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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 .  Levelton  A Thesis Submitted i n P a r t i a l F u l f i l m e n t The Requirements f o r t h e Degree of MASTER OF APPLIED SCIENCE i n the Department  of  CHEMICAL ENGINEERING  The U n i v e r s i t y o f B r i t i s h > May,  1948.  Columbia  of  THE THERMAL COItDTTCTI VTTIES OP SOME HYDROCARBONS  oy Bruce H. L e v e l t o n  ABSTRACT  The Bates C a l o r i m e t e r f o r measuring the heat cond u c t i v i t i e s o f hydrocarbons was p a r t i a l l y r e c o n s t r u c t e d so as t o d i m i n i s h the heat l o s s through the w a l l s o f the i r o n container*  T h i s was done by imbedding some nichrome w i r e  h e a t i n g elements i n the i n s u l a t i n g m a t e r i a l s j u s t o u t s i d e iron wall.  The c u r r e n t sent through t h i s c o i l was  so con-  t r o l l e d as t o 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 s e v e r a l hydrocarbons  gave the r e s u l t s  below.  Trans decahydronaphthalene  £35 -  Cis  ^33 - O.OOII78  »  0.001155  N  decane  £33 » O.OOO652  N  dodecane  £33 = 0.0006^4  N tetradecane  k33 - O.OOO65O  N  k 3 = O.OCO650  hexadecane  5  ACKBTOWLEDGEMENT  The a u t h o r w i s h e s t o acknowledge a d v i c e and. s u g g e s t i o n s  the  o f Dr« W, F , S e v e r under  whose d i r e c t i o n t h i s r e s e a r c h was u n d e r t a k e n *  LIST OF FIGURES TO TABLES Figures . 1.  Page  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 T e s t C e l l  4-  6 . Temperature G r a d i e n t Curve f o r Water  19  7i Correction Factors  19  8 . Temperature G r a d i e n t Curve f o r C i s and T r a n s D e e a l i n and Water  \9  9.  «  it  it  Dodeoane and  it  \Q  Tetradecane 10.  rt  "  n  "  Deeane and Hexadecane  11.  K f o r Normal P a r a f f i n s v s Temperature  12.  n  n  n  w  w  Number of 0 Atoms  1 3 . S m i t h * s R e s u l t s f o r Normal P a r a f f i n s 14.  \ 9 t 9 \9 »9  Temperature V a r i a t i o n of K f o r C i s , T r a n s 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 .  19  Tables. 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 3.  "  4.  •»  «  5.  n  n  6. 7.  " •*  " »  n  17  "  Trans  "  u Deeane  ' 7  »  N Dodeoane  18  "  N Tetradecane N Hexadecane  rt  n  i7  1& \&  TABLE OF CONTENTS Page I. II. . III.  Introduction  1  D e s c r i p t i o n of Apparatus  2  Changes i n A p p a r a t u s  4  (a)  4  Secondary Guard H e a t e r  (b) Replacement o f Thermocouple W e l l s  4  (o) Replacement o f Thermocouples  5  (d) New T e s t and Guard H e a t e r s  6  (e) New Water B a t h H e a t e r s  6  I V . C a l i b r a t i o n of Test C e l l  7  V. Procedure  8  T I . Theory o f Thermal C o n d u c t i v i t y  9  VII. Results  15  (a) C o m p u t a t i o n o f 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)  17  rt  (d)  n  (e)  n  " " w  £f)  H  n  (g)  »  «»  V I I I . D i s c u s s i o n of R e s u l t s I X . Suggestions X. Bibliography  Cis  n  rt  M  "  H Decane  17  H Dodeoane  1?  n u Tetradeoane  18  TS Hexadeoane  18  w  19 21 25  THE THERMAL CONDUCTIVITIES OF SOME HYDROCARBONS  I.  INTRODUCTION  R o b i n s o n and Younger i n 1946 b u i l t an a p p a r a t u s measuring t r u e c o e f f i c i e n t s ous h y d r o c a r b o n s ;  for  of thermal c o n d u c t i v i t i e s of v a r i -  They d e t e r m i n e d 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.  Their  a p p a r a t u s 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 at the Massachusettes  Institute  of Technology i n  1932. I n 1947 P e r r i s r e b u i l t t h e a p p a r a t u s , and r e c a l c u l a t e d t h e v a l u e s f o r t h e t h e r m a l c o n d u c t i v i t i e s o f d e c a l i n as w e l l as m e a s u r i n g the t r u e c o e f f i c i e n t  o f c o n d u c t i v i t y f o r o y o l o hexane.  The purpose of r e s e a r c h t h i s y e a r 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 t o 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 h y d r o c a r b o n s .  2 II.  APPARATUS  The method o f B a t e s i s a m o d i f i c a t i o n o f t h e t h i c k d i s c method.  B r i e f l y , t h e p r o c e d u r e 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 h e a t e d f r o m t h e t o p and c o o l e d f r o m t h e b o t t o n u  The h e a t e r  s u r f a c e and c y l i n d e r bottom a r e f l a t and a r e a b s o l u t e l y p a r a l l e l t o one a n o t h e r *  G r a d i e n t thermocouples a t measured h e i g h t s  g i v e the t e m p e r a t u r e d i s t r i b u t i o n w i t h d e p t h , and t h e amount of heat f l o w i n g t h r o u g h a known a r e a i s d e t e r m i n e d by m e a s u r i n g the t e m p e r a t u r e change and r a t e of f l o w o f t h e c o o l i n g w a t e r . B a t e s f o u n d by v a r i o u s e x p e r i m e n t s t h a t  convection  i n s u c h 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 t o t h e thermocouples can n o t be  detected.  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 o f a t h i n s t e e l c y l i n d e r 135.7 cm. i n d i a m e t e r and 7 cm. h i g h was s i l v e r s o l d e r e d t o 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 d i a m e t e r 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 t h e u n d e r s i d e o f the r i n g and t h e 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  surface;  I n s i d e t h e s t e e l c y l i n d e r and r e s t i n g on the  steel  p l a t e i s a 3.4 cm. l e n g t h o f t r a n s i t e p i p i n g 12*1 cm. i n s i d e d i a m e t e r 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 t h e  o u t s i d e o f t h e 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  transits  p i p i n g 13.8 cm. i n s i d e d i a m e t e r 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 d i a m e t e r were d r i l l e d a t o p p o s i t e s i d e s o f t h e c y l i n d e r a t each o f f i v e l e v e l s . Through t h e s e h o l e s were p l a c e d t h i n copper t u b e s 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 t h e c e n t r e o f a  steel  drum and packed w i t h 8^% magnesia and r o c k w o o l . The c e n t r e 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 o f copper w i t h p a r a l l e l s p i r a l g r o o v e s 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 o v e r t h e g r o o v e s .  I n t h i s way t h e r e  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 g u a r d 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 o f t h e 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 t e m p e r a t u r e s 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 o o p p e r - c o n s t a n t o n , JO gauge, d u p l e x , g l a s s - i n s u l a t e d * Leeds and U o r t h r u p thermocouples in series,  A t h e r m o p i l e was p l a c e d a t t h e 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 w a t e r was s u p p l i e d f r o m a t a n k at a h e i g h t o f J>4 i n c h e s .  The w a t e r was m a i n t a i n e d a t a c o n s t a n t  t u r e by means of f o u r b l a d e h e a t e r s ,  tempera-  two o f w h i o h were connected  I n s e r i e s w i t h t e m p e r a t u r e r e l a y and a mercury gap s e n s i t i v e t o l / l O o f one d e g r e e . 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. t o 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 .  THERMOCOUPLE.  Q O ^ ^ E R  SOLOER  FIG 1  HEATER  DETAIL.  HOLE  R I N G  RG. 2  THERMOCOUPLE. POSITIONS  COLD JUNCTION  MoT JUNCTION  .  REVERSING  SWITCH  TENTlOMETEH  RG 3  THERMOCOUPLE  CIRCUIT  »  Sec  GUAV^O  -wwwv GuiVRB  HEATER  HEATER  •wyvwv TEST  HEWER  FIG. 4  HEATING  CIRCUIT  1  TENSION  Z  L\ou>o  SPVOMG. THERMOCOUPLE  Cu  OUTER  5  S e c . GUARD  7  <*• GUARO  TE'-iT  CAL.  11  ~TRAMS\TE: C Y L I N D E R  T N ^ E R T E S T  TE&T  9  CALORIMKTERS  THERMOCOUPLE.  WiLLS  ~THERK/\ocovjf»LE.. G U I D E  3 4 6  8  MEATEP  ~TRANSITE. «-  G U A R D  C\t.lMTjeR  QV£R.PLOW  12.  SEME'S  \3  STetL. CYL.VMOE.PI  THERMOCOuPl_e  H E A T E R S  RG 5  ASSEMBLE  TUBE  OF T E S T  CELL  CO  ^ PLATE  GUARD  4.  III.  (a)  CHANGES^ I N APPARATUS  Secondary Guard H e a t e r P e r r i s f o u n d t h a t i t was n e c e s s a r y 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 d e t e r m i n e d 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 t h e a p p a r a t u s w i t h d i s t i l l e d w a t e r whose c o e f f i c i e n t o f t h e r m a l 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 *  Since these c o r r e c t i o n s v a r i e d  f r o m 15f. a t 25°C t o 42^ a t 45°C, i t was f e l t t h a t some i m p r o v e ment must be made* The edge o r s i d e l o s s o f h e a t 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 p r e v e n t  l o s s a secondary g u a r d h e a t e r o f Ho» 22 B and S gauge, Ghromel A w i r e was wound around t h e o u t s i d e o f the c y l i n d e r as shown i n f i g * J>*  this  bare,  transite  T h i s p r e c a u t i o n r e d u c e d the m a x i -  mum d e v i a t i o n f r o m aooepted v a l u e s t o a p p r o x i m a t e l y 5% i n t h e t e m p e r a t u r e range u s e d * (b) Replacement o f Thermocouple W e l l s S e v e r a l thermocouples had t o be r e p l a c e d , and i t was f o u n d e x t r e m e l y h a r d t o make c o u p l e s 1 7 , proof a f t e r replacement.  1 6 , 14 and 13 l e a k -  I t was c o n c l u d e d t h a t a b e t t e r a r r a n g e -  ment t h a n a D e k h o t i n s k y s e a l c o u l d be d e v i s e d , and so t h e f o l l o w i n g arrangement was u s e d *  The f o r m e r 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 t o p r e v e n t t h e c o u p l e , ends from b e i n g crowded t o g e t h e r .  The thermocouples were r u n  t h r o u g h 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 d o u b l e 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 t h e Tee t o make a t i g h t j o i n t by m e r e l y t h r e a d i n g the n u t onto t h e 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 p r e v e n t e d any l e a k a g e a l o n g t h e thermocouple w i r e s . (c)  Replacement o f Thermocouples. A l l c o u p l e s u s e d were of Leeds and N o r t h r u p ,  constantan,  g l a s s i n s u l a t e d , 30 gauge, d u p l e x w i r e s *  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 t h e  oopper-? Leeds  boiling  p o i n t o f w a t e r and g l y c e r o l , and t h e 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 t h e o f t h e 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 .  tips  Dueo was u s e d  t o i n s u l a t e t h e b a r e w i r e s , s i n c e no where was i t exposed t o hydrocarbons or other c o r r o s i v e l i q u i d s .  G l y p t a l was f o u n d t o  s w e l l and c r a c k 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, 1 9 ,  6 , 11  were s o l d e r e d a t t h e j u n c t i o n and t h e n emeried u n t i l  (see  fig.2)  smooth.  G r e a t c a r e was t a k e n t h a t t h e s e c o u p l e s d i d not s h o r t t o t h e screws on t h e t e n s i o n a d j u s t e r s .  I t was f o u n d t h a t the  glass  i n s u l a t i o n tended t o rub o f f i f i t was b e n t 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 t h e h e a t f l o w from t h e secondary g u a r d heater.  I t was e s s e n t i a l t h a t a t no t i m e s h o u l d the  readings  o f t h e s e t h e r m o c o u p l e s be h i g h e r t h a n the r e a d i n g o f t h e g r a d i ent thermocouple a t t h e 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 t h e g u a r d heater. (d) Hew T e s t and Guard H e a t e r s I t was f e l t t h a t t h e f o r m e r h e a t e r s d i d n o t have a l a r g e enough c a p a c i t y t o work o v e r the d e s i r e d t e m p e r a t u r e r a n g e , 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  copper heater s u r f a c e .  d i d not short to  the  Such a s h o r t d e v e l o p e d once, w i t h the  r e s u l t t h a t t h e g r a d i e n t thermocouples p i c k e d up t h e s t r a y  emf's  completely 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 H e a t e r s 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  formerly.  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 t h e tempera t u r e o f w a t e r from the m a i n s .  Of t h e 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 t h e o t h e r two were i n s e r i e s w i t h t h e temperature r e g u l a t o r .  17.  CALIBRATION OF TEST CELL  Because t h e t e s t c e l l had u n a v o i d a b l e h e a t l o s s e s due t o c o n d u c t i o n and i m p e r f e c t g u a r d i n g , i t was n e c e s s a r y t o c a l i b r a t e t h e a p p a r a t u s by u s i n g a l i q u i d whose t h e r m a l c o n d u c t i v i t y was  established.  D i s t i l l e d w a t e r was chosen as t h e s t a n d a r d , s i n c e c o n d u c t i v i t y i s known o v e r the d e s i r e d t e m p e r a t u r e r a n g e . g r a p h o f dx f o r v a r i o u s w a t e r r u n s i s shown i n f i g . 6.  IT  its The  From  t h e 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 r o m K = Q, dx where 0, i s heat f l o w i n  calories  laT p e r second and A i s t h e a r e a 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 d e t e r m i n e d v a l u e s o f E were compared t o  the  s t a n d a r d 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 was computed.  temperature  The r e s u l t s a r e shown i n t a b l e 1 and on f i g .  7.  A l l t h e r u n s were made under t h e 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 runs* c o i l was c o n s t a n t ,  That i s , t h e c u r r e n t t h r o u g h each h e a t e r  and t h e c o o l i n g w a t e r r a t e was a p p r o x i m a t e l y  t h e 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  w a t e r remained a t t h e same temperature  (22.4°C) a l l t h e  time.  8.  V.  1.  PROCEDURE  The t e s t e e l l was f i l l e d w i t h the h y d r o c a r b o n under examination.  2.  H e a t e r was p l a c e d on and excess l i q u i d removed t h r o u g h the overflow p i p e .  3.  Water r a t e s t h r o u g h t h e c a l o r i m e t e r s were a d j u s t e d so t h e g u a r d c a l o r i m e t e r was on maximum f l o w and t h e  that  test  c a l o r i m e t e r a t 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 t u r n e d on and the c u r r e n t s a d j u s t e d t o  the  calibration values, 5.  A f t e r e q u i l i b r i u m (5-6 h o u r s ) the c o u p l e s were r e a d at s e t i n t e r v a l s and the w a t e r r a t e was measured by means a 250 o c . v o l u m e t r i c f l a s k and a s t o p w a t c h .  6.  When h y d r o c a r b o n s were changed the ejfell was washed out thoroughly w i t h petroleum e t h e r .  of  71.  THEORY OF THERMAL CONDUCTIVITY  F o u r i e r f i r s t presented a mathematical 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 where  Q  Q, «= amount of h e a t f l o w i n g i n  1  ^  ©  g.cal./seo.  K » c o e f f . of thermal c o n d u c t i v i t y A = test dt  area  or  . T •» temperature d i f f e r e n c e o v e r dx o r  cm. o f t e s t  x  substance.  © « time For u n i t time K » Q, dx X dx I f x i s p l o t t e d versus t ,  a temperature g r a d i e n t c u r v e I s  o b t a i n e d , and the s l o p e o f t h i s curve a t any temperature dx. dt"  Therefore,  the f o r e g o i n g equation provides a b a s i s  measurement o f c o e f f i c i e n t s range o f t e m p e r a t u r e .  is for  of thermal c o n d u c t i v i t i e s over a  The measurements a r e s i m p l e -  Q, = amount o f h e a t / u n i t A « a r e a of t e s t  time  calorimeter  dx = d e t e r m i n e d by r e a d i n g s and h e i g h t s of f i v e IS  thermocouples T h e o r e t i c a l a t t e m p t s t o e x p l a i n t h e meohanism o f 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 t h e 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 f r o m t h a t of oopper o r 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 f r o m about 2j>0 x 10~^ t o l^OO x 10~k»  W h i l e numerous measurements have been  made on t h e heat c o n d u c t i v i t i e s o f l i q u i d s , t h e r e i s s t i l l doubt as t o the a c c u r a c y o f the methods u t i l i z e d .  some  Bridgman s ,  method o f c o n c e n t r i c c y l i n d e r s has been u s e d e x t e n s i v e l y f o r h y d r o c a r b o n s and o t h e r homologous s e r i e s  such as t h e  alcoholsj  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 t h e m s e l v e s 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 o f v i e w .  However, h i s v a l u e f o r  w a t e r 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 t h e r i n v e s t i g a t o r s . B a t e s enumerates some o f t h e s o u r c e s o f e r r o r p r e s e n t i n t h i s method.  An e r r o r n o t mentioned by B a t e s i s the heat  leak  t h r o u g h t h e two end p l a t e s o f 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  tube.  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 t h e m e t a l l i c ends o f t h e c o n c e n t r i c c y l i n d e r s o f B r i d g m a n * s a p p a r a t u s amounts t o about 4% o f the t o t a l heat  supplied.  Some y e a r s ago 0 . K . B a t e s a t M . I . T . c o n s t r u c t e d a t a l l column t y p e o f c a l o r i m e t e r h o p i n g t o overcome the r a i s e d a g a i n s t the t h i n f i l m t y p e o f c a l o r i m e t e r .  objections  The d e t a i l s  o f c o n s t r u c t i o n and performance of h i s a p p a r a t u s have been d e s c r i b e d i n t h e 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 a r e two d i s t i n c t d i s a d v a n t a g e s t o B a t e s t y p e 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 o v e r j?00 o c . o f t e s t l i q u i d and secondly the bafcelite w a l l s are r e s i s t a n t number o f s u b s t a n c e s .  to only a l i m i t e d  I t was f o u n d n e c e s s a r y 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 t o i n t r o d u c e o t h e r  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 p a p e r 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  equation  1/ -  where  A  =  (^Vp)**  /y^ » mass o f a m o l e c u l e i n grams » density i n grams/cc. <*  .- gas c o n s t a n t « 2.02 x l O " ^ e r g s / ° C .  ^  « v e l o c i t y o f sound i n the  1  liquid.  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 , t h e 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 a c c e p t e d v a l u e s .  The m a x i -  mum d e v i a t i o n o v e r a l a r g e number of s u b s t a n c e s was 38$ and t h e average d e v i a t i o n was 16.6"£.  Smith u s i n g dimensional  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 separation)  that the  (mean  equation  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  to  B r i d g m a n s e q u a t i o n and A « 2d- • 1  K a r d o s 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 t h e s i z e of m o l e c u l e s and o b t a i n e d where C p » s p e c i f i c heat a t c o n s t a n t ^  K = /° P ^ C  ^  pressure  = mean d i s t a n c e between edges o f 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 K a r d o s assumed  t o be c o n s t a n t  for  a l l l i q u i d s , but computations showed t h a t t h e v a l u e s o f t h e r m a l c o n d u c t i v i t y so o b t a i n e d v a r i e d by as much as 100$ from s t a n d a r d values.  Smith* i n checking Kardos  1  work, concluded that  certain  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 &  See  «=r\<A O?  tWesis  1  2  »  w i t h whioh D r . K a r d o s agreed a f t e r he had reexamined h i s w o r k . An e m p i r i c a l e q u a t i o n was suggested by Weber i n K = 0.003s*  c  P  3  1880.  y  The c o n s t a n t has s i n c e been changed t o 0.0043 t o f i t known values better.  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 t e f r o m s t a n d a r d values* by a maximum o f 41% and an average  of  14.8%. I n 1930 S m i t h 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 equat i o n of the form K  p = 8.1 *\o  c  iv\  p  "  ».,  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 , b u t s i n c e t h e n i t has been f o u n d t h a t i n some oases t h e error i s rather large.  I n 1931 S m i t h 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 t o h e a t 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 accurate 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 t h e 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 X M  = c o m p r e s s i b i l i t y / u n i t volume a  m molecular weight =  /°  t h e r m a l e x p a n s i o n / u n i t volume  viscosity-centipoises  " specific gravity  &  A /°  a a  constant  • density g./cc.  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 , S m i t h was u n a b l e t o check t h i s e q u a t i o n c o m p l e t e l y . on a n o t h e r t y p e o f e q u a t i o n .  I n 1936 Smith decided  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 f o u n d t h a t  K =  O.OOC3W  3C  *  '  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 .  This equation  was e q u i v a l e n t t o is • . „ ^ K o.oooot + —  v  -  o A S  :  \ss  ) —^  *  , f £ V ^ ">* —  4-  . 4  goo  —"  sooea  T h i s checked t h e d a t a a v a i l a b l e on the l i q u i d s u s e d w i t h a maximum e r r o r o f 1 6 % and an average o f 6.7%. I n 1948,  P a l m e r p r e s e n t e d an e x p l a n a t i o n f o r the ap^  p a r e n t a n o m a l i e s 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 t h e f o r m a t i o n o f m o l e c u l a r a g g r e g a t e s 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  sensitive  t o hydrogen b o n d i n g and f o u n d the e n t r o p y of v a p o r i z a t i o n ( T r o u t o n s constant) f  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 s e q u a t i o n s i n c e i t was t h e f  simplest  of 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 o f Trouton* s c o n s t a n t was assumed, but on o v e r a l l average c o n s t a n t was d e t e r m i n e d , r e s u l t i n g i n L  where  Ly T  83  V-r  l a t e n t heat of v a p o r i z a t i o n  = absolute  temperature  T h i s e q u a t i o n and Smiths f i v e c o n s t a n t  e q u a t i o n s 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 p r e s e n t e d a d i m e n s i o n l e s s e q u a t i o n  r e l a t i n g t h e r m a l c o n d u c t i v i t y t o t h e l a t e n t heat o f 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 = molal enthalpy of v a p o r i z a t i o n at 1 R • gas  atmosphere  constant  T « absolute  temperature  a and b a r e +Q.I83 and - 2 . 2 f o r w a t e r +0.20  M  -1.8  n  organic  T h i s e q u a t i o n was d e v e l o p e d f o r e s t i m a t i n g f i l m f o r heat t r a n s f e r ,  liquids coefficients  b u t i s not a c c u r a t e f o r p r e d i c t i n g t h e r m a l  c onduc 1 1 v i t i e s . The B u r e a u o f S t a n d a r d s e q u a t i o n f o r p e t r o l e u m p r o d u c t s i s a development of one suggested by Cragoe i n 1929. K = .813 d  (l~0.003(t-32))  where d • s p e c i f i c g r a v i t y o f 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 w a t e r 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./hr/sq.ft./°F/inch  A t 30°C the e q u a t i o n r e d u c e s t o s i m p l y K = 0.80 d The average e r r o r o v e r 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  VII. (a)  RESULTS  Computation of 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  Couple Temp.  1  18  64.1  55.25  19 47.60  - Mareh 4 - Water 6  11  39.75  30.00  D i f f . between c o u p l e s 16 and 13 = Temp. d i f f . » .205  -  4U041J  Water r a t e « 250  1.25°C .657  m  30T  Q. » . 6 5 7 ( 1 . 2 5 ) •  .205 mv.  '  oe/seo.  .821  A =  cal/sec.  37.66 c m A dx o (.821-)-_(2.4)  I ^  (37.6l)(33)  - .OOI58 c a l  2  onT^seo"  1  The s l o p e dx i n r u n s on w a t e r was f o u n d t o be p r a c t i c ed a l l y a straight 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 c u r v e v e r y s l i g h t l y concave upwards i n some o a s e s , nevertheless,  t h e b e s t s t r a i g h t l i n e was u s e d i n a l l c a s e s ,  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 w a t e r r a t e s and t e m p e r a t u r e 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 t a k e n f r o m 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 e a s e s , 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 o v e r Runs 1 6 , 17,  1 9 , . 20 and 21 on  d i s t i l l e d w a t e r was f o u n d t o be i00148 c a l * c m * * s e c " C " * . 1  lo  1  16.,  A c t u a l l y , a s mentioned b e f o r e ,  the thermal c o n d u c t i v i t y proba-  b l y ranged f r o m .00147 t o .00149 i n t h e c a l i b r a t i o n  temperature  range* b u t s e e i n g how d i f f i o u l t i t was t o draw a tangent  to  such a f l a t c u r v e , t h e v a l u e .00148 was a c c e p t e d f o r a l l temperatures.  To c o r r e c t  f o r the true v a l u e , the accepted value f o r K  a t any temperature was d i v i d e d b y t h e e x p e r i m e n t a l v a l u e e . g . a t 25°C t h e a c c e p t e d v a l u e f o r w a t e r i s .00143 the  correction factor  cal.om" seo" C~ . 1  l o  1  i s .001425 - ;968 .0014t  > Table 1 - C o r r e c t i o n  Factors Corr.  Factor  Temp.  True K  Exp; K  25  .00143  .001480  30  •i 00145  35  .00147  »  40  .00149  tt  1.006  45  .001505  n  Ii0l6  50  .001525  tt  1.030  55  .00154  n  1.042  60  .00156  tt  1.053  *968 .980 >994  The temperature g r a d i e n t c u r v e s 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 g r a p h p a p e r .  The, c u r v e s i n c l u d e d i n  t h i s t h e s i s a r e s m a l l c o p i e s and a r e 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 o f 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% p u r e a c c o r d i n g t o 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.  T a b l e 2 - K f o r Trans D e c a l i n Temp. °C K-C.GS.  (c)  33  40  45  50  55  60  .001153  .001140  .001080  .001022  .00095  .OOO883  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 -  lation;  and was f o u n d t o be a p p r o x i m a t e l y 98.5% p u r e .  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 r o m the Kodak Company.  Both  Eastman  F o u r r u n s were made on t r a n s and f i v e on c i s ;  t h e t a b u l a t e d r e s u l t b e i n g an average o f t h e s e  results.  T a b l e 3 •* K f o r C i s D e c a l i n Temp. °C K  35  40  .001178  .001150  45 .001091  55  50 .001040  60  .000958  .000899  (d) Thermal C o n d u c t i v i t y o f K Decane A l l t h e p a r a f f i n s u s e d were o b t a i n e d f r o m t h e f i e d C h e m i c a l Company o f M o n t r e a l , Canada.  Certi-  The Decane was  f o u n d t o be v e r y n e a r l y p u r e as the e x p e r i m e n t a l l y  determined  v a l u e of t h e f r e e z i n g p o i n t was o n l y 0.2°C l o w e r t h a n the  value  g i v e n b y t h e Texas Company. T a b l e 4 - K f o r 1" Decane Temp. °C K (e)  35  40  45  50  55  &0  .000652  .000645  .000622  .000575  .000572  .000535  Thermal C o n d u c t i v i t y o f IT Dodecane The dodecane u s e d was f a i r l y p u r e , the  experimental  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 t h a n t h e s t a n d a r d v a l u e .  18. A f t e r f o u r r u n s t h e c o l o u r had changed f r o m clear t o a l i g h t y e l l o w , a phenomenon n o t n o t i c e d i n deeane.  However,  tetra-  decane and hexadeoane t u r n e d c o l o u r w i t h t e t r a d e c a n e g i v i n g the more pronounced  change.  T a b l e 5 - K f o r E Dodeoane Temp; °C K  (f)  35  40  45  .000654  .000650  .000635  50 i000579  55  60  .000575  .000569  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 o v e r l i 5 ° C l o w e r t h a n t h e s t a n d a r d v a l u e , i n d i c a t i n g considerable  impurities.  Table 6 - g f o r K T e t r a d e c a n e Temp; °C K (g)  35  40  ;000650  .OOO656  45 .000645  50  55  60  i000622  .000621  .000577  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  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 t h a n t h e value.  freez-  accepted  A l l f r e e z i n g p o i n t s were measured b y means o f 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. T a b l e 7 - K f o r E Hexadeoane Temp. °C K  35  40  ;000650  .OOO656  45 .000645  50  55  60  .000622  .000621  ;000577  2.80  2.4-0  2.00  I 60  \. 2.0  080  0A-O  O O O  1?.  Villi  DISCUSSION OF RESULTS  The s t r i k i n g f a c t about t h e r e s u l t s o b t a i n e d i s  that  t h e y a r e c o n s i s t e n t l y much h i g h e r t h a n r e s u l t s o b t a i n e d by other i n v e s t i g a t o r s using d i f f e r e n t apparatuses.  This  is  r a t h e r r e m a r k a b l e because t h e a p p a r a t u s u s e d i n t h i s  research  gave t h e a c c e p t e d c o n d u c t i v i t y o f w a t e r v e r y c l o s e l y .  True,  t h e t e m p e r a t u r e 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 t h e c o r r e c t i o n f a c t o r was a t t h e 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 w a t e r  b e f o r e and a f t e r the r u n s on the p a r a f f i n s t o d e t e c t any changes i n b e h a v i o u r of t h e c e l l . w i t h i n a few p e r c e n t ,  A l l these runs f o r water  i n d i c a t i n g c o n s i s t e n c y of  checked  results.  The h y d r o c a r b o n s u s e d a r e d e f i n i t e l y not 100% pure as shown by t h e f r e e z i n g p o i n t t e s t s and t h e c o l o u r changes on heating.  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 b e h a v i o u r 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 a r e  higher  t h a n t h o s e o b t a i n e d by P e r r i s , but are o f the same o r d e r . i n t h e a p p a r a t u s w i l l account f o r t h e s e d i f f e r e n c e s between  Changes the  values of c o n d u c t i v i t y . B a t e s remarks t h a t h i s t h e r m a l c o n d u c t i v i t i e s a p p r e c i a b l y h i g h e r t h a n v a l u e s o b t a i n e d by o t h e r  are  investigators.  The t h i c k d i s c o r t a l l c y l i n d e r method may t h e n i n g e n e r a l higher values than other apparatuses w i l l g i v e . may be p r e s e n t  give  Convection  i n such a l a r g e volume o f l i q u i d and so  increase  2Q>. t h e h e a t f l o w t o a h i g h e r t h a n t r u e amount, but B a t e s * 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 .  prelimin-  The a p p a r -  a t u s used i n t h i s r e s e a r c h was s m a l l e r t h a n B a t e s " and some c o n v e c t i o n may have been p r e s e n t , of why t h e t r u e c o e f f i c i e n t f a i r l y accurately,  but t h e r e i s no e x p l a n a t i o n  of w a t e r s h o u l d have been  w h i l e the c o e f f i c i e n t s  o f the  obtained  paraffins  a p p a r e n t l y were h i g h . The t e s t h y d r o c a r b o n s d i d not c o n t a i n gases w h i c h might have a f f e c t e d t h e r a t e o f heat f l o w .  S e v e r a l of  1  the  charges were d e - g a s s e d under a vacuum of about 6j> t o 70 em. of mercury w i t h no v i s i b l e  results.  I t would appear then, i f t h e s e r e s u l t s f o r the normal p a r a f f i n s are t o o h i g h , t h a t under t h e t e s t c o n d i t i o n s  the  h y d r o c a r b o n s e x h i b i t * some b e h a v i o u r t h a t d i s t i l l e d w a t e r 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  conclu-  s i o n i s s i m p l y t h a t the r e s u l t s a r e n o t t o o - h i g h and a r e rect  cor-  as'measured. A l l t h e r m a l 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  e q u a t i o n s h e r e t o d e v e l o p e d show a  p o s i t i v e d e v i a t i o n from s t a n d a r d v a l u e s .  constant  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 .  It  appears  t h e n 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 b e h a v i o u r u n a c c o u n t - ' a b l e f o r by t h e o r y .  21.  IX.  SUGGESTION  The p r i m a r y f a u l t w i t h the a p p a r a t u s used i s i t i s too s m a l l .  At least  three times the present  s u r f a c e a r e a i s needed f o r good g u a r d i n g .  that  calorimeter  The d e p t h c o u l d be  r e d u c e d t o keep down the volume o f t e s t c h a r g e , 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 t h e dx curve l e s s  oT  accurate.  The c a p a c i t y o f t h e g u a r d r i n g c a l o r i m e t e r s h o u l d be much l a r g e r t h a n a t p r e s e n t .  The e x i t t e m p e r a t u r e s o f b o t h  the t e s t and g u a r d c a l o r i m e t e r s must be the same; a n d , t o o b t a i n t h i s r e s u l t , t h e g u a r d r i n g w i t h i t s much g r e a t e r  sur-  f a c e a r e a 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 w a t e r r a t e . F o r convenience i n a s s e m b l i n g and r e p a i r i n g , the t e s t c e l l s h o u l d be c o m p l e t e l y a c c e s s i b l e .  T r o u b l e was encountered  i n t h e p r e s e n t c e l l when t r y i n g t o r e p l a c e the t h e r m o p i l e s 17, 16  t  14 and 1 3 , because t h e w e l l s a r e r i g h t under t h e  calor-  i m e t e r s w h i c h i n t u r n a r e o n l y a few i n c h e s from t h e 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 s h o u l d be i n s t a l l e d on the heating c i r c u i t .  The p r e s e n t 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 c o n s t a n t a t t e n t i o n ; e s p e c i a l l y when t h e 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 f r o m 100 to  135. The v a l v e s on b o t h w a t e r l i n e s s h o u l d be r e p l a c e d by  22  more a c c u r a t e t y p e s .  The w a t e r r a t e t o t h e t e s t  calorimeter  v a r i e d even though t h e v a l v e s e t t i n g remained c o n s t a n t . A new secondary g u a r d h e a t e r s h o u l d be wound.  It  would b e s t be made f r o m say JO gauge e o n s t a n t a n o r H i g h Temper would c l o s e l y n e a r the top o f 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 a p a r t down t h e c e l l as t h e temperature  decreased.  T h i s t y p e o f c e l l c o u l d be u s e d f o r m e a s u r i n g the thermal c o n d u c t i v i t i e s of the h i g h e r molecular weight hydrocarbons i n t h e 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  state.  Such measurements have been made b e f o r e , and i t i s c l a i m e d t h a t f o r some substances a sharp change i s o b s e r v e d a t melting point.  the  Oare would be n e c e s s a r y t h a t no c o n v e c t i o n e x i s -  t e d i n t h e 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 obtained.  ' 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  o f 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 t h e 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 o x i d e f i l m s and a v o i d e d the need f o r p o l i s h i n g the surfaces frequently, The t h i n s t e e l c y l i n d e r between t h e two t r a n s i t s c y l i n d e r s s h o u l d 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 o r antimony i f p r o c u r a b l e a r e b o t h p o o r c o n d u c t o r s of h e a t ,  and c o u l d be s o l d e r e d t o s t e e l t o make a t i g h t  joint.  23.  X.  BIBLIOGRAPHY  1*  B a t e s and H a z z a r d , I n d . E n g . Chem. 3 7 , 193 ( 1 9 4 5 ) .  2.  B a t e s and Hazzard^ I n d . E n g . Chem. 33» 375 ( 1 9 4 1 ) .  3.  B a t e s , H a z z a r d and P a l m e r ,  4*  S t u l l , I n d . E n g . Chem; 3 9 , 517  5.  S m i t h , T r a n s * Am. S e e . M e c h . E n g . 5 8 , 719 ( 1 9 3 6 ) ; »  6. 7.  9.  (1947).  I n d . E n g . Chem. 2 2 , 1246 ( 1 9 3 0 ) . w  n  »  8.  I n d . E n g . Chem. 1 0 , 314 ( 1 9 3 8 ) .  »  " 2 3 , 416 ( 1 9 3 1 ) .  Meoh. E n g .  5 6 , 304 ( 1 9 3 4 ) .  Denbigh* .T.Soe. Chem. I n d . 6 5 , 61 ( 1 9 4 6 ) .  10.  B r i d g m a n , P r o c * Am. A c a d . A r t s and S c i e n c e s 5 9 , 141 (1923)  11.  M a r t i n and L o n g , P r o c . P h y s . S o c . o f London 4 5 , 529 (1933).  12.  0 . K . B a t e s , I n d . E n g . Chem. 25 431 ( 1 9 3 3 ) .  13.  "  14.  R o b i n s o n and Younger, M . A . S c . T h e s i s ( U . B . C . ) 1 9 4 6 .  15.  G . P e r r i s , M . A . S c . T h e s i s ( U . B . C . ) 1947.  «  »  "  »  »  2 8 , 494 ( 1 9 3 6 ) .  E x t r a c t of P . T . Bridgman s A r t i c l e 1  P r o o . Am. Acad* o f A r t s and S c i e n c e s - 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 t h e m o l e c u l e s i n s i m p l e c u b i c a r r a y , the s e p a r a t i o n of centres being S • gradient de.  L e t t h e r e be i n t h e l i q u i d a temperature  The energy of a m o l e c u l e i s Z°tQ  TEE  (half potential  and h a l f k i n e t i c ) ; where o< i s t h e gas c o n s t a n t and & i s absolute temperature.  The d i f f e r e n c e o f energy between n e i g h -  b o r i n g m o l e c u l e s i n the d i r e c t i o n o f the temperature is  2oi £ dQ  .  the  gradient  T h i s energy d i f f e r e n c e i s t o be c o n c e i v e d as  dx.  handed down a row of m o l e c u l e s w i t h the v e l o c i t y o f s o u n d .  The  t o t a l energy t r a n s f e r r e d a o r o s s a f i x e d p o i n t o f any row p e r u n i t time i s the p r o d u c t of the energy d i f f e r e n c e and t h e number o f such energy s t e p s c o n t a i n e d i n a row 2 o t  ^ ekf  /  |&~  •  cm. l o n g , o r  The t o t a l t r a n s f e r a o r o s s u n i t  cross  s e c t i o n i s t h e p r o d u c t o f t h e t r a n s f e r a c r o s s a s i n g l e row and the number o f r o w s , o r  2^/^-  ^ dx  $  .  But by t h e  t i o n of t h e r m a l 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 Comparing c o e f f i c i e n t s we o b t a i n  defini-  also  K - Z<*nt-$  T h i s s i m p l e e x p r e s s i o n n o t o n l y g i v e s the t h e r m a l c o n d u c t i v i t y approximately, 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 o f t h e temperature 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 o r g a n i c  coefliquid  both  and $  - X  decrease with" r i s i n g t e m p e r a t u r e , 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 f o u n d experimentally.  F o r w a t e r , on t h e o t h e r hand^ ^ i n c r e a s e s  r i s i n g t e m p e r a t u r e a t a r a t e more t h a n compensating f o r t h e - 2 .  decrease  of £  f  so t h a t t h e n e t e f f e c t i s an i n c r e a s e  of  conductivity. 3  I n these equations  £  =  .(^)  /  where  3  (jp^)  i s a f a c t o r p r o p o r t i o n a l t o t h e mean s e p a r a t i o n between the o e n t r e s o f the m o l e o u l e s .  with  

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