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The thermal conductivities of some hydrocarbons Levelton, Bruce H. 1948

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THE THERMAL CONDUCTIVITIES OF SOME HYDROCARBONS by Bruoe H . L e v e l t o n A T h e s i s Submit ted i n P a r t i a l F u l f i l m e n t o f The Requirements f o r the Degree of MASTER OF APPLIED SCIENCE i n the Department o f CHEMICAL ENGINEERING The U n i v e r s i t y o f B r i t i s h Columbia > May, 1948. THE THERMAL COItDTTCTI VTTIES OP SOME HYDROCARBONS oy Bruce H. Levelton ABSTRACT The Bates Calorimeter f o r measuring the heat con-d u c t i v i t i e s of hydrocarbons was p a r t i a l l y reconstructed so as to diminish the heat l o s s through the walls of the i r o n container* This was done by imbedding some nichrome wire heating elements i n the i n s u l a t i n g materials just outside i r o n w a l l . The current sent through t h i s c o i l was so con-t r o l l e d as to reduce the heat l o s s from the l i q u i d at t h i s point, A s e r i e s of measurements on several hydrocarbons gave the r e s u l t s below. Trans decahydronaphthalene Cis » N decane N dodecane N tetradecane N hexadecane £35 - 0 .001155 ^33 - O.OOII78 £33 » O.OOO652 £33 = 0.0006^4 k33 - O.OOO65O k 5 3 = O.OCO650 ACKBTOWLEDGEMENT The author wishes t o acknowledge the a d v i c e and. suggest ions o f Dr« W, F , Sever under whose d i r e c t i o n t h i s r e s e a r c h was undertaken* LIST OF FIGURES TO TABLES F i g u r e s . Page 1. Heater D e t a i l .4. 2 . Thermocouple P o s i t i o n s ^_ 3 . Thermocouple C i r c u i t ^_ 4. H e a t i n g C i r c u i t 4. 5 . Assembly o f Test C e l l 4-6. Temperature G r a d i e n t Curve f o r Water 19 7 i C o r r e c t i o n F a c t o r s 19 8 . Temperature G r a d i e n t Curve f o r C i s and Trans D e e a l i n \9 and Water 9 . « it it it Dodeoane and \Q Tetradecane 10. rt n " " Deeane and Hexadecane \ 9 11 . K f o r Normal P a r a f f i n s v s Temperature t 9 1 2 . n n n w w Number of 0 Atoms \ 9 1 3 . Smi th*s R e s u l t s f o r Normal P a r a f f i n s »9 14 . Temperature V a r i a t i o n of K f o r C i s , Trans and Water 19 1 5 . P a l m e r * s R e s u l t s f o r P a r a f f i n s and A l c o h o l s . 1 9 T a b l e s . 1. Table of C o r r e c t i o n F a c t o r s 16 2* Thermal C o n d u c t i v i t y of C i s D e c a l i n 17 3 . " n " Trans n i 7 4. •» « " u Deeane ' 7 5 .  n n » N Dodeoane 18 6 . " " rt N Tetradecane 1& 7 . •* » " N Hexadecane \& TABLE OF CONTENTS Page I . I n t r o d u c t i o n 1 I I . D e s c r i p t i o n o f Apparatus 2 . I I I . Changes i n Apparatus 4 (a) Secondary Guard Heater 4 (b) Replacement o f Thermocouple W e l l s 4 (o) Replacement o f Thermocouples 5 (d) New Test and Guard Heaters 6 (e) New Water B a t h Heaters 6 I V . C a l i b r a t i o n o f Test C e l l 7 V . Procedure 8 T I . Theory of Thermal C o n d u c t i v i t y 9 V I I . R e s u l t s 15 (a) Computat ion of C o r r e c t i o n F a c t o r s 15 (b) Thermal C o n d u c t i v i t y of Trans D e o a l i n 16 (o) rt " n C i s " 17 (d) n " rt H Decane 17 (e) n w M H Dodeoane 1? £ f ) H n n u Tetradeoane 18 (g) » «» w TS Hexadeoane 18 V I I I . D i s c u s s i o n of R e s u l t s 19 I X . Suggest ions 21 X . B i b l i o g r a p h y 25 THE THERMAL CONDUCTIVITIES OF SOME HYDROCARBONS I . INTRODUCTION Robinson and Younger i n 1946 b u i l t an apparatus f o r measuring t r u e c o e f f i c i e n t s o f thermal c o n d u c t i v i t i e s of v a r i -ous hydrocarbons ; They determined the c o n d u c t i v i t i e s o n l y o f c i s and t r a n s decahydronaphthalene ( d e c a l i n ) , a c y c l i c h y d r o -carbon of c o n s i d e r a b l e i n t e r e s t to t h i s department. T h e i r apparatus was an a d a p t a t i o n o f t h a t c o n s t r u c t e d o r i g i n a l l y by 0 . K . Bates a t the Massachuset tes I n s t i t u t e of Technology i n 1932. I n 1947 P e r r i s r e b u i l t the a p p a r a t u s , and r e c a l c u l a t e d the v a l u e s f o r the thermal c o n d u c t i v i t i e s of d e c a l i n as w e l l as measuring the t r u e c o e f f i c i e n t of c o n d u c t i v i t y f o r oyolo hexane. The purpose of r e s e a r c h t h i s year was t o recheok the a l r e a d y computed v a l u e s f o r d e c a l i n , and to measure c o n d u c t i v i -t i e s o f s e v e r a l more s t r a i g h t c h a i n hydrocarbons . 2 I I . APPARATUS The method of Bates i s a m o d i f i c a t i o n o f the t h i c k d i s c method. B r i e f l y , t h e procedure i s as f o l l o w s - The t e s t l i q u i d i s p l a c e d i n an i n s u l a t e d c y l i n d r i c a l c o n t a i n e r and i s heated from the top and c o o l e d from the bottonu The h e a t e r s u r f a c e and c y l i n d e r bottom are f l a t and are a b s o l u t e l y p a r a l l e l t o one another* G r a d i e n t thermocouples a t measured h e i g h t s g i v e the temperature d i s t r i b u t i o n w i t h d e p t h , and the amount of heat f l o w i n g through a known area i s determined by measuring the temperature change and r a t e of f l o w of the c o o l i n g w a t e r . Bates found by v a r i o u s experiments t h a t c o n v e c t i o n i n such a system i s n e g l i g i b l e , and a l s o t h a t r a d i a t i o n from the h e a t e r s u r f a c e to the thermocouples can not be d e t e c t e d . The c e l l i s c o n s t r u c t e d as shown i n f i g . 5. The bottom edge of a t h i n s t e e l c y l i n d e r 135.7 cm. i n diameter and 7 cm. h i g h was s i l v e r s o l d e r e d to a t h i n s t e e l a n n u l a r p l a t e 12.1 cm. i n s i d e diameter and 15.5 cm. o u t s i d e d i a m e t e r . The guard r i n g c a l o r i m e t e r was s o l d e r e d t o the u n d e r s i d e of the r i n g and the t e s t c a l o r i m e t e r was f i t t e d i n t o the a n n u l a r space t o g i v e a p e r f e c t l y f l a t s u r f a c e ; I n s i d e the s t e e l c y l i n d e r and r e s t i n g on the s t e e l p l a t e i s a 3.4 cm. l e n g t h of t r a n s i t e p i p i n g 12*1 cm. i n s i d e d iameter and 13.7 cm. o u t s i d e d i a m e t e r . F i t t i n g around the o u t s i d e o f the s t e e l c y l i n d e r i s a 7 cm. l e n g t h o f t r a n s i t s p i p i n g 13.8 cm. i n s i d e diameter and 15.5 em* o u t s i d e d i a m e t e r . 3 . H o r i z o n t a l h o l e s 0#3l8 cm, i n diameter were d r i l l e d a t o p p o s i t e s i d e s of the c y l i n d e r a t each o f f i v e l e v e l s . Through these h o l e s were p l a c e d t h i n copper tubes f o r g r a d i e n t thermocouple g u i d e s . The whole c e l l was packed i n the centre o f a s t e e l drum and packed w i t h 8^% magnesia and r o c k w o o l . The centre c a l o r i m e t e r c o n s i s t s o f a t h i c k d i s o of copper w i t h p a r a l l e l s p i r a l grooves out i n one f a c e and a t h i n sheet o f copper s o l d e r e d over the g r o o v e s . I n t h i s way there i s c o u n t e r - c u r r e n t f l o w a t any p o i n t , e n s u r i n g a u n i f o r m temperature d i s t r i b u t i o n over the s u r f a c e . The guard c a l o r i -meter c o n s i s t s of copper t u b i n g wound s p i r a l l y on the bottom of the s t e e l a n n u l a r p l a t e mentioned b e f o r e . Water temperatures were measured by means of f o u r , t h e r m o p i l e s , each c o n s i s t i n g o f f o u r oopper -cons tanton , JO gauge, d u p l e x , g l a s s - i n s u l a t e d * Leeds and Uorthrup thermocouples i n s e r i e s , A t h e r m o p i l e was p l a c e d at the i n l e t and o u t l e t of each c a l o r i m e t e r . C o o l i n g water was s u p p l i e d f rom a tank at a h e i g h t o f J>4 i n c h e s . The water was m a i n t a i n e d at a constant tempera-t u r e by means of f o u r b l a d e h e a t e r s , two of whioh were connected I n s e r i e s w i t h temperature r e l a y and a mercury gap s e n s i t i v e to l / l O of one degree . T h e r m o e l e c t r i c emtfs were measured by means o f a Leeds ITorthrup N o , 8662 P o r t a b l e P r e c i s i o n P o t e n t i o m e t e r , whioh w i l l r e a d emfs. to 1 m i c r o v o l t . The c i r c u i t i s shown i n f i g , . 3 . S O L O E R T H E R M O C O U P L E . H O L E Q O ^ ^ E R R I N G FIG 1 HEATER DETAIL . RG. 2 THERMOCOUPLE. POSITIONS COLD JUNCTION MoT JUNCTION . R E V E R S I N G SWITCH T E N T l O M E T E H RG 3 THERMOCOUPLE CIRCUIT » S e c GUAV^O HEATER - w w w v G u i V R B HEATER • w y v w v T E S T H E W E R FIG. 4 HEATING CIRCUIT 1 T E N S I O N SPVOMG. Z L\ou>o T H E R M O C O U P L E 3 Cu ~THERK/\ocovjf»LE.. G U I D E 4 O U T E R ~TRAMS\TE: CYLINDER 5 S e c . G U A R D M E A T E P 6 T N ^ E R ~ T R A N S I T E . C \ t . l M T j e R 7 T E S T «- G U A R D H E A T E R S 8 T E & T <*• GUARO C A L O R I M K T E R S 9 TE'-iT CAL. THERMOCOUPLE. WiLLS 11 QV£R.PLOW T U B E 12. S E M E ' S THERMOCOuPl_e C O GUARD \3 STetL. CYL.VMOE.PI ^ P L A T E RG 5 ASSEMBLE OF T E S T C E L L 4. I I I . CHANGES^ I N APPARATUS (a) Secondary Guard Heater P e r r i s found t h a t i t was necessary t o a p p l y c o r r e c t i o n f a c t o r s t o the e x p e r i m e n t a l l y determined v a l u e s of K . These c o r r e c t i o n s were o b t a i n e d by c a l i b r a t i n g the apparatus w i t h d i s t i l l e d water whose c o e f f i c i e n t o f thermal c o n d u c t i v i t y has been a c c u r a t e l y e s t a b l i s h e d * S i n c e these c o r r e c t i o n s v a r i e d from 15f. a t 25°C t o 42^ a t 45°C, i t was f e l t t h a t some improve-ment must be made* The edge or s i d e l o s s of heat on such a s m a l l c a l o r i -meter as t h i s one i s c o n s i d e r a b l e and so a l a r g e e r r o r w i l l r e s u l t i n the e v a l u a t i o n o f the c o n d u c t i v i t y . To prevent t h i s l o s s a secondary guard h e a t e r of Ho» 22 B and S gauge, b a r e , Ghromel A w i r e was wound around the o u t s i d e of the t r a n s i t e c y l i n d e r as shown i n f i g * J>* T h i s p r e c a u t i o n reduced the m a x i -mum d e v i a t i o n from aooepted v a l u e s to a p p r o x i m a t e l y 5% i n the temperature range used* (b) Replacement o f Thermocouple W e l l s S e v e r a l thermocouples had to be r e p l a c e d , and i t was found extremely h a r d t o make couples 17, 16 , 14 and 13 l e a k -p r o o f a f t e r replacement . I t was concluded t h a t a b e t t e r a r range-ment than a Dekhot insky s e a l c o u l d be d e v i s e d , and so the f o l l o w i n g arrangement was used* The former b r a s s Tees were r e p l a c e d where p o s s i b l e by l a r g e r s i z e to prevent the couple , ends from b e i n g crowded t o g e t h e r . The thermocouples were r u n through l/4 i n c h oopper t u b i n g one end of w h i c h was f i t t e d w i t h a double t a p e r e d c o l l a r and a n u t . The copper tube was f o r c e d a g a i n s t the Tee to make a t i g h t j o i n t by mere ly t h r e a d i n g the nut onto the Tee as shown i n f i g . 5. The tube was f i l l e d w i t h m o l t e n p a r a f f i n , and so prevented any leakage a l o n g the thermo-couple w i r e s . (c) Replacement o f Thermocouples. A l l couples used were of Leeds and N o r t h r u p , oopper-? c o n s t a n t a n , g l a s s i n s u l a t e d , 30 gauge, duplex w i r e s * Leeds E o r t h r u p 38 c a l i b r a t i o n t a b l e s were checked by the b o i l i n g p o i n t of water and g l y c e r o l , and the f r e e z i n g p o i n t of w a t e r . Thermocouple J u n c t i o n s were made by f u s i n g the t i p s of the two w i r e s under a s m a l l r e d u c i n g f l a m e . Dueo was used to i n s u l a t e the bare w i r e s , s i n c e no where was i t exposed t o hydrocarbons or o ther c o r r o s i v e l i q u i d s . G l y p t a l was found to s w e l l and c rack a f t e r p r o l o n g e d immersion i n w a t e r , and so i t was d i s c a r d e d as an i n s u l a t o r . The g r a d i e n t thermocouples 1, 18, 19, 6, 11 (see f i g . 2 ) were s o l d e r e d a t the j u n c t i o n and then emeried u n t i l smooth. Great care was t a k e n t h a t these couples d i d not s h o r t to the screws on the t e n s i o n a d j u s t e r s . I t was found t h a t the g l a s s i n s u l a t i o n tended to rub o f f i f i t was bent s e v e r a l t i m e s . Two new o o u p l e s , n o ! s 7 and 5 were i n s t a l l e d as shown i n f i g . 2 t o c o n t r o l the heat f l o w from the secondary guard h e a t e r . I t was e s s e n t i a l t h a t a t no t ime s h o u l d the r e a d i n g s of these thermocouples be h i g h e r than the r e a d i n g of the g r a d i -ent thermocouple a t the same l e v e l . A h i g h e r r e a d i n g would i n d i c a t e t h a t heat was f l o w i n g i n t o the l i q u i d from the guard h e a t e r . (d) Hew Test and Guard Heaters I t was f e l t t h a t the former h e a t e r s d i d not have a l a r g e enough c a p a c i t y to work over the d e s i r e d temperature range , and so much l a r g e r ones where c o n s t r u c t e d as shown i n f i g . 1 . Care was t a k e n t h a t the h e a t e r s d i d not s h o r t to the copper h e a t e r s u r f a c e . Such a shor t developed once, w i t h the r e s u l t t h a t the g r a d i e n t thermocouples p i c k e d up the s t r a y emf 's c o m p l e t e l y d i s r u p t i n g the r e a d i n g s . (e) New Water B a t h Heaters Two new h e a t e r s were i n s t a l l e d i n p l a c e of one f o r m e r l y . These h e a t e r s were connected i n s e r i e s w i t h a r h e o -s t a t so t h a t h e a t i n g c o u l d be r e g u l a t e d depending oh the temper-a t u r e of water from the m a i n s . Of the f o u r h e a t e r s two were on a t a l l t i m e s , and the o ther two were i n s e r i e s w i t h the temperature r e g u l a t o r . 17. CALIBRATION OF TEST CELL Because the t e s t c e l l had u n a v o i d a b l e heat l o s s e s due to conduct ion and i m p e r f e c t g u a r d i n g , i t was necessary to c a l i b r a t e the apparatus by u s i n g a l i q u i d whose thermal con-d u c t i v i t y was e s t a b l i s h e d . D i s t i l l e d water was chosen as the s t a n d a r d , s i n c e i t s c o n d u c t i v i t y i s known over the d e s i r e d temperature range . The graph of dx f o r v a r i o u s water runs i s shown i n f i g . 6. From IT the average v a l u e o f dx a t any temperature the c o r r e s p o n d i n g K IT was computed f rom K = Q, dx where 0, i s heat f l o w i n c a l o r i e s laT p e r second and A i s the area of the t e s t c a l o r i m e t e r . The e x p e r i m e n t a l l y determined v a l u e s o f E were compared to the s tandard v a l u e s , and a c o r r e c t i o n f a c t o r f o r each temperature was computed. The r e s u l t s are shown i n t a b l e 1 and on f i g . 7 . A l l the runs were made under the same c o n d i t i o n s o f the c a l i b r a t i o n r u n s * That i s , the c u r r e n t through each h e a t e r c o i l was c o n s t a n t , and the c o o l i n g water r a t e was a p p r o x i m a t e l y the same f o r a l l r u n s . The 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 c o o l i n g water remained a t the same temperature (22.4°C) a l l the t i m e . 8 . V. PROCEDURE 1. The t e s t e e l l was f i l l e d w i t h the hydrocarbon under e x a m i n a t i o n . 2 . Heater was p l a c e d on and excess l i q u i d removed through the o v e r f l o w p i p e . 3 . Water r a t e s through the c a l o r i m e t e r s were a d j u s t e d so t h a t the guard c a l o r i m e t e r was on maximum f l o w and the t e s t c a l o r i m e t e r at about 40 c o . p e r m i n u t e . 4 . A l l h e a t e r s were turned on and the c u r r e n t s a d j u s t e d to the c a l i b r a t i o n v a l u e s , 5 . A f t e r e q u i l i b r i u m (5-6 hours) the couples were read at set i n t e r v a l s and the water r a t e was measured by means o f a 250 o c . v o l u m e t r i c f l a s k and a s topwatch . 6 . When hydrocarbons were changed the ejfell was washed out t h o r o u g h l y w i t h petro leum e t h e r . 7 1 . THEORY OF THERMAL CONDUCTIVITY F o u r i e r f i r s t presented a mathemat ica l d e f i n i t i o n of heat c o n d u c t i v i t y i n h i s e q u a t i o n Q 1 ^ © where Q, «= amount of heat f l o w i n g i n g . c a l . / s e o . K » c o e f f . of thermal c o n d u c t i v i t y A = t e s t a r e a d t or . T •» temperature d i f f e r e n c e over dx or x cm. o f t e s t substance . © « t ime F o r u n i t t ime K » Q, dx X dx I f x i s p l o t t e d v e r s u s t , a temperature g r a d i e n t curve I s o b t a i n e d , and the s lope of t h i s curve a t any temperature i s d x . T h e r e f o r e , the f o r e g o i n g equat ion p r o v i d e s a b a s i s f o r dt" measurement o f c o e f f i c i e n t s of thermal c o n d u c t i v i t i e s over a range of t empera ture . The measurements are s imple -Q, = amount of h e a t / u n i t t ime A « area of t e s t c a l o r i m e t e r dx = determined by r e a d i n g s and h e i g h t s of f i v e I S thermocouples T h e o r e t i c a l at tempts to e x p l a i n the meohanism of heat c o n d u c t i o n i n l i q u i d s have so f a r been r a t h e r u n s u c c e s s f u l , u n l i k e s o l i d s where the c o e f f i c i e n t of heat c o n d u c t i v i t y v a r i e s 10 . w i d e l y from t h a t of oopper or s i l v e r t o t h a t of q u a r t z o r g l a s s , l i q u i d s have c o n d u c t i v i t i e s whioh range o n l y from about 2j>0 x 10~^ t o l^OO x 10~k» Whi le numerous measurements have been made on the heat c o n d u c t i v i t i e s of l i q u i d s , t h e r e i s s t i l l some doubt as t o the accuracy o f the methods u t i l i z e d . B r i d g m a n , s method of c o n c e n t r i c c y l i n d e r s has been used e x t e n s i v e l y f o r hydrocarbons and o ther homologous s e r i e s such as the a l c o h o l s j w i t h r e s u l t s a p p a r e n t l y c o n s i s t e n t i n themselves but q u e s t i o n -a b l e from an a b s o l u t e p o i n t of v i e w . However, h i s v a l u e f o r water agrees w i t h t h a t o b t a i n e d by s e v e r a l o ther i n v e s t i g a t o r s . Bates enumerates some of the sources of e r r o r present i n t h i s method. An e r r o r not mentioned by Bates i s the heat l e a k through the two end p l a t e s of the c y l i n d e r s , as w e l l as heat l o s s e s a l o n g h e a t e r and thermocouple l e a d s and the f i l l i n g t u b e . C a l c u l a t i o n s show t h a t the heat t r a n s p o r t e d by the m e t a l l i c ends of the c o n c e n t r i c c y l i n d e r s of Bridgman*s apparatus amounts t o about 4% o f the t o t a l heat s u p p l i e d . Some years ago 0 . K . Bates a t M .I .T. c o n s t r u c t e d a t a l l column type of c a l o r i m e t e r hoping to overcome the o b j e c t i o n s r a i s e d a g a i n s t the t h i n f i l m type of c a l o r i m e t e r . The d e t a i l s of c o n s t r u c t i o n and performance of h i s apparatus have been d e s c r i b e d i n the J o u r n a l of I n d u s t r i a l and E n g i n e e r i n g C h e m i s t r y . There are two d i s t i n c t d isadvantages t o Bates type of a p p a r a t u s . F i r s t the c e l l r e q u i r e s w e l l over j?00 o c . of t e s t l i q u i d and secondly the bafce l i te w a l l s are r e s i s t a n t to o n l y a l i m i t e d number of subs tances . I t was found necessary i n the present r e s e a r c h t o r e p l a c e b a k e l i t e by t r a n s i t s and to i n t r o d u c e o ther 11 . changes as d e s c r i b e d e a r l i e r i n t h i s t h e s i s and a l s o i n the paper by G . P e r r i s . I n 1923 Bridgman suggested the t h e o r e t i c a l equat ion 1/ -where A = (^Vp)** /y^ » mass of a molecule i n grams » d e n s i t y i n grams/cc . <* .- gas constant « 2.02 x l O " 1 ^ e r g s / ° C . ^ « v e l o c i t y of sound i n the l i q u i d . F o r a p u r e l y t h e o r e t i c a l e q u a t i o n , the r e s u l t s o b t a i n e d were s u r p r i s i n g l y good when compared t o accepted v a l u e s . The m a x i -mum d e v i a t i o n over a l a r g e number of substances was 38$ and the average d e v i a t i o n was 16.6"£. Smith u s i n g d i m e n s i o n a l a n a l y s i s showed t h a t by c o n s i d e r i n g o n l y K , v and ^ (mean s e p a r a t i o n ) t h a t the e q u a t i o n K- ^ c o u l d be o b t a i n e d . T h i s of course i s p e r f e c t l y analagous t o Bridgman 1 s e q u a t i o n and A « 2d- • Kardos i n 1924 m o d i f i e d Bridgmans e q u a t i o n by a l l o w i n g f o r the s i z e of molecules and o b t a i n e d K = /° C P ^ ^ where C p » s p e c i f i c heat a t constant p r e s s u r e ^ = mean d i s t a n c e between edges of m o l e c u l e s . As a f i r s t a p p r o x i m a t i o n Kardos assumed t o be constant f o r a l l l i q u i d s , but computations showed t h a t the v a l u e s of thermal c o n d u c t i v i t y so obta ined v a r i e d by as much as 100$ from standard v a l u e s . Smith* i n check ing K a r d o s 1 work, concluded t h a t c e r t a i n e r r o r s had been made i n development and c a l c u l a t i o n s , a c o n c l u s i o n & S e e «=r\<A O? tWesis 1 2 » w i t h whioh D r . Kardos agreed a f t e r he had reexamined h i s work. An e m p i r i c a l e q u a t i o n was suggested by Weber i n 1880. K = 0.003s* c P 3 y The constant has s i n c e been changed t o 0.0043 to f i t known v a l u e s b e t t e r . The m o d i f i e d e q u a t i o n g i v e s v a l u e s whioh d e v i -a te f rom s tandard values* by a maximum of 41% and an average of 14.8%. I n 1930 Smith p r e s e n t e d an e n t i r e l y e m p i r i c a l equa-t i o n of the form p c p iv\ K = 8.1 *\o " » . , 2 "" ' T h i s e q u a t i o n s a t i s f i e d a l l l i q u i d s f o r w h i c h d a t a were a v a i l -a b l e , but s i n c e then i t has been found t h a t i n some oases the e r r o r i s r a t h e r l a r g e . I n 1931 Smith a p p l i e d d i m e n s i o n a l a n a l -y s i s to heat c o n d u c t i v i t y and o b t a i n e d an e q u a t i o n w h i c h gave f a i r l y accura te r e s u l t s . A f t e r some s i m p l i f i c a t i o n the equa-t i o n became where K = thermal c o n d u c t i v i t y Cp e s p e c i f i c heat k = c o m p r e s s i b i l i t y / u n i t volume X a thermal e x p a n s i o n / u n i t volume M m m o l e c u l a r weight = v i s c o s i t y - c e n t i p o i s e s /°& " s p e c i f i c g r a v i t y A a a constant / ° • d e n s i t y g . / c c . 13. F o r l a c k o f s u f f i c i e n t a c c u r a t e d a t a at the t i m e , Smith was unable to check t h i s e q u a t i o n c o m p l e t e l y . I n 1936 Smith d e c i d e d on another type of e q u a t i o n . By t a k i n g v a r i a t i o n s from a p p r o x i -mate mean v a l u e s he found t h a t , ^  • K3C= O.OOC3W * N L F S ' + Y"ivi o z o / 0 0 0 ° where "0 « k i n e m a t i c v i s c o s i t y i n o e n t i s t o k e s . T h i s e q u a t i o n was e q u i v a l e n t t o * , f £ is • . „ ^ - o A S ) 4- V ^ . v K : o.oooot + — —^ ">* — 4 —" \ss goo sooea T h i s checked the d a t a a v a i l a b l e on the l i q u i d s used w i t h a maximum e r r o r o f 16% and an average of 6.7%. I n 1948, Palmer presented an e x p l a n a t i o n f o r the ap^ parent anomalies i n the heat c o n d u c t i v i t i e s o f a l c o h o l s and g l y c o l s , based on the f o r m a t i o n o f m o l e c u l a r aggregates by hydrogen b o n d i n g . He t h e r e f o r e searched f o r a f a c t o r s e n s i t i v e t o hydrogen bonding and found the entropy of v a p o r i z a t i o n ( T r o u t o n f s constant) t o be most p r o m i s i n g . He a p p l i e d t h i s m o d i f y i n g f a c t o r t o Weber f s e q u a t i o n s i n c e i t was the s i m p l e s t o f the e m p i r i c a l e q u a t i o n s . F o r e v a l u a t i o n no v a l u e of Trouton* s constant was assumed, but on o v e r a l l average constant was determined, r e s u l t i n g i n LV-r where Ly 8 3 l a t e n t heat of v a p o r i z a t i o n T = a b s o l u t e temperature T h i s e q u a t i o n and Smiths f i v e constant equat ions when checked on 36 l i q u i d s gave r e s p e c t i v e l y average e r r o r s of 8.3% and 1 4 . 8.4%. * I n 1946 Denbigh presented a d i m e n s i o n l e s s equat ion r e l a t i n g thermal c o n d u c t i v i t y t o the l a t e n t heat of v a p o r i z a t i o n where P r = P r o n d t l number * C B . A H = m o l a l en tha lpy o f v a p o r i z a t i o n a t 1 atmosphere R • gas constant T « a b s o l u t e temperature a and b are +Q.I83 and - 2 . 2 f o r water +0.20 M - 1 . 8 n o r g a n i c l i q u i d s T h i s e q u a t i o n 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 s not accura te f o r p r e d i c t i n g thermal c onduc 1 1vi t i e s . The Bureau of Standards e q u a t i o n f o r pet ro leum p r o d u c t s i s a development of one suggested by Cragoe i n 1929. K = .813 ( l ~ 0.003 ( t - 3 2 ) ) d where d • s p e c i f i c g r a v i t y of l i q u i d a t 60°F d i v i d e d by d e n s i t y of water a t 6 0 ° F . t =» temperature °F K • thermal c o n d u c t i v i t y - B . T . U . / h r / s q . f t . / ° F / i n c h A t 30°C the e q u a t i o n reduces t o s i m p l y K = 0.80 d The average e r r o r over the o i l s t e s t e d i s 12.4% and the maximum e r r o r i s 39%. 15 V I I . RESULTS (a) Computat ion o f C o r r e c t i o n F a c t o r s T y p i c a l Data - Run fid - Mareh 4 - Water Couple 1 18 19 6 11 Temp. 64 .1 55.25 47.60 39.75 30.00 D i f f . between couples 16 and 13 = .205 mv. Temp. d i f f . » .205 - 1.25°C 4U041J Water r a t e « 250 m .657 o e / s e o . 30T Q. » .657(1 .25) • ' .821 c a l / s e c . A = 37.66 cm 2 A dx o (.821-)-_(2.4) - .OOI58 I ^ (37.6l)(33) c a l onT^seo"1 The s lope dx i n runs on water was found t o be p r a c t i c -ed a l l y a s t r a i g h t l i n e , a l t h o u g h i t would have been p o s s i b l e t o draw a curve v e r y s l i g h t l y concave upwards i n some oases , n e v e r t h e l e s s , the best s t r a i g h t l i n e was used i n a l l cases , s i n c e the e r r o r i n t r o d u c e d was n e g l i g i b l e . The water r a t e s and temperature d i f f e r e n c e were c a r e f u l l y s e l e c t e d v a l u e s taken from r e a d i n g s on any one r u n a f t e r e q u i l i b r i u m was a t t a i n e d . I n some eases , averages of d i f f e r e n t v a l u e s were t a k e n . The average K over Runs 16, 17, 19 , . 20 and 21 on d i s t i l l e d water was found to be i00148 c a l * c m * * 1 s e c " l o C " * 1 . 16., A c t u a l l y , as mentioned b e f o r e , the thermal c o n d u c t i v i t y p r o b a -b l y ranged from .00147 to .00149 i n the c a l i b r a t i o n temperature range* but s e e i n g how d i f f i o u l t i t was t o draw a tangent t o such a f l a t c u r v e , the v a l u e .00148 was accepted f o r a l l tempera-t u r e s . To c o r r e c t f o r the t r u e v a l u e , the accepted v a l u e f o r K a t any temperature was d i v i d e d by the exper imenta l v a l u e e . g . a t 25°C the accepted v a l u e f o r water i s .00143 c a l . o m " 1 s e o " l o C ~ 1 . the c o r r e c t i o n f a c t o r i s .00142 5 - ;968 .0014t > Table 1 - C o r r e c t i o n F a c t o r s Temp. True K E x p ; K C o r r . F a c t o r 25 .00143 .001480 *968 30 •i 00145 .980 35 .00147 » >994 40 .00149 tt 1.006 45 .001505 n I i 0 l 6 50 .001525 tt 1.030 55 .00154 n 1 .042 60 .00156 tt 1.053 The temperature g r a d i e n t curves were o r i g i n a l l y p l o t t e d on 20 x 30 i n c h graph p a p e r . The, curves i n c l u d e d i n t h i s t h e s i s are s m a l l c o p i e s and are u s e f u l o n l y f o r comparisons . (b) The Thermal c o n d u c t i v i t y of Trans D e c a l i n . The Trans 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 i n a Stedman Column and was about 98% pure a c c o r d i n g to f r e e z i n g p o i n t t e s t s r u n on i t . 17. Table 2 - K f o r Trans D e c a l i n Temp. °C 33 40 45 50 55 60 K - C . G S . .001153 .001140 .001080 .001022 .00095 .OOO883 (c) The 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 a l s o was o b t a i n e d by vacuum d i s t i l -l a t i o n ; and was found to be a p p r o x i m a t e l y 98.5% p u r e . B o t h c i s and t r a n s were o b t a i n e d as a m i x t u r e f rom the Eastman Kodak Company. Four runs were made on t r a n s and f i v e on c i s ; the t a b u l a t e d r e s u l t b e i n g an average of these r e s u l t s . Table 3 •* K f o r C i s D e c a l i n Temp. °C 35 40 45 50 55 60 K .001178 .001150 .001091 .001040 .000958 .000899 (d) Thermal C o n d u c t i v i t y of K Decane A l l the p a r a f f i n s used were o b t a i n e d from the C e r t i -f i e d Chemica l Company of M o n t r e a l , Canada. The Decane was found to be v e r y n e a r l y pure as the e x p e r i m e n t a l l y determined v a l u e of the f r e e z i n g p o i n t was o n l y 0.2°C lower than the v a l u e g i v e n by the Texas Company. Table 4 - K f o r 1" Decane Temp. °C 35 40 45 50 55 &0 K .000652 .000645 .000622 .000575 .000572 .000535 (e) Thermal C o n d u c t i v i t y o f IT Dodecane The dodecane used was f a i r l y p u r e , the exper imenta l f r e e z i n g p o i n t b e i n g about 1°C l o w e r than the s tandard v a l u e . 18. A f t e r f o u r runs the c o l o u r had changed from clear to a l i g h t y e l l o w , a phenomenon not n o t i c e d i n deeane. However, t e t r a -decane and hexadeoane t u r n e d c o l o u r w i t h te t radecane g i v i n g the more pronounced change. Table 5 - K f o r E Dodeoane Temp; °C 35 40 45 50 55 60 K . 0 0 0 6 5 4 . 0 0 0 6 5 0 . 0 0 0 6 3 5 i000579 .000575 . 0 0 0 5 6 9 ( f ) Thermal C o n d u c t i v i t y of IS Tetradecane The f r e e z i n g p o i n t of t h i s p a r a f f i n as determined e x p e r i m e n t a l l y was over l i 5 ° C l o w e r than the s tandard v a l u e , i n d i c a t i n g c o n s i d e r a b l e i m p u r i t i e s . Table 6 - g f o r K Tetradecane Temp; °C 35 40 45 50 55 60 K ; 0 0 0 6 5 0 .OOO656 . 0 0 0 6 4 5 i000622 .000621 .000577 (g) Thermal C o n d u c t i v i t y of H Hexadeoane. The hexadeoane was f a i r l y pure as shown by i t s f r e e z -i n g p o i n t b e i n g o n l y 0 . 5 - 0.75°C l o w e r than the accepted v a l u e . A l l f r e e z i n g p o i n t s were measured by means of a p l a t i n -um r e s i s t a n c e thermometer and a r e s i s t a n c e b r i d g e r e a d i n g t o . 0 0 0 1 . ohms. Table 7 - K f o r E Hexadeoane Temp. °C 35 40 45 50 55 60 K ; 0 0 0 6 5 0 .OOO656 . 0 0 0 6 4 5 .000622 .000621 ;000577 2 . 8 0 2.4-0 2 . 0 0 I 6 0 \. 2.0 080 0 A - O O O O 1?. V i l l i DISCUSSION OF RESULTS The s t r i k i n g f a c t about the r e s u l t s o b t a i n e d i s t h a t they are c o n s i s t e n t l y much h i g h e r than r e s u l t s o b t a i n e d by o ther i n v e s t i g a t o r s u s i n g d i f f e r e n t appara tuses . T h i s i s r a t h e r remarkable because the apparatus used i n t h i s r e s e a r c h gave the accepted c o n d u c t i v i t y o f water v e r y c l o s e l y . T r u e , the temperature v a r i a t i o n o f c o n d u c t i v i t y was v e r y s l i g h t , but s e e i n g the c o r r e c t i o n f a c t o r was at the most o n l y 5% no l a r g e e r r o r c o u l d be i n t r o d u c e d . Runs were made on d i s t i l l e d water b e f o r e and a f t e r the runs on the p a r a f f i n s to de tec t any changes i n behaviour of the c e l l . A l l these runs f o r water checked w i t h i n a few p e r c e n t , i n d i c a t i n g c o n s i s t e n c y of r e s u l t s . The hydrocarbons used are d e f i n i t e l y not 100% pure as shown by the f r e e z i n g p o i n t t e s t s and the c o l o u r changes on h e a t i n g . Tetradecane e s p e c i a l l y i s b e l i e v e d t o be impure", and i t s behaviour as shown by f i g . 11 and 12 i s not n o r m a l . The c o e f f i c i e n t s f o r c i s and t r a n s d e c a l i n are h i g h e r than those obta ined by P e r r i s , but are o f the same o r d e r . Changes i n the apparatus w i l l account f o r these d i f f e r e n c e s between the v a l u e s of c o n d u c t i v i t y . Bates remarks t h a t h i s thermal c o n d u c t i v i t i e s are a p p r e c i a b l y h i g h e r than v a l u e s o b t a i n e d by o ther i n v e s t i g a t o r s . The t h i c k d i s c or t a l l c y l i n d e r method may then i n g e n e r a l g i v e h i g h e r v a l u e s than o ther apparatuses w i l l g i v e . C o n v e c t i o n may be present i n such a l a r g e volume of l i q u i d and so i n c r e a s e 2Q>. the heat f l o w to a h i g h e r than t r u e amount, but Bates* p r e l i m i n -a r y t e s t s i n d i c a t e ! t h a t c o n v e c t i o n was n e g l i g i b l e . The appar-a tus used i n t h i s r e s e a r c h was s m a l l e r than Bates" and some c o n v e c t i o n may have been p r e s e n t , but there i s no e x p l a n a t i o n of why the t r u e c o e f f i c i e n t of water should have been o b t a i n e d f a i r l y a c c u r a t e l y , w h i l e the c o e f f i c i e n t s o f the p a r a f f i n s a p p a r e n t l y were h i g h . The t e s t hydrocarbons d i d not c o n t a i n gases w h i c h 1 might have a f f e c t e d the r a t e of heat f l o w . S e v e r a l of the charges were de-gassed under a vacuum of about 6j> to 70 em. of mercury w i t h no v i s i b l e r e s u l t s . I t would appear then, i f these r e s u l t s f o r the normal p a r a f f i n s are too h i g h , t h a t under the t e s t c o n d i t i o n s the hydrocarbons e x h i b i t * some behaviour t h a t d i s t i l l e d water does not show under i d e n t i c a l c o n d i t i o n s . The a l t e r n a t i v e c o n c l u -s i o n i s s i m p l y t h a t the r e s u l t s are not t o o - h i g h and are c o r -r e c t as 'measured . A l l thermal c o n d u c t i v i t i e s computed by the e m p i r i c a l and t h e o r e t i c a l equat ions hereto developed show a constant p o s i t i v e d e v i a t i o n from s tandard v a l u e s . That i s , the average e r r o r over a l a r g e number of l i q u i d s i s always p o s i t i v e ; a l -though i n d i v i d u a l oases show n e g a t i v e d e v i a t i o n s . I t appears then t h a t e i t h e r some f a c t o r has been n e g l e c t e d i n t h e o r y , or e l s e t h a t l i q u i d s under t e s t e x h i b i t some behaviour unaccount - ' a b l e f o r by t h e o r y . 21 . I X . SUGGESTION The p r i m a r y f a u l t w i t h the apparatus used i s t h a t i t i s too s m a l l . A t l e a s t three t imes the present c a l o r i m e t e r s u r f a c e area i s needed f o r good g u a r d i n g . The depth c o u l d be reduced to keep down the volume of t e s t charge, but such a r e d u c t i o n would crowd the g r a d i e n t thermocouples and make the dx curve l e s s a c c u r a t e . oT The c a p a c i t y o f the guard r i n g c a l o r i m e t e r should be much l a r g e r than at p r e s e n t . The e x i t temperatures of bo th the t e s t and guard c a l o r i m e t e r s must be the same; and , to o b t a i n t h i s r e s u l t , the guard r i n g w i t h i t s much g r e a t e r s u r -face area s h o u l d have a c o r r e s p o n d i n g l y l a r g e r water r a t e . F o r convenience i n assembl ing and r e p a i r i n g , the t e s t c e l l should be comple te ly a c c e s s i b l e . Trouble was encountered i n the present c e l l when t r y i n g to r e p l a c e the t h e r m o p i l e s 17, 1 6 t 14 and 13 , because the w e l l s are r i g h t under the c a l o r -i m e t e r s which i n t u r n are o n l y a few i n c h e s from the bottom of i the c o n t a i n i n g s t e e l drum. t A v o l t a g e r e g u l a t o r should be i n s t a l l e d on the h e a t i n g c i r c u i t . The present D . C . b a t t e r y v o l t a g e f l u c t u a t e d b a d l y and r e q u i r e d constant a t t e n t i o n ; e s p e c i a l l y when the b a t t e r i e s were b e i n g charged and the v o l t a g e jumped from 100 to 135. The v a l v e s on both water l i n e s should be r e p l a c e d by 22 more accura te t y p e s . The water r a t e to the t e s t c a l o r i m e t e r v a r i e d even though the v a l v e s e t t i n g remained c o n s t a n t . A new secondary guard h e a t e r should be wound. I t would bes t be made from say JO gauge eonstantan or H i g h Temper would c l o s e l y near the top of the c e l l and i n c r e a s i n g l y f a r t h e r apar t down the c e l l as the temperature decreased . T h i s type of c e l l c o u l d be used f o r measuring the t h e r m a l c o n d u c t i v i t i e s of the h i g h e r m o l e c u l a r weight h y d r o -carbons i n the s o l i d s t a t e as w e l l as i n the l i q u i d s t a t e . Such measurements have been made b e f o r e , and i t i s c la imed t h a t f o r some substances a sharp change i s observed at the m e l t i n g p o i n t . Oare would be necessary t h a t no c o n v e c t i o n e x i s -t e d i n the l i q u i d s t a t e , or a f a l s e l y h i g h v a l u e would be o b t a i n e d . ' I t would be w e l l t o i n c o r p o r a t e as many as p o s s i b l e of the f e a t u r e s o f B a t e ' s second c e l l . H i s chromium p l a t i n g of the h e a t i n g and c o o l i n g s u r f a c e s e l i m i n a t e d any t r o u b l e -some copper ox ide f i l m s and avoided the need f o r p o l i s h i n g the s u r f a c e s f r e q u e n t l y , The t h i n s t e e l c y l i n d e r between the two t r a n s i t s c y l i n d e r s should be r e p l a c e d by a l e s s c o n d u c t i n g m e t a l . Ger-man s i l v e r or antimony i f p r o c u r a b l e are b o t h poor conductors of h e a t , and c o u l d be s o l d e r e d to s t e e l to make a t i g h t j o i n t . 2 3 . X . BIBLIOGRAPHY 1* Bates and H a z z a r d , I n d . E n g . Chem. 37, 193 (1945) . 2. Bates and Hazzard^ I n d . E n g . Chem. 33» 375 (1941) . 3 . B a t e s , Hazzard and P a l m e r , I n d . E n g . Chem. 10, 314 ( 1938) . 4* S t u l l , I n d . E n g . Chem; 39 , 517 (1947) . 5 . S m i t h , Trans* Am. See. Mech. E n g . 5 8 , 719 (1936); 6 . » I n d . E n g . Chem. 22 , 1246 ( 1930) . 7 . n w » " 2 3 , 416 (1931) . 8 . » Meoh. E n g . 56 , 304 (1934) . 9 . Denbigh* .T.Soe. Chem. I n d . 65 , 61 (1946) . 1 0 . Br idgman, P r o c * Am. A c a d . A r t s and Sc iences 5 9 , 141 (1923) 1 1 . M a r t i n and L o n g , P r o c . P h y s . S oc . of London 45 , 529 (1933). 1 2 . 0 . K . B a t e s , I n d . E n g . Chem. 25 431 ( 1933) . 1 3 . " « » " » » 28, 494 (1936) . 14 . Robinson and Younger, M . A . S c . T h e s i s ( U . B . C . ) 1946. 1 5 . G . P e r r i s , M . A . S c . T h e s i s ( U . B . C . ) 1947. E x t r a c t of P . T . Br idgman 1 s A r t i c l e P r o o . Am. Acad* o f A r t s and Sc iences - 1923* V o l . 59 "The p h y s i c a l p i c t u r e i n terms of whioh t h i s expres -s i o n f o r t h e r m a l c o n d u c t i v i t y may be o b t a i n e d as f o l l o w s . Imagine the molecules i n s imple c u b i c a r r a y , the s e p a r a t i o n of c e n t r e s b e i n g S • L e t t h e r e be i n the l i q u i d a temperature g r a d i e n t d e . The energy of a molecule i s Z°tQ ( h a l f p o t e n t i a l TEE and h a l f k i n e t i c ) ; where o< i s the gas constant and & i s the a b s o l u t e temperature . The d i f f e r e n c e of energy between n e i g h -b o r i n g molecules i n the d i r e c t i o n of the temperature g r a d i e n t i s 2oi £ dQ . T h i s energy d i f f e r e n c e i s to be conce ived as d x . 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 s f e r r e d aoross a f i x e d p o i n t o f any row p e r u n i t t ime i s the product of the energy d i f f e r e n c e and the number o f such energy s teps c o n t a i n e d i n a row cm. l o n g , or 2 o t ^ e k f / | & ~ • The t o t a l t r a n s f e r aoross 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, or 2 ^ / ^ - ^ $ . But by the d e f i n i -d x t i o n of thermal c o n d u c t i v i t y t h i s t r a n s f e r i s a l s o Comparing c o e f f i c i e n t s we o b t a i n K - Z<*nt-$ T h i s s imple e x p r e s s i o n not o n l y g i v e s the thermal c o n d u c t i v i t y a p p r o x i m a t e l y , but a l s o accounts f o r the s i g n , a l t h o u g h not the n u m e r i c a l magnitude of the temperature coef -f i c i e n t of c o n d u c t i v i t y . Thus f o r an o r d i n a r y organic l i q u i d - X both and $ decrease with" r i s i n g temperature , g i v i n g a c o n d u c t i v i t y d e c r e a s i n g w i t h temperature r i s e ; as found e x p e r i m e n t a l l y . F o r w a t e r , on the o ther hand^ ^ i n c r e a s e s w i t h r i s i n g temperature at a r a t e more than compensating f o r the - 2 . decrease o f £ f so t h a t the net e f f e c t i s an i n c r e a s e of c o n d u c t i v i t y . 3 / I n these equat ions £ = . ( ^ ) where (jp^) 3 i s a f a c t o r p r o p o r t i o n a l to the mean s e p a r a t i o n between the oentres of the m o l e o u l e s . 

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