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Specific heat of cis decahydronaphthalene Graham, Harold Morton 1944

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J?/  SPECIFIC  HEAT  01 CIS  DECAHIDRONAPHTHALENE  By  H a r o l d Morton Graham, B.A.Sc.  A Thesis submitted i n p a r t i a l f u l f i l m e n t of the requirements f o r the Degree o f MASTER OF APPLIED SCIENCE i n the Department of  CHEMICAL ENGINEERING  The U n i v e r s i t y of B r i t i s h Columbia #  April,"1944  (i)  ACKNOWLEDGMENT  I would here l i k e t o express my a p p r e c i a t i o n t o Dr. W. IP. Seyer f o r h i s s u g g e s t i o n s , c r i t i c i s m s , and h e l p f u l tance i n c a r r y i n g out t h i s  assis-  investigation.  TABLE  OE  CONTENTS Page  Acknowledgement  (1)  Introduction  1  Choice of Method  3  P u r i t y of Compound  5  Apparatus . . . . . .  5  Bath Medium. . .  6  Thermo-regulator  6  Measurements and T h e i r A c c u r a c i e s Accuracy of A d i a b a t i c C o n t r o l .  10 .10  Measurement of Temperature  11  Measurement o f Energy Input  13  E r r o r s I n v o l v e d and T h e i r E f f e c t s on A c c u r a c i e s  17  Heat o f S t i r r i n g .  17  Evaporation.  20  Lags . . j  22  Calibration Operation  ' .....  22 23  Method of C a l c u l a t i o n o f S p e c i f i c Heats . ~. . . 25 Results  25  Discussion of Results  28  LIST  OF  ILLUSTRATIONS  Figure  Page  1  F i r s t and Second-order T r a n s i t i o n s  2  2  P h o t o e l e c t r i c Operated R e l a y  7  3  Conversion Fact.or f o r Changing Res i s t a n c e I n t e r v a l s t o Temperature Intervals  4  T o t a l E x t e r n a l R e s i s t a n c e at V a r i o u s Bath Temperatures  5  Heats o f E v a p o r a t i o n  21  6  S p e c i f i c Heat of C i s d e c a l i n  27  14  lj?  INTRODUCTION . Investigations  of the p h y s i c a l  p r o p e r t i e s of  c i s dec.ahydronaphthalene have been conducted i n t h i s laboratory f o r several years.  The s u r f a c e t e n s i o n , v i s -  c o s i t y , d e n s i t y , and vapor p r e s s u r e have been measured. Discontinuities  i n t h e ^surface t e n s i o n , v i s c o s i t y , and  vapor p r e s s u r e curves at a p p r o x i m a t e l y 51 degrees C suggest a t r a n s i t i o n i n the l i q u i d at t h i s temperature. Further indications  of a t r a n s i t i o n a t t h i s temperature  have been f u r n i s h e d by t h e P h y s i c s Department i n measurements of t h e Raman and Farady e f f e c t s o f e i s decahydronaphthalene. I f a t r a n s i t i o n does take p l a c e i n the l i q u i d , i t must c e r t a i n l y be- a second-order t r a n s i t i o n .  A clear  d i s t i n c t i o n between f i r s t and second-order t r a n s i t i o n s i s drawn by Zemansky.^  I n t h e f a m i l i a r f i r s t - o r d e r phase  t r a n s i t i o n s t h e r e a r e entropy and volume changes, whereas i n a second-order phase t r a n s i t i o n b o t h of these remain c o n s t a n t .  The d i f f e r e n c e  quantities  i n t h e two types o f t r a n -  s i t i o n s can be seen from f i g u r e 1. Since  Cfi /as \ _ _ T 'dT'p ~ " ar =  z  the s p e c i f i c heat curve w i l l be the f i r s t - o r d e r 1  derivative  Zemansky, Heat and Thermodynamics, second e d i t i o n , Chapter XV,  - 2-  Fig. 1  of the entropy c u r v e .  And s i n c e i n second-order t r a n s i -  t i o n s , the s l o p e of the entropy curve changes at the t r a n s i t i o n p o i n t , the s p e c i f i c heat curve should be d i s c o n t i n u o u s a t the t r a n s i t i o n p o i n t . Measurements of the d e n s i t y of c i s decahydronaphthalene show t h a t no volume change t a k e s p l a c e a t the suspected t r a n s i t i o n p o i n t .  T h i s would then l i m i t  t r a n s i t i o n to the second-order t y p e .  any  I t was the purpose  of t h i s i n v e s t i g a t i o n t o o b t a i n more c o n c l u s i v e evidence for  a second-order t r a n s i t i o n by t e s t i n g f o r d i s c o n t i n u i -  t i e s i n t h e s p e c i f i c heat c u r v e .  CHOICE  OF  METHOD The method used i n t h i s i n v e s t i g a t i o n was the  a d i a b a t i c method, f i r s t used by Person (1849), and brought to the f o r e by T. W. R i c h a r d s .  T h i s method r e q u i r e s the  m a n i p u l a t i o n of the j a c k e t temperature t o keep i t n e a r l y equal t o the c a l o r i m e t e r temperature.  S i n c e the r a t e of  heat f l o w between two bodies w i l l be p r o p o r t i o n a l t o the d i f f e r e n c e i n temperature of the two b o d i e s ; t h a t i s , &  *  K  AT  i t f o l l o w s t h a t a s m a l l v a l u e of A T w i l l r e s u l t i n a s m a l l amount o f heat f l o w between the two b o d i e s .  There-  f o r e , by a d j u s t i n g the temperature of the j a c k e t t o t h a t of the cup, the l o s s of heat from the cup t o the surround-  - 4 ings can be reduced, t o z e r o , and no c o r r e c t i o n f o r heat f l o w from t h e cup i s n e c e s s a r y .  However, i n experiments  of s h o r t p e r i o d , t h e e r r o r r e s u l t i n g from a c a l c u l a t i o n of the heat l o s s i s o f t e n l e s s than t h a t caused by a d j u s t ment of the j a c k e t temperature.  F o r t h i s reason the  a d i a b a t i c method i s not always p r e f e r a b l e i n experiments of s h o r t p e r i o d s . The g r e a t e s t advantage of t h e a d i a b a t i c method i s r e a l i z e d when r e l a t i v e l y slow heat changes a r e b e i n g studied.  F o r such p r o c e s s e s , e v a p o r a t i o n o f the c a l o r i -  meter l i q u i d and c o n v e c t i o n cause i n c o n s t a n c i e s i n the v a l u e o f K, and thus make any c o r r e c t i o n f o r r a d i a t i o n loss unreliable.  Hence t h e a d i a b a t i c method i s g e n e r a l l y  regarded as i n d i s p e n s a b l e i n p r o t r a c t e d experiments such as t h e p r e s e n t i n v e s t i g a t i o n . Furthermore, s i n c e a suspected t r a n s i t i o n o c c u r s i n t h e neighborhood o f 50 degrees 0, i t was thought adv i s a b l e t o keep t h e l i q u i d a t s l i g h t l y above t h i s temperat u r e f o r some time b e f o r e s t a r t i n g t o t a k e r e a d i n g s . T h i s would a l l o w a complete change from one m o l e c u l a r form t o the o t h e r , and the s p e c i f i c heats measured above t h e t r a n s i t i o n temperature would be d e f i n i t e l y those of t h e second m o l e c u l a r form. I n f u t u r e work i t i s planned t o modify s l i g h t l y the present apparatus t o o b t a i n t h e s p e c i f i c heat curve  at temperatures below 50 degrees C.  The v i s c o s i t y of  g l y c e r i n e i s r e l a t i v e l y h i g h below 50 degrees C, so t h a t temperature g r a d i e n t s i n a bath of g l y c e r i n e are d i f f i c u l t to e l i m i n a t e .  F o r t h i s reason i t i s planned to use water  as the bath medium f o r temperatures below 50 degrees C. I t should be p o s s i b l e , then, t o o b t a i n an a c c u r a t e s p e c i f i c heat curve from 10 degrees C t o 50 degrees C. A d i s c o n t i n u i t y i n these two s p e c i f i c heat curves at 50 degrees C would then i n d i c a t e a second-order phase t r a n s i t i o n a t t h i s temperature.  PURITY  OF  COMPOUND The isomers of decahydronaphthalene were separa-  ted by vacuum d i s t i l l a t i o n i n a Stedman column of commercial d e c a l i n f r o m the Eastman Kodak Company.  The c i s isomer  was f u r t h e r p u r i f i e d by r e c r y s t a l l i z a t i o n u n t i l a c o n s t a n t f r e e z i n g p o i n t of -43.22 degrees* C was o b t a i n e d .  APPARATUS The c a l o r i m e t e r used was the same as t h a t used by Mead and M c L e l l a n , b e i n g c o n s t r u c t e d s i m i l a r l y t o the c a l o r i m e t e r of R i c h a r d s and of W i l l i a m s and D a n i e l s .  It  i s adequately d e s c r i b e d i n the theses o f Mead and M c L e l l a n .  Bath Medium. The bath c o n s i s t e d o f two g a l l o n s of g l y c e r i n e i n w h i c h was d i s s o l v e d 20 grams of f e r r i c c h l o r i d e t o make i t an e l e c t r o l y t i c conductor.  I t was heated e x t e r -  n a l l y by a 300 watt h e a t i n g c o i l , and i n t e r n a l l y by passage of an a l t e r n a t i n g c u r r e n t d i r e c t l y through t h e b a t h . Rheostats i n the e x t e r n a l h e a t i n g c i r c u i t , and r h e o s t a t s and a p h o t o e l e c t r i c a l l y operated r e l a y i n the e l e c t r o l y t i c c i r c u i t a l l o w e d e f f i c i e n t temperature c o n t r o l . At f i r s t , c o n s i d e r a b l e d i f f i c u l t y was e x p e r i e n c e d w i t h e l e c t r o l y s i s produced by the a l t e r n a t i n g c u r r e n t . T h i s was thought to: be due t o water which might have been absorbed i n the g l y c e r i n e .  Consequently, a new b a t c h of  g l y c e r i n e and f e r r i c c h l o r i d e was mixed, and the e l e c t r o l y s i s was decreased to a n e g l i g i b l e amount. Two h i g h speed p r o p e l l o r s h a f t s at o p p o s i t e s i d e s o f the bath p r o v i d e d ample^ s t i r r i n g .  One was p l a c e d  f a i r l y c l o s e to the thermometer and t h e r m o - r e g u l a t o r t o prevent any temperature g r a d i e n t e x i s t i n g between these two i n s t r u m e n t s . Thermo-regulator A new-thermopile c o n t a i n i n g f i v e j u n c t i o n s of c o p e l and constantan w i r e was c o n s t r u c t e d , and used t o i n d i c a t e a temperature g r a d i e n t between the cup and the bath.  One l e g of the t h e r m o p i l e was i n the cup and one  - 7 l e g was i n the bath.  Any temperature d i f f e r e n c e between  the two l e g s would then s e t up an emf, which c o u l d be made t o a c t i v a t e a b a l i s t i c galvanometer.  By r e f l e c t i n g  a beam  of l i g h t from the m i r r o r of the galvanometer, a photoe l e c t r i c c e l l and r e l a y c o u l d then be used t o a u t o m a t i c a l l y keep the b a t h temperature a t t h a t of the cup. shows the automatic c o n t r o l scheme.  Seam  Fig.  2  Figure 2  When the cup temperature was h i g h e r than t h e bath temperature, an emf was s e t up i n t h e t h e r m o p i l e and the  galvanometer was d e f l e c t e d .  This caused the r e f l e c t e d  beam o f l i g h t t o pass o f f t h e p h o t o e l e c t r i c c e l l , thus a c t i v a t i n g the r e l a y and h e a t i n g the bath.  As the bath  temperature approached the cup temperature, the beam was g r a d u a l l y d e f l e c t e d onto t h e c e l l a g a i n and t h e power was a u t o m a t i c a l l y stopped. However, t h e r e i s a l a g i n the o p e r a t i o n of t h e p h o t o e l e c t r i c c e l l r e l a y , which c o u l d be reduced by some method s i m i l a r t o t h a t used by S t u l l .  He p o i n t s out  t h a t , " F o r the r e l a y to engage, t h e f i e l d o f t h e photoe l e c t r i c c e l l must be, l e t us say, 80 percent i l l u m i n a t e d , but once engaged, the r e l a y s t a y s engaged u n t i l t h e photoe l e c t r i c c e l l i s o n l y 20 p e r c e n t i l l u m i n a t e d .  This l a g  can be l a r g e l y overcome i f the l i g h t beam i s p e r i o d i c a l l y broken, i . e . , made t o go t o zero^ i l l u m i n a t i o n f o r a s m a l l f r a c t i o n o f a second.  To do t h i s , a c l o c k - a c t u a t e d pendu-  lum was p l a c e d so t h a t : i t spent a v e r y s h o r t time i n t h e beam at t h e end of i t s swing.  Thus t h e r e l a y was d i s -  engaged once a second, and i f the i l l u m i n a t i o n f e l l t o say 75 p e r c e n t , t h e r e l a y would not re-engage u n t i l t h e i l l u m i n a t i o n reached the 80 p e r c e n t v a l u e a g a i n . "  2  D a n i e l R. S t u l l ,  I n the  J . Am. Chem. Soc., 59, 2726 (1937).  f u t u r e , then, i t might be a d v i s a b l e t o i n s t a l l some such arrangement to reduce the l a g of the r e l a y . The t h e r m o p i l e was made from f i v e j u n c t i o n s of number 36 copper enamelled w i r e and number 30, insulated, copel wire.  The w i r e s were bared of i n s u l a t i o n  f o r a p p r o x i m a t e l y f i v e mm f i v e times at each end. i n t o molten s o l d e r .  cloth  at each end, then t w i s t e d t o g e t h e r These j u n c t i o n s were then dipped  I n s u l a t i o n of the j u n c t i o n s was a t -  t a i n e d by c o a t i n g each j u n c t i o n w i t h G l y p ^ l v a r n i s h , d r y i n g o v e r n i g h t i n the a i r , and then baking i n an oven at degrees C f o r 16 hours.  130  The t h e r m o p i l e was then t i e d  t o g e t h e r w i t h l i n e n t h r e a d and i n s e r t e d i n a Y - tube. The ends of the Y - tube were s e a l e d o f f , blown t h i n , and f i l l e d w i t h a l i t t l e  l i g h t o i l to provide a  l a r g e r r a t e of heat t r a n s f e r t o the t h e r m o p i l e .  This  r e s u l t e d i n a q u i c k e r response of the thermo-regular t o temperature changes i n the bath and cup.  One end of the  Y - tube passed through the l i d of t h e copper c o n t a i n e r i n t o the c a l o r i m e t e r cup.  T h i s l e g was  s e a l e d t o the l i d  by p a s s i n g through a copper tube box, p a c k i n g the box w i t h asbestos c o r d , t h e n f i t t i n g a s m a l l washer around the l e g and screwing down the cap t i g h t l y .  A little  l i q u i d porce-  l a i n cement was then a p p l i e d around the j o i n t t o f u r t h e r i n s u r e a good s e a l .  - 10  -  A f t e r the t h e r m o p i l e was  i n s t a l l e d , i t s voltage  per degree temperature d i f f e r e n c e between l e g s was measured. One l e g was  p l a c e d i n a f r e e z i n g mixture of d i s t i l l e d water  w h i l e the other l e g was  kept at the constant room  The v o l t a g e set up i n the t h e r m o p i l e was a Type K p o t e n t i o m e t e r .  temperature.  then measured by  From these measurements i t was  found t h a t a temperature d i f f e r e n c e of one degree C between the two l e g s s e t up a v o l t a g e o f 192 m i c r o v o l t s . The thermo-regulator  was c o m p l e t e l y immersed i n  the bath, so t h a t the o n l y heat which c o u l d be conducted from the cup t o the c o l d e r room would be along the leads from the t h e r m o p i l e .  These l e a d s were f i n e magnet w i r e  so t h a t heat conduction a l o n g them would be n e g l i g i b l e .  MEASUREMENTS  AND  THEIR  ACCURACIES  Adiabatic Control From the galvanometer c o n s t a n t s and from a measurement of the v o l t a g e generated per degree temperat u r e g r a d i e n t between the cup and bath, i t was p o s s i b l e t o c a l c u l a t e the d e f l e c t i o n o f the beam on the p h o t o e l e c t r i c c e l l f o r a g i v e n temperature g r a d i e n t between t h e cup bath.  I t was  and  c a l c u l a t e d t h a t a g r a d i e n t of 0.005 degrees  C d e f l e c t e d the beam f o u r cm.  T h i s was  c i e n t d e f l e c t i o n t o a c t i v a t e the r e l a y .  usually a suffiBy a r r a n g i n g the  - 11 zero p o i n t of t h e r e f l e c t e d beam a p p r o x i m a t e l y two cm t o one s i d e o f the photo c e l l , the beam o s c i l l a t e d about t h e zero p o i n t .  Any e r r o r s then would be compensating. 3  Mead  r e p o r t s t h a t from the v a l u e o f K, the  t h e r m a l leakage c o n s t a n t , a g r a d i e n t o f f i v e degrees 0 i s s u f f i c i e n t f o r an accuracy of one per m i l l e .  Since the  bath and cup temperatures" were u s u a l l y w e l l w i t h i n 0.01 degrees G, an accuracy o f one per m i l l e was e a s i l y assured Measurement o f Temperature Temperatures o f the bath were measured by a r e s i s t a n c e thermometer  connected t o a Leeds and Northrup 4  Type G - l M u e l l e r B r i d g e .  McLellan  g i v e s a complete des-  c r i p t i o n o f t h e method used. I t was found t h a t a change o f 0.0001 ohms i n the p l a t i n u m r e s i s t a n c e , e q u i v a l e n t t o a temperature chang of 0.01 degrees C, caused a d e f l e c t i o n o f t h e b a l l i s t i c galvanometer o f two mm on the s c a l e .  With c a r e , t h e n ,  temperatures could be measured to 0.005 degrees C.  Since  the temperature d i f f e r e n c e used i n t h e c a l c u l a t i o n s was a p p r o x i m a t e l y f i v e degrees C, t h e temperatures c o u l d be 3  B. R. Mead, M.A.Sc. T h e s i s , 1940.  4  Donald E. M c L e l l a n , M.A.Sc. T h e s i s , 1943.  - 12 measured t o an accuracy o f + 0 . 1 p e r c e n t .  T h i s accuracy  i s c o n s i s t e n t w i t h t h a t f o r which the c a l o r i m e t e r was 5 designed, namely, one p e r m i l l e .  However, as White  points  out, f o r an assured degree of p r e c i s i o n o f one p e r m i l l e , each s i n g l e e r r o r should be as s m a l l as 0 . 1 p e r m i l l e . Of course the degree o f p r e c i s i o n o f the temperature measurements c a n be i n c r e a s e d by u s i n g l a r g e r temperature differences i n the c a l c u l a t i o n s .  F o r i n s t a n c e , i f the  temperatures were a c c u r a t e to 0.005 degrees C f o r a temp e r a t u r e d i f f e r e n c e of 20 degrees C, an accuracy o f t 0.025 percent would be o b t a i n e d . However, as noted by W i l l i a m s 6 and D a n i e l s ,  t h i s method g i v e s an average s p e c i f i c heat  over a c o n s i d e r a b l e range of temperature and any i r r e g u l a r i t i e s i n t h e s p e c i f i c heats a t d i f f e r e n t temperatures, which a r e o f p a r t i c u l a r i n t e r e s t , are wiped o u t .  For this  reason i t was decided t o measure the a b s o r p t i o n o f heat over c o m p a r a t i v e l y s m a l l temperature ranges o f f i v e degrees C, w i t h an accuracy of ± 0 . 1 p e r c e n t . F a c t o r s f o r t h e c o n v e r s i o n of r e s i s t a n c e i n t e r v a l s t o temperature i n t e r v a l s were c a l c u l a t e d f o r v a r i o u s v a l u e s o f the mean r e s i s t a n c e .  The c o n s t a n t s used i n the  c a l c u l a t i o n s were those f o r thermometer number 317868, 5  W. P. White, The Modern C a l o r i m e t e r , p. 183.  6  Z. W i l l i a m s and F. D a n i e l s , J". Am. Chem. S o c , 4 6 ,  (1924).  - 13 and were as f o l l o w s :  -  R = 2.5266 F = 0.99157 3 = 1.493 The v a r i a t i o n of the f a c t o r f o r v a r i o u s mean r e s i s t a n c e s i s shown i n f i g u r e 3 . Measurement of Energy Input A complete d e s c r i p t i o n of the apparatus used i n measuring t h e energy i n p u t t o the cup i s g i v e n i n McLellan's thesis.  A few minor changes were made i n the c i r c u i t ; two  storage . b a t t e r i e s , connected i n p a r a l l e l , p r o v i d e d t h e c u r r e n t , and a new r e s i s t a n c e box, f o r c u r r e n t r e g u l a t i o n , was p l a c e d i n t h e c i r c u i t .  I t was thought t h a t the two  b a t t e r i e s would g i v e a s t e a d i e r c u r r e n t t h a n a s i n g l e one. The r e s i s t a n c e o f t h a t p a r t of the l e a d s which passed through the bath changed w i t h t h e bath temperature, whereas .the r e s i s t a n c e of t h e remaining  s e c t i o n o f the  l e a d s was constant w i t h constant/room temperature.  Assum-  i n g t h a t a l l s e c t i o n s o f t h e l e a d s p a s s i n g through the bath were a t t h e bath temperature, the t o t a l e x t e r n a l r e s i s t a n c e of l e a d s and standard r e s i s t a n c e was c a l c u l a t e d f o r v a r i o u s bath temperatures.  See f i g u r e 4 .  The v o l t a g e drop a c r o s s  t h i s e x t e r n a l r e s i s t a n c e c o u l d then be found a t any temperature.  This v o l t a g e was s u b t r a c t e d from t h e measured  v o l t a g e t o g i v e t h e v o l t a g e drop across the h e a t e r .  The  time of power i n p u t t o t h e cup was measured by an e l e c t r i c  - 16 t i m e r , which had been checked a g a i n s t a stop watch f o r l o n g and s h o r t p e r i o d s .  The energy i n p u t i n j o u l e s was  then obtained by m u l t i p l y i n g t h e v o l t a g e drop across t h e h e a t i n g c o i l by the c u r r e n t i n amperes and the time o f i n p u t i n seconds. C o n s i d e r a b l e d i f f i c u l t y was found i n o b t a i n i n g a steady c u r r e n t through the h e a t e r .  To o b t a i n steady  b a t t e r y c u r r e n t s , t h e b a t t e r i e s should n o t be l e f t  idle  f o r l o n g p e r i o d s and should be charged t o 1.275 on the hydrometer.  Poor c o n t a c t s i n the b a t t e r y c i r c u i t a r e a l s o  a d e t r i m e n t t o p r e c i s i o n work.  Any c o n t a c t s which c o u l d  not be s o l d e r e d were cleaned w i t h carbon t e t r a c h l o r i d e and made f i r m . S i n c e potentiometer readings were u s u a l l y acc u r a t e t o 0.00001 v o l t s , the c u r r e n t i n p u t , which was a p p r o x i m a t e l y 0.5 amperes, c o u l d be measured t o ± 0.00J percent p r e c i s i o n , and the v o l t a g e from t h e v o l t box, IT  which was a p p r o x i m a t e l y 0.05 v o l t s , t o t 0.02 percent precision.  The l i m i t o f e r r o r of the v o l t box was t 0.04  percent, probably smaller.  With these measurementsj then,  an accuracy of the power i n p u t was assured t o t 0.04 per7 cent.  As p o i n t e d out by White,  t h i s accuracy i s i d e a l l y  s u f f i c i e n t f o r the h i g h e s t c a l o r i m e t r i c accuracy.  Tem-  p e r a t u r e i n t e r v a l s o f approximately f i v e degrees C were 7  i b i d . , p. 155.  - 17 used, i n c a l c u l a t i o n s , r e s u l t i n g i n time i n t e r v a l s o f app r o x i m a t e l y 2500 seconds.  S i n c e t h e t i m i n g was a c c u r a t e  to one second, a p r e c i s i o n o f ± 0 . 0 4 percent was o b t a i n a b l e i n t h e time i n t e r v a l s .  Hence, an assured accuracy o f  tO.OA- percent was a t t a i n e d i n t h e measurement o f energy input.  ERRORS  INVOLVED  AND  THEIR  EFFECTS  ON  ACCURACIES  Heat o f S t i r r i n g S i n c e the heat produced by s t i r r i n g o f the l i q u i d i s a v e r y d i f f i c u l t q u a n t i t y t o measure, i t i s u s u a l l y best t o make t h e heat o f s t i r r i n g n e g l i g i b l e r a t h e r than t o attempt a c a l c u l a t i o n as t o i t s s i z e .  I f the heat of  s t i r r i n g causes an i n c r e a s e i n t h e cup temperature of 0.001 degrees per minute, and temperature i n t e r v a l s o f f i v e degrees C w i t h r e s u l t i n g t i m e i n t e r v a l s of 2500 seconds are  used i n c a l c u l a t i o n s , an accuracy g r e a t e r than ± one  percent cannot be assured.  F o r t h i s reason i t was d e c i d e d  to lower t h e r a t e o f s t i r r i n g t o g i v e a h e a t i n g e f f e c t o f 0.0001 degrees C per minute. the  F o r one per m i l l e p r e c i s i o n  e r r o r due t o the h e a t . o f s t i r r i n g would t h e n be n e g l i -  g i b l e , b e i n g of- the o r d e r of ± 0 . 1 p e r c e n t . E x p e r i m e n t a l d e t e r m i n a t i o n showed t h a t a s t i r r i n g r a t e o f 75 rpm produced a h e a t i n g e f f e c t o f not more than 0.0001 degrees G per  minute a t a temperature o f 50 degrees C.  - 18 8 I t has been shown  t h a t the power consumed by a  paddle s t i r r e r may be r e p r e s e n t e d by  F o r a g i v e n s t i r r e r and c o n t a i n e r w i t h a constant speed of s t i r r i n g , the o n l y v a r i a b l e s are the v i s c o s i t y and density of the f l u i d .  The power r e q u i r e d to. move t h e  s t i r r e r a t a g i v e n speed i s t h e power r e q u i r e d t o overcome the f r i c t i o n of t h e moving l i q u i d and p r o p e l l o r s .  Since  t h i s f r i c t i o n a l " l o s s " i s converted t o heat, an e s t i m a t e of t h e power i n p u t r e q u i r e d by t h e s t i r r e r w i l l be an estimate o f t h e heat o f s t i r r i n g .  " V a r i a t i o n s i n the heat  of s t i r r i n g w i t h v a r i a t i o n s i n t h e p h y s i c a l p r o p e r t i e s of the l i q u i d can then be p r e d i c t e d .  The r a t i o of t h e heat  of s t i r r i n g at 120 degrees C t o t h a t a t 50 degrees C should then be  or 0 . 8 7 .  I t i s seen, then, that i f t h e s t i r r i n g heat was  n e g l i g i b l e a t 50 degrees C i t would decrease s t i l l f u r t h e r at h i g h e r temperatures,  p r o v i d i n g the speed of s t i r r i n g  remained c o n s t a n t .  8  White, Brenner, P h i l l i p s , and M o r r i s o n ; Trans. Am. I n s t . Chem. Eng.; 30; 570-584. and White and Brenner, i b i d 5 8 5 - 5 9 7 (1933).  - 19 Another p o i n t which had t o be c o n s i d e r e d when d e c i d i n g on the r a t e of s t i r r i n g was the e f f e c t o f the s t i r r i n g speed on t h e v a l u e of t h e heat t r a n s f e r f i l m c o e f f i c i e n t , h.  The r a t e o f heat t r a n s f e r from the c o i l  to t h e l i q u i d was governed by the v a l u e o f the f i l m coefficient  f o r the decalin.  The v a l u e of h can be p r e d i c t e d  •from the e m p i r i c a l e q u a t i o n  where n  Q  0.6 i f the f l u i d i s being heated. No d a t a was a v a i l a b l e f o r v a r i a t i o n s w i t h tem-  p e r a t u r e o f K, t h e thermal c o n d u c t i v i t y of d e c a l i n , but from d a t a on o t h e r hydrocarbons i t was assumed t h a t the v a l u e o f K w i l l decrease 3 percent from 75 degrees C t o 140 degrees C.  D, t h e diameter of the f i l m , was c o n s t a n t ;  Cp i n c r e a s e d 20 percent from 50 degrees C t o 140 degrees C; xU, the v i s c o s i t y , decreased 70 p e r c e n t .  The mass v e l o c i t y ,  G-, o f t h e d e c a l i n f l o w i n g p a s t the c o i l c o u l d be assumed c o n s t a n t , s i n c e the d e n s i t y decreased w h i l e t h e v e l o c i t y i n c r e a s e d w i t h i n c r e a s i n g temperature.  From the v a r i a t i o n s  i n these f a c t o r s , i t was c a l c u l a t e d t h a t t h e v a l u e of h would i n c r e a s e 70 p e r c e n t i n g o i n g from 50 degrees C t o 140 degrees C. T h i s v a r i a t i o n i n t h e heat t r a n s f e r c o e f f i c i e n t  9  Walker, L e w i s , McAdams, and G - i l l i l a n d , P r i n c i p l e s o f Chemical E n g i n e e r i n g , p. 111.  - 20 probably a f f e c t e d the l a g s i n t h e cup, but these were v e r y d i f f i c u l t t o estimate.  I t would be advantageous t o o b t a i n  a constant heat t r a n s f e r by r e g u l a t i n g t h e s t i r r i n g speed, but u n l e s s t h i s speed were r e g u l a t e d a c c u r a t e l y , the e r r o r i n t r o d u c e d by poor r e g u l a t i o n would be f a r g r e a t e r than t h a t i n t r o d u c e d by a v a r y i n g heat t r a n s f e r c o e f f i c i e n t . F o r t h i s reason i t was "decided t o use a constant speed and n e g l e c t v a r i a t i o n s i n t h e heat t r a n s f e r  stirring coeffi-  cient . Evaporation As p o i n t e d out i n W h i t e , e v a p o r a t i o n  o f the  c a l o r i m e t e r l i q u i d i s the most c o m p l i c a t e d , and u s u a l l y the most i r r e g u l a r v a r i a b l e .  With a d i a b a t i c c a l o r i m e t r y ,  e v a p o r a t i o n merely i n c r e a s e s the vapour content i n the c a l o r i m e t e r chamber, beginning immediately a f t e r any temp e r a t u r e r i s e , but accomplished  i n a t i m e which i s g e n e r a l l y  unknown. The a i r space of the c a l o r i m e t e r chamber was estimated at 400 c c , and the change i n vapour p r e s s u r e p e r degree f o r c i s d e c a l i n was noted "from t h e vapour p r e s s u r e curves o f Rush.  S i n c e the heat o f v a p o u r i z a t i o n of c i s  d e c a l i n i n . t h e temperature 70 c a l o r i e s p e r g r a m , .10 11  11  r e g i o n concerned  i s approximately  the heat r e q u i r e d f o r t h e evapora-  i b i d . , p. 99M o r e l , Watson and Y i p , B.A.Sc. T h e s i s , 1940.  - 21 t i o n t o m a i n t a i n s a t u r a t i o n d u r i n g a temperature r i s e  could  be estimated,' and i s shown i n f i g u r e 5 . Temperature of Cup °C  Evaporation heat J o u l e s / gm / °C  85  5.3  95  5-5  105  7.6  120  1.0  10-* -4 10  130  1.4  ID"  4  140  1.8  lo-  4  Fig.  5  The time r e q u i r e d t o accomplish t h e s a t u r a t i o n 12 i s of great importance.  White  has made c a l c u l a t i o n s on  the r a t e o f s a t u r a t i o n by the method which Andrews and Johnston based on t h e work of W i l l i a m s o n and Adams.  This  involved a s o l u t i o n of F i c k ' s equation f o r d i f f u s i o n i n a s i n g l e dimension.  From these c a l c u l a t i o n s he has shown  t h a t i f t h e r a t e of h e a t i n g i s constant, the s a t u r a t i o n e f f e c t w i l l be s m a l l .  any v a r i a t i o n s i n  Furthermore, s i n c e  the s a t u r a t i o n e f f e c t i t s e l f was below 0.01 p e r c e n t o f the s p e c i f i c heat at temperatures below 140 degrees G, any v a r i a t i o n s i n t h i s e f f e c t due t o t h e time r e q u i r e d f o r 12  ibid..  p. 100.  - 22 s a t u r a t i o n , can be n e g l e c t e d .  The  e r r o r i n v o l v e d i n the  s a t u r a t i o n e f f e c t , then, i s c o n s i s t e n t w i t h the d e s i r e d accuracy of one per m i l l e . jjggg. As a r e s u l t of i m p e r f e c t temperature e q u a l i z a t i o n s i n the c a l o r i m e t e r , c e r t a i n l a g s were i n t r o d u c e d t o the system.  As t h e temperatures of the cup and bath were r a i s e d ,  l a g s were i n t r o d u c e d to the b a t h and cup, and t o the thermop i l e and thermometer. was  At 60 degrees C, a l a g of 10 seconds  present i n the r e s i s t a n c e thermometer, w h i l e a l a g of 6 seconds was  approximately  present i n the  thermo-regulator.  These l a g s of course would depend t o a l a r g e extent on  the  v i s c o s i t y of the l i q u i d s , so that at h i g h e r temperatures they would be decreased.  I t has a l r e a d y been p o i n t e d  out  under "Heat of S t i r r i n g " t h a t a v a r y i n g f i l m c o e f f i c i e n t has an e f f e c t on the l a g s . 13 however, White  With experimental  p o i n t s out that,- a l l constant  calibration, l a g s are  n e g l i g i b l e , so t h a t no c o r r e c t i o n f o r the l a g s was The  l a g i n the p h o t o e l e c t r i c c e l l -has  applied.  already  been d i s c u s s e d under "Thermo-regulator". CALIBRATION  '  The v a l u e f o r the water e q u i v a l e n t of the meter was 13  taken to be the same as t h a t found by  i b i d . , p.  88.  calori-  McLellan,  namely, 38.0  j o u l e s p e r degree C a t 30 degrees C, w i t h an  i n c r e a s e o f 0.1 j o u l e s p e r degree C f o r each 10 degrees r i s e i n temperature.  S p e c i f i c heat v a l u e s c a l c u l a t e d w i t h  t h i s v a l u e checked w i t h those o f M c L e l l a n and Mead. Any i n a c c u r a c y i n the value o f t h e water e q u i v a l e n t would merely s h i f t the o r d i n a t e s of t h e s p e c i f i c heat curve, but would not a f f e c t the shape of the curve.  Since  the o b j e c t o f t h e i n v e s t i g a t i o n was t o d e t e c t d i s c o n t i n u i t i e s i n t h e s p e c i f i c heat curve, an exact value o f the water e q u i v a l e n t was not of f i r s t importance.  OPERATION A p p r o x i m a t e l y 160 cc of t h e p u r i f i e d l i q u i d was weighed t o 10 m i l l i g r a m s , and c o r r e c t e d f o r the buoyancy of the a i r .  The copper sleeve was then i n s e r t e d i n the  f i b r e r i n g , and the whole f i t t e d i n t o the l a r g e r copper container.  A f t e r a l i t t l e grease had been a p p l i e d t o the  t h r e a d s , the l i d was screwed down t i g h t l y .  The whole  assembly was then c a r e f u l l y s e t i n t o t h e bath, and suspended from t h e s t i r r i n g motor.  The t h e r m o p i l e l e a d s  were then s o l d e r e d t o the galvanometer l e a d s .  After f i t t i n g  the cover i n t o p l a c e , t h e h e a t i n g c o i l l e a d s and the e l e c t r o l y t i c bath h e a t e r l e a d s were connected.  The b a t t e r y  c u r r e n t was then passed through the dummy h e a t e r , and the bath was heated t o a temperature s l i g h t l y above 51 degrees  - 24 C.  The l i q u i d i n the oup was then brought t o t h e same  temperature, and the whole a l l o w e d to reach e q u i l i b r i u m at t h a t temperature f o r about one hour.  The battery- c u r -  r e n t was then switched from the dummy h e a t e r t o t h e cup h e a t e r , and the bath temperature r e g u l a t e d a u t o m a t i c a l l y by t h e p h o t o e l e c t r i c a l l y operated r e l a y .  When steady  c o n d i t i o n s were o b t a i n e d , r e a d i n g s were t a k e n a t 1.5 t o 2 degree i n t e r v a l s .  The most s a t i s f a c t o r y procedure f o r tak-  i n g temperature r e a d i n g s was t o s e t the M u e l l e r B r i d g e f o r a d e s i r e d temperature, and then t o note the time when s i m u l t a n e o u s l y t h e s c a l e read z e r o and t h e t h e r m o p i l e showed no d e f l e c t i o n . At times t h e beam o f l i g h t a c t i v a t i n g t h e photoe l e c t r i c c e l l would swing a c r o s s the c e l l t o the wrong side.  When t h i s happened, the bath would continue t o be  heated and become out o f c o n t r o l .  F o r t h i s reason i t was  necessary t o p e r i o d i c a l l y check t h e p o s i t i o n of t h e l i g h t beam.  I t might be p o s s i b l e , i n t h e f u t u r e , t o remedy  t h i s d e f e c t by a method s i m i l a r t o that used by S t u l l , as d e s c r i b e d under "Thermo-regulator".  :  C o n s i d e r a b l e e x p e r i m e n t i n g was done w i t h the rate of heating.  A t f i r s t i t . seemed a d v i s a b l e t o use a  v e r y low r a t e o f h e a t i n g , approximately one-half w a t t . However, w i t h t h i s r a t e , t h e e r r o r due t o t h e heat o f s t i r r i n g seemed to be aggravated.  Furthermore, t h e time  - 25  -  f o r c o m p l e t i o n of a r u n was too l o n g .  A h i g h r a t e of  h e a t i n g was a l s o u n d e s i r a b l e , s i n c e t h e n , f o r a g i v e n temperature i n t e r v a l , a s h o r t e r time i n t e r v a l was  involved.  The a b s o l u t e e r r o r i n the t i m i n g would then lower the percentage p r e c i s i o n i n the t i m i n g .  Between these two ex-  tremes, a compromise had t o be reached, and a h e a t i n g r a t e of a p p r o x i m a t e l y one watt was found most s a t i s f a c t o r y .  METHOD  OF  CALCULATION  OF  SPECIFIC  HEATS  The method used i n c a l c u l a t i n g the s p e c i f i c heats at mean temperatures was e x a c t l y the same as t h a t used by MeLeiIan and Mead.  An adequate d e s c r i p t i o n of the proce-  dure i s g i v e n i n t h e i r t h e s e s .  For a time i t was  thought  a d v i s a b l e t o use l a r g e r temperature i n t e r v a l s i n the c a l c u l a t i o n s , but t h i s method was abandoned because of the reasons mentioned under the heading, "Temperature  Measure-  ments" .  RESULTS A number of e x p e r i m e n t a l runs were'made d u r i n g the  i n v e s t i g a t i o n , but o n l y the r e s u l t s c a l c u l a t e d from  the  most c o n s i s t e n t r e a d i n g s are r e c o r d e d .  R e s u l t s from  s e v e r a l of the runs were d i s c a r d e d because of d i f f i c u l t i e s e x p e r i e n c e d w i t h the s t i r r i n g  motor.  "Values f o r the s p e c i f i c heat at temperature i n t e r -  - 26 v a l s of.one and o n e - h a l f t o two degrees are t a b u l a t e d below.  These r e s u l t s showed an average d e v i a t i o n of  0.007 j o u l e s p e r gram per degree C from a smooth curve drawn through the p o i n t s .  Values a t f i v e degree i n t e r v a l s  were t a k e n from the curve and are p l o t t e d i n f i g u r e e  S p e c i f i c Heat J o u l e s / gram /  57.0  1.828  58.8  1.843  60.2  1.853  61.8  1.858  63.4  1.857  64.8  1.843  66.5 68.1  1.853 1.868  69.5  I.869  71.1  1.887  72.5 74.1  1.885  75.6  I.891  77.1 78.6  1.877 1.890  80.2  1.872  82.1  1.890  1.882  83.4  1.902  85.I 86.8  1.901 1.899  88.3 89.8  1.894 1.907  C  6.  SjO£c//=-/c MEAT  -27-.Socles/0/^7/°c  - 28 -  DISCUSSION  OF  RESULTS  From t h e r e s u l t s obtained t h e r e seems t o be no d i s c o n t i n u i t i e s i n t h e s p e c i f i c heat curve from 55 degrees C t o 90 degrees C.  The average d e v i a t i o n s o f the data are  w i t h i n 0.4 p e r c e n t , or 4 per m i l l e .  However, by paying  more a t t e n t i o n to t h e s t i r r i n g motor, i t should be p o s s i b l e t o g e t the d e v i a t i o n s t o w i t h i n 0.1 p e r c e n t .  BIBLIOGRAPHY  Davies, G. E., M.A.Sc. T h e s i s , (1939). D i c k i n s o n , J . , B u i . Bur. S t d s . , 9, 229 (1913) and 11, 43 (1915) Giauque and Wiebe, J . Am. Chem. Soc., 50, 50-101 (1928). M c L e l l a n , D. E., M.A.Sc. T h e s i s , (1943). Mead, B. R., M.A.Sc. T h e s i s , (1940). M o r e l , Watson, Y i p , B.A.Sc. T h e s i s , (1940). R i c h a r d s , J . Am. Chem. S o c , 31, 1275 (1909). Rubin, T. R., Levedahl, and Y o s t , J . Am. Chem. S o c , 66, 279 (1944). S t u l l , D. R., J . Am. Chem. Soc., 59, 2726 (1937). Walker, Lewis, McAdams, and G i l l i l a n d , P r i n c i p l e s o f Chemical E n g i n e e r i n g . White, W. P., The Modern C a l o r i m e t e r . White, Brenner, P h i l l i p s , and M o r r i s o n , Trans. Am. I n s t . Chem. Eng., 30, 570-584. W i l l i a m s and D a n i e l s , J . Am. Chem. Soc., 46, 903-917, (1924). Zemansky, Heat and Thermodynamics, Second E d i t i o n .  

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