c e l l based on the same p r i n c i p l e s as Bridgman's c e l l and i s o f f e r e d h e r e w i t h . ACKNOWLEDGEMENTS The author wishes to acknowledge the sponsorship of the Standard O i l Company of B.C., L t d . , and the a s s i s t a n c e of Dr. Wm. P. Seyer under whose s u p e r v i s i o n t h i s work was performed. TABLE OP CONTENTS Page I . I n t r o d u c t i o n «... 1 I I . Theory 2 I I I . Apparatus • 10 IV. Procedure 18 V. R e s u l t s (a) C a l i b r a t i o n o f C e l l 21 (b) Thermal C o n d u c t i v i t y of Trans D e c a l i n 23 (c) Thermal C o n d u c t i v i t y o f C i s D e c a l i n • 25 VI. D i s c u s s i o n of R e s u l t s 25 V I I . Suggestions 28 V I I I . Proposed C e l l 29 IX. Appendix 33 X. B i b l i o g r a p h y 35 LIST OP ILLUSTRATIONS Page P i g . 1 D e t a i l s o f S e l l 13 P i g . 2 Assembly of Apparatus 16 P i g . 3 E l e c t r i c a l C o n t r o l Diagram 17 P i g . 4 Photograph of C e l l 19 P i g . 5 Photograph of Equipment 19(a) P i g . 6 Graph of C e l l Constant vs Temperature. 22 P i g . 7 Thermal C o n d u c t i v i t y of Trans D e c a l i n . 24 P i g . 8 Thermal C o n d u c t i v i t y of C i s D e c a l i n .. 26 P i g . 9 D e t a i l s o f Proposed C e l l 31 I. INTRODUCTION A l t h o u g h the t h e r m a l c o n d u c t i v i t i e s o f the m a t e r i a l s used i n t h i s work have been measured by L e v e l t o n ( 9 ) , i t was f e l t t h a t a check, u s i n g an independent method, was d e s i r a b l e . A t l the same time a comparison o f the r e s u l t s by the two methods, t h a t o f Bates as used by L e v e l t o n and the method o f Bridgman as was f o l l o w e d i n t h i s work, s h o u l d g i v e an i n d i c a t i o n o f the v a r i a t i o n t o be e x p e c t e d from the methods s i n c e i d e n t i c a l m a t e r i a l s were u s e d . 2. I I . THEORY Experimental s t u d i e s of the f l o w of heat i n a body l e a d to the f o l l o w i n g laws: 1. The q u a n t i t y o f heat i n a body i s p r o p o r t i o n a l to i t s mass and to i t s temperature. 2. Heat flows from a h i g h e r to a lower temperature. 3. The r a t e of flow across an area i s p r o p o r t i o n a l to the area and to the temperature g r a d i e n t , i . e . , the r a t e of change of temperature w i t h r e s p e c t to d i s t a n c e , normal to the area. Prom t h i s we get F o u r i e r ' s law which i s u s u a l l y g i v e n i n the form: Q = K A f where Q = r a t e of heat flow ^ = temperature g r a d i e n t A ~ area of the w a l l , p e r p e n d i -c u l a r to heat f l o w . K r a constant, which i s a p r o p e r t y of the m a t e r i a l and i s c a l l e d the thermal c o n d u c t i v i t y . T h i s constant may be d e f i n e d as the time r a t e of t r a n s -f e r of heat by donduction through u n i t t h i c k n e s s , across u n i t area f o r u n i t d i f f e r e n c e of temperature. In the process of conduction the heat energy d i f f u s e s through a body by the a c t i o n of molecules poss-e s s i n g a g r e a t e r k i n e t i c energy on those with l e s s . In l i q u i d s and gases t h i s takes p l a c e by c o l l i s i o n between molecules with a net t r a n s f e r o f k i n e t i c energy i n the d i r e c t i o n o f heat f l o w . Although thermal c o n d u c t i v i t y has been t r e a t e d q u i t e e x t e n s i v e l y i n the gaseous and s o l i d phases, t h e o r e t i c a l developments have f a i l e d to produce any equations f o r the l i q u i d phases which are completely s a t i s f a c t o r y . I t has been r e c o g n i z e d that the mechanism of conduction i n a l i q u i d must be d i f f e r e n t from that i n a gas. In the gas there i s an i n t i m a t e c o n n e c t i o n w i t h the l e n g t h o f f r e e m o l e c u l a r f l i g h t , c o n d u c t i v i t y being concerned with the t r a n s f e r o f energy and v i s c o s i t y with the t r a n s f e r o f momentum. The r e l a t i o n between these i s e x h i b i t e d by the equ a t i o n : K - *\ C where: i s the v i s c o s i t y C i s the s p e c i f i c heat That there i s no such r e l a t i o n f o r l i q u i d s may be shown i n the f i r s t p l a c e by s u b s t i t u t i n g numerical v a l u e s i n t o t h i s equation; the thermal c o n d u c t i v i t y w i l l be found to be of the or d e r o f ten f o l d too s m a l l . The f a i l u r e of a r e l a t i o n between c o n d u c t i v i t y and v i s c o s i t y has a l s o been found by experiments i n which the v i s c o s i t y of a s o l u t i o n o f g e l a t i n e i n water has been v a r i e d by a f a c t o r of many f o l d , w i t h o n l y s l i g h t changes i n the thermal c o n d u c t i v i t y . 4. Probably the f i r s t attempt to r e l a t e thermal con-d u c t i v i t y to o t h e r p h y s i c a l constants o f a l i q u i d was tha t proposed by Weber (18) about 1880. His equ a t i o n took the form o f : K f S I ) ' / 3 * +. = a constant where: /o i s the d e n s i t y of the l i q u i d M i s i t s m o l e c u l a r weight C i s i t s s p e c i f i c heat Subsequent i n v e s t i g a t i o n has shown that Weber's constant v a r i e s not o n l y f o r d i f f e r e n t compounds but a l s o v a r i e s with temperature f o r any s i n g l e compound. In 1923 Bridgman (6) p u b l i s h e d a paper i n which he suggested the equ a t i o n : where: o{ i s the gas constant v i s the v e l o c i t y of sound i n the l i q u i d £ i s the mean d i s t a n c e o f s e p a r a t i o n of the cent e r s of the molecules, assuming c u b i c a l jL arrangement o f the molecules, and c a l c u l a t i n g 3^ by the formula S -~ ("//>) 3 where "m" i s the absolute weight i n grams of one molecule o f the l i q u i d . He a r r i v e d at t h i s e q u a t i o n by c o n s i d e r i n g a body of l i q u i d i n which there i s a temperature g r a d i e n t d@/dx. The energy o f a molecule i s 2<*£(half p o t e n t i a l and h a l f k i n e t i c ) , where 0 i s the absolute temperature. The d i f f e r e n c e i n energy between n e i g h b o r i n g molecules i n the 5 d i r e c t i o n of the temperature g r a d i e n t i s 2 £ dQ/dx. T h i s energy d i f f e r e n c e i s to be conceived as handed down a row of molecules w i t h the v e l o c i t y of sound. The t o t a l energy t r a n f e r r e d across a f i x e d p o i n t of any row o f molecules per u n i t time i s the product of the energy d i f f e r e n c e and the number of such energy steps c o n t a i n e d i n a row "v" cms. l o n g , o r 2 « £ (dO/dx)v / < T . The t o t a l t r a n s f e r across u n i t c r o s s s e c t i o n i s the product of the t r a n s f e r across a s i n g l e row and the number of rows, o r 2 vc< (dQ/dx) S , but by the d e f i n i t i o n o f thermal con-d u c t i v i t y t h i s t r a n s f e r i s also A C J ^ f • Thus f o r thermal c o n d u c t i v i t y we get K= Z<*v*, When t h i s equation was checked a g a i n s t experimental v a l u e s i t showed an average d e v i a t i o n of 16$, with a maximum of 3 9 $ . Bridgman a l s o attempted to adapt Debye's eq u a t i o n f o r the thermal c o n d u c t i v i t y of a s o l i d to l i q u i d s . He showed t h a t by s u b s t i t u t i n g a p p r o p r i a t e l i q u i d v a l u e s f o r the s o l i d v a l u e s used by Debye, he o b t a i n e d the same equation as h i s own except f o r a constant | r i n s t e a d o f 2, and s i n c e Bridgman's equation g i v e s the approximate mag-n i t u d e , Debye's equation was not i n v e s t i g a t e d f u r t h e r . In 1931 Smith (15) a p p l i e d dimensional a n a l y s i s to the problem. He reasoned t h a t thermal c o n d u c t i v i t y c o u l d be g i v e n as a f u n c t i o n of seven o t h e r v a r i a b l e s ; v i s c o s i t y , d e n s i t y , s p e c i f i c heat, m o l e c u l a r weight, thermal expan-s i o n , c o m p r e s s i b i l i t y , and the gas c o n s t a n t . Since these v a r i a b l e s may a l l be expressed i n terms o f f o u r 6. fundamental dimensions, he developed f o u r d imensionless groups. Then by p l o t t i n g experimental v a l u e s he i n t e r p r e t e d the r e s u l t s i n the form of the f o l l o w i n g equation: K ^ r *~ 1 } where: K i s the thermal c o n d u c t i v i t y /o i s the d e n s i t y C i s the s p e c i f i c heat A i s the constant Z i s the c o m p r e s s i b i l i t y > i s the thermal expansion M i s the m o l e c u l a r weight >\ i s the v i s c o s i t y In 1936 Smith (16) p u b l i s h e d another paper i n which he developed an e n t i r e l y new equ a t i o n by t a k i n g v a r i a t i o n s from approximate mean v a l u e s . He found t h a t at 30° G. /s'^r Q oo /o, ooo where V i s the kinematic v i s c o s i t y i n c e n t i s t o k e s . Using t h i s e q u a t i o n on 46 l i q u i d s f o r which va l u e s were known he found the average e r r o r to 6.7$. In 1932 D a n i l o f f (7) i n an attempt to determine the v a r i a t i o n of thermal c o n d u c t i v i t y o f s u c c e s s i v e members of homologous s e r i e s with m o l e c u l a r weight and temperature, t e s t e d s e v e r a l o f the normal primary s a t u r a t e d a l c o h o l s . When he p l o t t e d the thermal c o n d u c t i v i t i e s a g a i n s t m o l e c u l a r weight he found the e x i s t e n c e o f a marked m i n i -mum of thermal c o n d u c t i v i t y f o r n-hexyl a l c o h o l . 7. P o i n t i n g out t h a t maxima andirimima of p h y s i c a l p r o p e r t i e s i n homologous s e r i e s f o r the member c o n t a i n i n g s i x carbon atoms are not i n f r e q u e n t , he e x p l a i n e d t h i s minimum on the b a s i s o f m o l e c u l a r c o n f i g u r a t i o n . Since the angles between the bonds of the carbon atom are 120°, the s p i r a l s formed by open c h a i n hydrocarbons could be expected to e x h i b i t s i n g u l a r s p a t i a l r e l a t i o n s when the number o f carbon atoms present i n the c h a i n i s a m u l t i p l e of t h r e e . At the time X-ray s t u d i e s seemed to support t h i s explan-a t i o n . In 1946 Denbigh (8) presented a dimensionless equation r e l a t i n g thermal c o n d u c t i v i t y to the l a t e n t heat of v a p o r i z a t i o n : l o g (prj=- ^ J^- + ^ where: Pr i s the P r a n d t l number ~ Cp 1_ K H i s the molal enthalpy of v a p o r i z a t i o n at 1 atm. R Is the gas constant T i s the absolute temperature a and b are 0.183 and -2.2 f o r water 1.20 and -1.8 f o r o r g a n i c l i q u i d s T h i s e quation was developed f o r e s t i m a t i n g f i l m c o e f f i c i e n t s f o r heat t r a n s f e r , but i t i s not accurate f o r p r e d i c t i n g thermal c o n d u c t i v i t i e s . In 1948 Palmer (11) made a review of the e n t i r e f i e l d o f thermal c o n d u c t i v i t y of l i q u i d s . In attempting to c o r r e l a t e the r e s u l t s which had been o b t a i n e d he found t h a t there seemed to be a tendency f o r l i q u i d s to d i v i d e i n t o two c l a s s e s ; those t h a t can be f i t t e d w i t h 8. e m p i r i c a l equations and those that d e v i a t e c o n s i d e r a b l y . In the l a t t e r c l a s s are found the a s s o c i a t e d l i q u i d s such as water and the a l c o h o l s . T h i s c o u l d be expected, f o r i f there are a d d i t i o n a l f o r c e s c o n s t r u c t i n g the molecules, the t r a n s m i s s i o n of heat from one molecule to the next w i l l be a l t e r e d . He used the a d d i t i o n a l f o r c e s due to hydrogen bonds to e x p l a i n c e r t a i n anomalies i n thermal c o n d u c t i v i t y . Prom p r e v i o u s work i t has been shown t h a t one of the most important f a c t o r s i n thermal c o n d u c t i v i t y i s m o l e c u l a r weight, c o n d u c t i v i t y g e n e r a l l y d e c r e a s i n g w i t h i n c r e a s i n g m o l e c u l a r weight. However, there are g l a r i n g e x c e p t i o n s . Symmetry may be a f a c t o r s i n c e carbon t e t r a c h l o r i d e with a h i g h e r m o l e c u l a r weight a l s o has a h i g h e r c o n d u c t i v i t y than c h l o r o f o r m . S i m i l a r i l y , symmetrical t r a n s - d i c h l o r o e t h y l e n e has a s u b s t a n t i a l l y h i g h e r c o n d u c t i v i t y than the c i s form. When e t h y l e t h e r and the b u t y l a l c o h o l s are compared, the p r e v i o u s r e s u l t s are r e v e r s e d , the a l c o h o l s h a ving h i g h e r thermal conduct-i v i t i e s . Palmer thought t h a t t h i s a f f o r d e d a c l u e to the cause of a b n o r m a l i t i e s . As a r e s u l t o f hydrogen bonding a l l h y d r o x y l compounds have some tendency to form chains or aggregates. Since g l y c e r o l has three h y d r o x y l groups and ethylene g l y c o l and proplyene g l y c o l each have two, s i m i l a r behaviour might be expected f o r them, r e s u l t i n g i n h i g h thermal conduct-i v i t i e s . T h i s i s found to be t r u e f o r g l y c e r o l and 9. ethylene g l y c o l , but propylene g l y c o l i s n e a r l y normal. I t was f e l t t h a t t h i s might be due to some i n t e r n a l bonding o r c h e l a t i o n . Comparing the b o i l i n g p o i n t s , propylene g l y c o l although p o s s e s s i n g a h i g h e r m o l e c u l a r weight than ethylene g l y c o l , b o i l s at a lower tempera-t u r e . T h i s , t o g e t h e r w i t h data f o r o t h e r compounds which show evidence of p r e f e r e n t i a l monomer f o r m a t i o n , gave r i s e to the suggestion t h a t the b o i l i n g p o i n t s of i s o m e r i c substances can be used as an index of r e l a t i v e conduct-i v i t i e s . These s p e c u l a t i o n s about the hydrogen bond then l e d to a c o n s i d e r a t i o n o f water. The h i g h c o n d u c t i v i t y and the p o s i t i v e temperature c o e f f i c i e n t have always been a problem, but no s p e c u l a t i o n s as to the mechanism have appeared i n the l i t e r a t u r e . C e r t a i n l y heat c o n d u c t i o n i n normal l i q u i d s i s r e l a t e d to v i b r a t i o n or c o l l i s i o n o f the p a r t i c l e s , but f o r a s s o c i a t e d l i q u i d s the p i c t u r e I s a l t e r e d . The f o r m a t i o n of hydrogen bonds p r o b a b l y a s s i s t s i n c o nduction of heat i n two ways: 1. by c a u s i n g o r i e n t a t i o n of the molecules i n the d i r e c t i o n of heat flow, and 2. by a f f o r d i n g an a d d i t i o n a l method f o r the t r a n s -f e r o f heat energy to take p l a c e . I t i s known t h a t hydrogen bonds i n the l i q u i d s t a t e are broken down a h i g h e r temperatures. T h e r e f o r e , s i n c e there i s a temperature g r a d i e n t i n heat conduction, hydrogen bonds must be b r e a k i n g at the h i g h e r temperatures, 10. t a k i n g up heat, and re f o r m i n g at lower temperatures, g i v i n g up he a t . Thus, c o n t i n u a l l y changing chains are formed, which are o r i e n t a t e d i n the d i r e c t i o n o f heat flow, so that the energy of f o r m a t i o n o f hydrogen bonds i s handed along the c h a i n s . With t h i s p i c t u r e o f the mechanism of heat conduction, Palmer then proceeded to b u i l d up an equation which would i n c l u d e the e f f e c t o f hydrogen bonding. D e c i d i n g t h a t the entropy o f v a p o r i z a t i o n ( i . e . Trouton's constant) p r o v i d e d the most promising f a c t o r , he m o d i f i e d Weber's equation by i n t r o d u c i n g the f a c t o r 21 Lv/T However, f o r experimental purposes he determined the o v e r a l l constant to be 0.0947 to o b t a i n the eq u a t i o n : K = 0.0947 /=> C (/VM) 1/ 5 L v / T When the equation was checked f o r 48 l i q u i d s , the average e r r o r was found to be 8.8$. I l l APPARATUS The methods used to i n v e s t i g a t e thermal c o n d u c t i v i t y i n the l i q u i d phase may c o n v e n i e n t l y be c l a s s i f i e d under f i v e g e n e r a l headings: (1) T a l l column or t h i c k d i s k methods. (2) T h i n d i s k o r s h e l l methods (3) C y l i n d r i c a l methods (S) C a l o r i m e t r i c methods (5) Impressed v e l o c i t y methods 11. However, i n v e s t i g a t o r s of the past f o u r t y years have c o n f i n e d themselves almost e x c l u s i v e l y to the f i r s t two. For purposes of comparison the methods of Bates and Bridgam w i l l be d i s c u s s e d , as they are the most wi d e l y accepted today. Bates' apparatus (1) c o n s i s t e d e s s e n t i a l l y of a drum shaped c o n t a i n e r which was e l e c t r i c a l l y heated at the top and c o o l e d by water c a l o r i m e t e r s forming the bottom o f the c o n t a i n e r . Thermal c o n t r o l was achieved by u s i n g a guard h e a t e r and guard c a l o r i m e t e r , which were p l a c e d c o n c e n t r i c a l l y about the h e a t e r and c a l o r -imeter r e s p e c t i v e l y . The temperature g r a d i e n t w i t h i n the l i q u i d was determined by thermocouples w i t h t h e i r j u n c t i o n s at known depths. The w a l l s of the c o n t a i n e r were made of m a t e r i a l w i t h low thermal c o n d u c t i v i t y i n order to reduce the heat t r a n s f e r r e d by them to a minimum. Bates s t a t e s t h a t by having the heat conducted downward c o n v e c t i o n i n the f l u i d i s n e g l i g i b l e . As a r e s u l t of h i s i n v e s t i g a t i o n s , Bates found the v a l u e s o f thermal c o n d u c t i v i t y determined by h i s apparatus c o n s i d e r a b l y h i g h e r than those p r e v i o u s l y accepted. However, he found the temperature g r a d i e n t at the metal-l i q u i d s u r f a c e much g r e a t e r than i n the main body of the l i q u i d . Thus he contended that the temperature g r a d i e n t measured by o t h e r i n v e s t i g a t o r s , who merely measured the 12. temperature drop from one metal boundary to the o t h e r , was h i g h e r than the t r u e value and so t h e i r values o f the thermal c o n d u c t i v i t y were too low. Bates' apparatus has the disadvantage t h a t i t r e q u i r e s a r e l a t i v e l y l a r g e volume of l i q u i d , which may be hard to o b t a i n i f the m a t e r i a l i s d i f f i c u l t to p u r i f y . In 1923 Bridgman (6) developed a c o n d u c t i v i t y c e l l based on the s h e l l method. In the adaption of h i s c e l l , used i n t h i s work, (see f i g . 1) the l i q u i d i s h e l d i n the annular space between two c o n c e n t r i c brass c y l i n d e r s . The c y l i n d e r s are s e a l e d t o g e t h e r at the ends by German s i l v e r washers 0.005 cm. t h i c k . The o u t e r diameter o f the i n n e r c y l i n d e r i s 0.95 cms. and the i n n e r diameter of the o u t e r c y l i n d e r i s 1.03 cms., g i v i n g a f i l m t h i c k n e s s of 0.04 cm. Bridgman's o r i g i n a l c e l l was 3.18 cms. i n l e n g t h but f o r t h i s i n v e s t i g a t i o n the l e n g t h was i n c r e a s e d to 6.36 cms. Heat i s s u p p l i e d to the i n n e r c y l i n d e r by p a s s i n g a c u r r e n t o f e l e c t r i c i t y through a h i g h r e s i s t a n c e wire i n the c e n t e r of the c y l i n d e r . The heat from the wire passes r a d i a l l y through the i n n e r c y l i n d e r , the annular l a y e r o f l i q u i d , the o u t e r c y l i n d e r and the c e l l j a c k e t i n t o the bath l i q u i d . There i s of course some heat l e a k from i n n e r to o u t e r c y l i n d e r at the two ends across the r i n g s . T h i s CONOuc TIVITY CELL Thermocoup/e We//s Heater \rJell Fi//incj Tube. Rrng Seal 14. Is small because o f the t M n n e s s o f the German s i l v e r and i t s poor thermal c o n d u c t i v i t y . The l e a k was f u r t h e r reduced by i n c r e a s i n g the r a d i a l s e p a r a t i o n o f the two c y l i n d e r s at both ends. By choosing the dimensions of the enlargement c o r r e c t l y , i t i s p o s s i b l e to make the decreased c o n d u c t i v i t y through the l i q u i d e x a c t l y comp-ensate the i n c r e a s e d c o n d u c t i v i t y through the German s i l v e r . The dimensions were so chosen t h a t t h i s com-p e n s a t i o n / should be exact f o r the average of the l i q u i d s used. The temperature d i f f e r e n c e of the c y l i n d e r s i s determined by three d i f f e r e n t i a l thermocouples. I t i s assumed that the temperature of the i n n e r c y l i n d e r at the diameter of the i n n e r thermocouple j u n c t i o n r i n g i s the same as t h a t at the i n n e r f a c e of the l i q u i d ; and t h a t the i temperature o f the o u t e r c y l i n d e r at the diameter of the o u t e r thermocouple j u n c t i o n r i n g i s the same as t h a t at the o u t e r f a c e of the l i q u i d . T h i s i s a v e r y c l o s e approximation owing to the very h i g h thermal c o n d u c t i v i t y o f the metal r e l a t i v e to the l i q u i d . The thermocouples were copper-constantan and were i n s t a l l e d i n such a manner t h a t t h e i r j u n c t i o n s came halfway down the c y l i n d e r s . T h i s avoided end e f f e c t s as f a r as p o s s i b l e . The thermocouples were made of 30-gauge, g l a s s - c o v e r e d duplex wire and were f u s e d t o g e t h e r under a r e d u c i n g flame u s i n g powdered borax as a f l u x and 15 . I n s u l a t e d w i t h s e v e r a l coats of g l y p t a l . The three thermocouples at 120-degree i n t e r v a l s were connected i n p a r a l l e l so t h a t a mean temperature d i f f e r e n c e c o u l d be o b t a i n e d . F i l l i n g o f the c e l l was accomplished by means o f the f i l l i n g tube which was connected to a brass r e s e r v o i r . To ensure complete removal o f trapped a i r , the apparatus was f i l l e d under vacuum. F o r p r o t e c t i o n from the bath l i q u i d the c e l l was i n s t a l l e d i n a brass c y l i n d e r . Thermal co n t a c t was maintained by means of a c l o s e l y machined s l i p f i t between the c e l l and the c y l i n d e r . The assembly was maintained at f a i r l y constant temperature by means of a t h e r m o s t a t i c a l l y c o n t r o l l e d bath o f water. R e g u l a t i o n was maintained by means o f a mercury thermo-r e g u l a t o r o f the DeKhotinsky type, which actuated a r e l a y t h a t c o n t r o l l e d the 120-watt k n i f e h e a t e r . At the h i g h e r temperatures I t was found necessary to supplement t h i s by an a d d i t i o n a l h e a t e r , because o f e x c e s s i v e heat l o s s e s to the atmosphere. With t h i s arrangement i t was found t h a t the bath temperature c o u l d be h e l d constant to w i t h i n 0.02 degrees at 30 degrees centrigra.de. The h e a t i n g c u r r e n t was s u p p l i e d by a s i x v o l t l e a d storage b a t t e r y , (see f i g . 3 ) . The c u r r e n t f l o w i n g was determined by measuring the p o t e n t i a l drop across a standard one-ohm r e s i s t o r connected i n s e r i e s with the c e l l h e a t e r . The p o t e n t i a l drop across the c e l l be a t e r , Thermae o up le. Gloss Tubes Rubber Stopper /?e5 er v o / > Cc// S/ee v e h/o-bz. •• Heotzr wire and poten tiol tap thrcoded through grooves cut /ong/tuditj a/ly m s / e e v e . Rubber gasket4 F,9. ^ ASSEMBLY OF APPARATUS 18 was measured by means o f two taps at the ends of the he a t e r w i r e . For both of these p o t e n t i a l measurements a Leeds and Northwup type K-2 potentiometer was used. A combira t i o n o f these measurements g i v e s the power input to the c e l l . To determine the emf. developed by the thermocouples the same potentiometer was used. T h i s emf. was converted to temperature readings by means o f a c a l i b r a t i o n da a r t based on the emf. developed by a s i m i l a r thermocouple c o n s t r u c t e d from the same wire ad the c e l l thermocouples, and c a l i b r a t e d at s e v e r a l temperatures between 0 and 100 degrees. The temperature o f the bath was measured by means of a n i c k e l - s h e a t h e d p l a t i n u m r e s i s t a n c e thermometer, c a l i b r a t e d by the N a t i o n a l Bureau of Standards i n 1947. IV. PROCEDURE P r e l i m i n a r y to every run the c e l l was washed thoroughly with e t h e r o r petroleum e t h e r , depending on the l i q u i d p r e v i o u s l y measured, and then d r i e d by warming and p l a c i n g i n a vacuum of.60-70 cms. f o r a p e r i o d o f s e v e r a l hours. The c e l l was then f i l l e d by p l a c i n g the l i q u i d i n the r e s e r v o i r and evac u a t i n g the b e l l j a r c o n t a i n i n g the c e l l . When a i r was readmitted the l i q u i d was f o r c e d i n t o the annular space between the two c y l i n d e r s . By r e p e a t i n g t h i s c y c l e s e v e r a l times, complete f i l l i n g of the c e l l was ensured. The c e l l was then p l a c e d i n the c e l l j a c k e t . 19. P i g . 4 PHOTOGRAPH OF CELL 19. Co* 20. The h e a t e r wires and thermocouples were then connected to the e l e c t r i c a l c i r c u i t s and measuring instruments. The apparatus was p l a c e d i n the bath and the bath h e a t e r s t u r n e d on. When the bath had reached the d e s i r e d temperature the c u r r e n t i n the c e l l h e a t e r was turned on and the complete system allowed to come to e q u i l i b r i u m as evidenced by a constant r e a d i n g f o r the thermocouple emf. When t h i s was achieved the v a r i o u s measurements were taken and re c o r d e d . The c e l l h e a t e r c u r r e n t was then turned o f f and the bath temperature r a i s e d to the next d e s i r e d temperature, at which p o i n t the procedure was repeated. Due to c e r t a i n changes made to f a c i l i t a t e c o n s t r u c -t i o n , there i s a c e r t a i n heat leakage between the two c y l i n d e r s o t h e r than through the l i q u i d . For t h i s reason the c e l l , i n i t s p r e s e n t form, cannot be used to determine absolute thermal c o n d u c t i v i t i e s but must f i r s t be c a l i b r a t e d a g a i n s t some l i q u i d f o r which the thermal c o n d u c t i v i t y i s known. For t h i s work d i s t i l l e d water was chosen s i n c e a great d e a l o f work has been done on i t . The v a l u e s o f the thermal c o n d u c t i v i t y o f water used i n the c a l i b r a t i o n are those of Bridgman: 0.00144 cals./cm./sec./°G. at 30°C. and 0.00154 c a l s . / ' cm./sec./°C. at 75°C. The c a l i b r a t i o n used was o f the form of a constant i n the equation Q _ K At and was C determined at s e v e r a l temperatures i n the expected range. 21. RESULTS (a) C a l i b r a t i o n of C e l l The water used f o r the c a l i b r a t i o n of the c e l l was p u r i f i e d by a double d i s t i l l a t i o n process a f t e r i t had been t r e a t e d with a s l i g h t amount of potassium permanganate to o x i d i z e any o r g a n i c m a t e r i a l p r e s e n t . When water from the same source was used by o t h e r workers i n vapor pressure and e l e c t r i c a l c o n d u c t i v i t y measurements, r e s u l t s showed t h a t the water c o n t a i n e d n e g l i g i b l e i m p u r i t i e s . In a l l measurements o f thermal c o n d u c t i v i t y the work was repeated u n t i l c o n s i s t e n t r e s u l t s had been obta i n e d , that i s , thermscouple readings ware checked to the n e a r e s t 0.1 m i c r o v o l t , o t h e r readings remaining c o n s t a n t . In c a l i b r a t i n g the c e l l an experimental shape f a c o t r was determined to r e p l a c e the q u a n t i t i e s h a v i n g to do with the dimensions of the c e l l i n the F o u r i e r heat flow equation. Thus the equation used f o r heat flow i n t h i s work was Q_ K&£ C where Q i s the r a t e of heat flow i n c a l s . / s e c K i s the thermal c o n d u c t i v i t y i n cals./cm./sec./°C. At i s the temperature d i f f e r e n c e across the f i l m i n °C. C i s the c e l l constant at the temperature of measurement i n l/cms. oof 25 •oai/5 ooiio] CELL CO/VSTANT v s TEMPERATURE^ •oo/oe 1 4-0 SO 60 Te m perat ure ° C 23 Temp. °C. C l / cms. 19.97 0.001247 30.55 0.001201 39.99 0.001148 50.08 0.001100 60.06 0.001059 70.09 0.001023 (b) Thermal C o n d u c t i v i t y o f Trans D e c a l i n . The t r a n s d e c a l i n was o b t a i n e d by vacuum d i s t i l -l a t i o n o f a mixture o f both isomers o b t a i n e d from the Eastman Kodak Company. The d i s t i l l a t e was f u r t h e r p u r i f i e d by f r a c t i o n a l c r y s t a l l i z a t i o n . The f i n a l step i n the p u r i f i c a t i o n was d r y i n g over sodium to remove a l l t r a c e s o f water. The f i n a l m a t e r i a l was found to have a f r e e z i n g p o i n t o f -31.60 °C. as compared to the t r u e f r e e z i n g p o i n t o f t r a n s d e c a l i n o f -31.47 °C. as g i v e n by Seyer and Walker (13). Temp. °C. K. Cals./cm./sec./°C. 19.90 0.0009594 30.55 0.0009517 40.24 0.0009249 49.44 0.0009034 61.13 0.0008654 69.86 0.0008311 24-(c) Thermal C o n d u c t i v i t y o f C i s D e c a l i n . The c i s d e c a l i n used was p u r i f i e d i n the same manner as the tr a n s d e c a l i n and was found to have a f r e e z i n g p o i n t o f -43.24 °C. as compared to the t r u e f r e e z i n g p o i n t of c i s d e c a l i n o f -43.26 °C. as g i v e n by Seyer and Walker (13). Temp. °C. K. Cals./cm./sec./°C. 20.12 0.001027 31.83 0.0009864 40.14 0.0009481 50.01 0.0009186 60.08 0.0008793 69.83 0.0008467 VI. DISCUSSION OF RESULTS A comparison o f the c e l l constant as ob t a i n e d by the c a l i b r a t i o n runs, with that o b t a i n e d from the dimen-si o n s o f the c e l l , w i l l show t h a t a c o n s i d e r a b l e p a r t o f the heat t r a n s f e r i s t a k i n g p l a c e by a means o t h e r than through the l i q u i d . No doubt the major p a r t o f t h i s e x c e s s i v e heat l e a k occurs through the end s e a l s , f o r although o r i g i n a l p l a n s s p e c i f i e d the same m a t e r i a l as was used i n Bridgman's c e l l , German s i l v e r o f the c o r r e c t t h i c k n e s s was not o b t a i n a b l e and so f o r the sake of expediency, brass s e a l s , 0.0127 cms. t h i c k , were used i n the c o n s t r u c t i o n . A f u r t h e r source of heat leakage THERMAL CONDUCTIVITY F E CAL IN 27. i s p resent i n the thermocouple and h e a t e r w i r e s . With the nature of the m a t e r i a l used f o r these c i r c u i t s i t would be v e r y d i f f i c u l t to decide on an accurate value f o r the r a t e o f heat l o s s by these r o u t e s . Upon comparing the r e s u l t s o b t a i n e d i n t h i s work w i t h those of P e r r i s ' s and L e v e l t o n ' s the two d i f f e r e n c e s to note are the lower v a l u e s o b t a i n e d f o r both the thermal c o n d u c t i v i t y and the temperature d o e f f i c i e n t . However, both these d i f f e r e n c e s might be expected from a s i m i l a r comparison of the r e s u l t s o f Bates and Bridgman. T h i s d e v i a t i o n might be accounted f o r , i n p a r t , on the b a s i s o f the p u r i t y o f the m a t e r i a l s used. Although L e v e l t o n d i d not s p e c i f y the exact f r e e z i n g p o i n t s o f h i s m a t e r i a l s he f e l t t h a t that c o u l d not be b e t t e r than 98$ pure. In the case of the m a t e r i a l s used i n the p r e s -ent work a comparison o f the f r e e z i n g p o i n t s would i n d i -cate b e t t e r than 99$ p u r i t y . F u r t h e r more, experience suggests that much o f t h i s d e v i a t i o n from the t r u e f r e e z i n g p o i n t can be e x p l a i n e d by s u p e r c o o l i n g o f the m a t e r i a l s d u r i n g the f r e e z i n g p o i n t t e s t . In the f i n a l a n a l y s i s there seems to be no c o r r -e l a t i o n o f the r e s u l t s o f the two apparatuses o t h e r than a g e n e r a l 10$ d i f f e r e n c e at 30 °C. and a much lower temperature c o e f f i c i e n t from Bridgman's apparatus. The h i g h e r temperature g r a d i e n t found by Bates at the l i q u i d boundaries might e x p l a i n most o f the d i f f e r e n c e but u n t i l the nature o f t h i s s u r f a c e f i l m i s more f u l l y understood 28. i t can be used o n l y as q u a l i t a t i v e e x p l a n a t i o n . V I I . SUGGESTIONS The most necessary a l t e r a t i o n i n the presen t apparatus i s some improvement i n the method of determining the temperature drop across the l i q u i d . With the p r e s e n t arrangement an e r r o r o f 0.1 m i c r o v o l t would cause an e r r o r o f n e a r l y 1$ i n the determined thermal c o n d u c t i v i t y . T h i s i s due e n t i r e l y to the accuracy o f the potentiometer being used s i n c e i t cannot measure p o t e n t i a l s c l o s e r than 0.1 m i c r o v o l t . I t has been suggested t h a t the thermocouples be connected i n s e r i e s , thus r e d u c i n g the e r r o r by two- t h i r d s and at the same time r e t a i n i n g the advantage o f .a mean value o f the temperature d i f f e r e n c e . T h i s , o f course, would n e c e s s i -t a t e the c a l i b r a t i o n o f an i d e n t i c a l t h e r m o p i l e . I f t h i s does not show s u f f i c i e n t improvement some oth e r method should be used f o r determing the thermocouple emf. Such a method i s suggested by Smith (16). With regard to the constant temperature bath i t was founqVthat w i t h the present arrangement there was a maxi-mum d e v i a t i o n o f approximately 0.02 °C. As t h i s tempera-tu r e d e v i a t i o n i s t r a n s m i t t e d almost i n s t a n t a n e o u s l y to the o u t e r c y l i n d e r o f the c e l l , i t caused c o n s i d e r a b l e d e v i a t i o n i n the thermocouple emf. In the present work, readings were taken at the same p e r i o d o f the h e a t i n g -c o o l i n g c y c l e i n an attempt to prevent t h i s d e v i a t i o n . 29. from causing e r r a t i c r e s u l t s . To reduce t h i s d e v i a t i o n the present l i q u i d bath, which h o l d s 13 l i t e r s , should be r e p l a c e d by one of g r e a t e r c a p a c i t y . Furthermore, i t i s suggested t h a t o i l be used i n the p l a c e of the present water i n an e f f o r t to reduce the e x c e s s i v e e v a p o r a t i o n which was encountered at the h i g h e r temperatures. With an o i l bath i t may be p o s s i b l e to use exposed he a t e r s without i n t r o d u c i n g s t r a y emf's. i n the thermocouple c i r c u i t . T h i s step should reduce the l a g of the h e a t e r s . With these improvements i t i s f e l t t h a t a more s a t i s -f a c t o r y accuracy c o u l d be a t t a i n e d w i t h the equipment. VIII. PROPOSED CELL Because Bridgman's o r i g i n a l c e l l was designed f o r the measurement of thermal c o n d u c t i v i t y at p r e s s u r e s g r e a t e r than atmospheric, i t i s f e l t by the author t h a t the c e l l c o u l d be c o n s i d e r a b l y s i m p l i f i e d f o r measure-ments at atmospheric p r e s s u r e . The purpose of such s i m p l i f i c a t i o n would be to e l i m i n a t e the s e v e r a l d i f f i -c u l t i e s encountered i n the present work, while at the same time r e t a i n i n g the advantages of the s h e l l method. I t was a l s o thought d e s i r a b l e to d e s i g n a c e l l t h a t c o u l d be c o n s t r u c t e d without the very h i g h degree of s k i l l r e q u i r e d by Bridgman's c e l l . The two main d i f f i c u l t i e s i n the c o n s t r u c t i o n of Bridgman's c e l l l a y i n p r o c u r i n g the c o r r e c t m a t e r i a l f o r the end s e a l s and i n assembling the c e l l . Although 30. great care was taken In assembling there was no way to make sure that the c y l i n d e r s were a b s o l u t e l y c o n c e n t r i c . Furthermore, i n o r d e r to e l i m i n a t e any p o s s i b l e l e a k s i t was n ecessary to use more s o l d e r than was d e s i r a b l e . I t was found t h a t a c e r t a i n amount of c o r r o s i o n had taken p l a c e when the c e l l had to be opened up a f t e r i t had been used f o r some time. I f access to the i n t e r i o r of the c e l l c ould s i m p l i f i e d a c l o s e r check on the amount o f t h i s c o r r o s i o n c o u l d be made. With these f a c t o r s i n mind an attempt has been made to design a new c e l l based on the same p r i n c i p l e s . (see f i g . 9). By l e a v i n g the top of the c e l l open i t would be q u i t e simple to check the c l e a r a n c e of the two c y l i n d e r s at a l l p o i n t s of t h e i r circumference, and at the same time i t would be p o s s i b l e to ensure complete f i l l i n g o f the c e l l . The one d i f f i c u l t y t h i s procedure i n v o l v e s i s the maintainence of a constant l i q u i d l e v e l i n the c e l l . T h i s d i f f i c u l t y may be overcome by always working w i t h i n c r e a s i n g temperatures a f t e r the c e l l has been f i l l e d . In t h i s way the l i q u i d w i l l be c o n t i n u a l l y expanding and any s u r p l u s w i l l be taken care of by the over-flow channel and w e l l . With the arrangement proposed i t i s necessary t h a t the channel f o r the h e a t e r wire be s l i g h t l y o f f c e n t e r . It i s f e l t t h a t the thermal c o n d u c t i v i t y of the metal should be h i g h enough so that the temperature 32. d i s t r i b u t i o n of the i n n e r c y l i n d e r should be even at the diameter of the i n n e r thermocouple j u n c t i o n r i n g . However, i f t h i s arrangement causes d e v i a t i o n s i t c o u l d be c o r r e c t e d by u s i n g three h e a t e r w e l l s arranged i n the same manner as the thermoucouple w e l l s w i t h the three h e a t e r wires i n p a r a l l e l . The h e a t e r wire remains f r e e at the top of the channel but i s s o l d e r e d to the c y l i n d e r at the bottom. T h i s s o l d e r w i l l a l s o serve to s e a l the h e a t e r channel from the l i q u i d - c o n t a i n i n g space of the c e l l . In t h i s way the c e l l i t s e l f w i l l be used as a p a r t o f the e l e c t r i c a l c i r c u i t f o r the h e a t e r c u r r e n t . From a thermal c o n s i d e r a t i o n of the c e l l I t can be seen t h a t there are two p o s s i b l e paths of heat conduction between the c y l i n d e r s , o t h e r than through the l i q u i d . Heat may be conducted along the thermocouple wires and through the support p i n s . Bridgman(6) has shown that the former need not be c o n s i d e r e d . The l a t t e r may be reduced to a n e g l i g i b l e amount by u s i n g p i n s of m a t e r i a l w i t h low thermal c o n d u c t i v i t y and h a v i n g them w e l l sharpened so t h a t t h e i r area of contact w i t h the i n n e r c y l i n d e r i s a minimum. I t i s r e a l i z e d t h a t a shape f a c t o r would have to be determined f o r the p a r t i c u l a r c e l l , p r o b a b l y by e x p e r i -mental means. Once t h i s has been decided upon, the c e l l should be q u i t e capable of determining absolute thermal c o n d u c t i v i t i e s . - 0 -33 IX. APPENDIX (a) C a l i b r a t i o n of C e l l Temp. °C. K H 20 T.C. Heater v o l t s Heater amps. T.C. eq. / f v / e C . F a c t o r C 19.97 0.001418 13.1 1.1426 1.3818 39.48 0.001247 30.55 0.001441 12.6 1.1437 1.3832 39.98 0.001201 39.99 0.001462 12.0 1.1436 1.3829 40.43 0.001148 50.08 0.001485 11.4 1.1410 1.3799 40.91 0.001100 60.06 ©.001507 10.9 1.1385 1.3776 41.38 0.001059 70.09 0.001529 10.4 1.1330 1.3715 41.86 0.001023 (b) Thermal C o n d u c t i v i t y o f Trans D e c a l i n Temp. °C. F a c t o r C T.C. v. Heater v o l t s Heater amps. T.C. eq. / f v / C. K 19.90 0.001247 11.5 0.8814 1.0642 39.47 0.0009594 30.55 0.001201 11.2 0.8770 1.0590 39.98 0.0009517 40.24 0.001147 11.1 0.8736 1.0540 40.44 0.0009249 49.44 0.001109 11.0 0.8709 1.0497 40.88 0.0009034 61.13 0.001060 9.9 0.8230 0.9925 41.44 0.0008654 69.86 0.001023 10.9 0.8560 1.0378 41.86 0.0008311 34. (c) Thermal C o n d u c t i v i t y o f C i s D e c a l i n Temp. °C. F a c t o r C T.C. •T'v. Heater v o l t s Heater amps. T.C. eq. //v/°C. K. 20.12 0.001232 10.0 1.0083 0.8685 39.53 0.001027 31.83 0.001183 10.1 1.0069 0.8673 40.03 0.0009864 40.14 0.001148 10.2 1.0059 0.8665 40.42 0.0009481 50.01 0.001106 10.3 1.0063 0.8670 40.91 0.0009186 60.08 0.001060 10.4 1.0040 0.8657 41.39 0.0008793 69.83 0.001023 10.4 1.0024 0.8638 41.73 0.0008467 (d) Comparison o f R e s u l t s Thermal C o n d u c t i v i t y o f Trans D e c a l i n L e v e l t o n P e r r i s 0.00111 0.001155 0.00107 0.001140 0.00097 0.001080 0.00085 0.001022 0.00095 0.000885 Thermal C o n d u c t i v i t y of C i s D e c a l i n Temp. Schoenlng L e v e l t o n P e r r i s 30 0.000993 0.00114 35 0.000974 0.001178 0.00112 40 0.000955 ' 0.001150 0.001005 45 0.000937 0.001091 0.00095 50 0.000918 0.001040 55 0.000899 0.000958 60 0.000881 0.000899 Temp. Schoening 30 0.000948 35 0.000939 40 0.000928 45 0.000915 50 0.000900 55 0.000885 60 0.000868 35. BIBLIOGRAPHY 1. Bates, Ind. Eng. Chem., 25, 431 (1933) 2. Bates, Ind. Eng. Chem., 28, 494 (1936) 3. Bates and Hazzard, Ind. Eng. Chem., 33, 375 (1941) 4. Bates and Hazzard, Ind. Eng. Chem., 37_, 193 (1945) 5. Bates, Hazzard and Palmer, Ind. Eng. Chem., A n a l . Ed., 10, 314 (1938) 6. Bridgman, Proc. Am. Acad. A r t s and S c i e n c e s , 59, 141 (1923) 7. D a n i l o f f , J.A.C.S., 54, 1328 (1932) 8. Denbigh, J . Soc. Chem. Ind., 65, 61 (1946) 9. L e v e l t o n , M.A.Sc. T h e s i s , U.B.C. (1948) 10. M a r t i n and Long, Proc. Phys. Soc. of London, 45, 529 (1933) 11. Palmer, Ind. Eng. Chem., 40, 89 (1948) 12. P e r r i s , M.A.Sc. T h e s i s , U.B.C. (1947) 13. Seyer and Walker, J.A.C.S., 60, 2125 (1938) 14. Smith, Ind. Eng. Chem., 22, 1246 (1930) 15. Smith, Ind. Eng. Chem., 23, 416 (1931) 16. Smith, Trans. Am. Soc. Mech. Eng., 58, 719 (1936) 17. S t u l l , Ind. Eng. Chem., 39_, 517 (1947) 18. Weber, Wied. Ann,, 10, 101 (1880) 

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