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Anomalous specific heat in the liquid phase 1946

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ANOMALOUS SPECIFIC HEAT IN THE LIQUID PHASE by Henry James Howie, H . A . S c . A Thes i s submit ted i n P a r t i a l F u l f i l m e n t of the Requirements f o r the Degree of MASTER OF APPLIED SCIENCE i n the Department of CHEMICAL ENGINEERING. THE UNIVERSITY OF BRITISH COLUMBIA < September, 1946, ACKUO WLEDGBMEN T S I would here l i k e to express my thanks to the f o l l o w i n g peop le : M r . S . j ) . Cavers , whose he lp was needed through- out a l l of the r e sea r ch . D r . W.F. Seyer under whose d i r e c t i o n the research was c a r r i e d ou t . M e s s r s . D . L . S tewar t , R . D . Sevans, O . K . M i n i a t o and R . J . Weldon who, as undergraduates , he lped separate c i s isomer of decahydronaphthalene used i n t h i s r e s e a r c h . TABLE OF CONTENTS Page 1. I n t r o d u c t i o n and summary o f p r e v i o u s work 1 2 . Object of the res arch 8 3 . Methods f o r measuring the s p e c i f i c heat of l i q u i d s 8 (a) The a d i a b a t i c method of J . W . W i l l i a m s and F . D a n i e l s 9 (b) The i so the rma l method of W . P . W h i t e . . . . . 9 4 . Apparatus . . . . 14 (a) The C a l o r i m e t e r . . . . 14 (b) Apparatus f o r mesauring temperature and energy i n p u t . . . . , 15 5. M a t e r i a l s used 19 6. C a l i b r a t i o n of the Apparatus • 19 (a) The thermopile . 19 (b) Water equ iva l en t of the c a l o r i m e t e r . . . . 27 (c) Heat of s t i r r i n g and e v a p o r a t i o n . 29 7. Procedure f o r de te rmin ing the s p e c i f i c heat of c i s d e c a l i n 31 8. Sample c a l c u l a t i o n of the s p e c i f i c heat of c i s d e c a l i n 34 9 . R e s u l t s 37 10 . Conc lus ions • 40 1 1 . Recommendations f o r f u r t h e r work 42 LIST OF ILLUSTRATIONS F i g u r e Page 1. V a r i a t i o n of the p a r t i a l p ressure w i t h temperature. 1 (a) L i q u i d he l i um at the A p o i n t of 2 . 2 ° K . . . 2 (b) C i s D e c a l i n a t 50° C . 2 2 . V a r i a t i o n of d e n s i t y w i t h temperature 3 (a) L i q u i d he l i um at the A p o i n t . . . 3 (b) C i s d e c a l i n at 50° C 3 (c) Water to steam at 100° C . 4 3 . V a r i a t i o n o f the surface t e n s i o n w i t h t empera ture . . 4 (a) L i q u i d he l ium at 2 . 2 ° J i . 4 (b) C i s d e c a l i n at 50° C 6 4. V a r i a t i o n of the d i e l e c t r i c constant w i t h t e m p e r a t u r e . . ; 5 (a) L i q u i d he l i um at 2 . 2 ° i i 5 lb) C i s d e c a l i n at 50° C 6 5. v a r i a t i o n o f the s p e c i f i c heat w i t h t e m p e r a t u r e . . . . 6 (a) L i q u i d he l ium at 2 . 2 ° K , 6 (b) C i s d e c a l i n around 50° C 7 (c) Water to steam at 100° C 7 6. C o o l i n g curve f o r i so the rma l s p e c i f i c heat de te rmina t ion 1 1 7. Diagram f o r measuring the power inpu t to the cup hea te r and the thermopi le read ing 17 8. P i c t u r e s of the apparatus 18 (a) Apparatus as a w h o l e . . 18 (b) The c a l o r i m e t e r c o n t a i n e r . . . . . 18 (c) The c a l o r i m e t e r and thermopi le 18 LIST OF ILLUSTRATIONS F i g u r e - Page 9 . Apparatus f o r thermopi le c a l i b r a t i o n 20 10* Graph showing the v a r i a t i o n o f the E . M . F . p e r °0 w i t h temperature d i f f e r e n c e between tne - thermopi le l e g s of the copper -cope l the rmopi le v . . . * . . * . . . 24 1 1 . Same as f i g u r e (10) f o r copper c o n s t a n t i n t h e r m o p i l e . . . . . . . . 25 12 . C o n s t r u c t i o n of the coppe r - cons t an t in thermopi le to reduce temperature l a g s 26 13 . C o o l i n g curve f o r de termining the heat of s t i r r i n g and e v a p o r a t i o n . . . . . . . . . . . . . . . . . . . . . . . 30 14. I so thermal c o o l i n g graph f o r de te rmin ing to s p e c i f i c heat of c i s d e c a l i n - r u n #28.. 35 15. Graph of s p e c i f i c heat of c i s d e c a l i n p l o t t e d aga ins t temperature f o r runs 1 - I 8 - . . . 39 16. Graph of s p e c i f i c heat of c i s . d e c a l i n p l o t t e d a aga ins t temperature f o r runs 18 - 3 6 . . 41 1 1 . INTRODUCTION AND SUMMARY OF PREVIOUS WORK An ex tens ive study of the p h y s i c a l p r o p e r t i e s of decahydronapthalene has been made i n the Chemical E n g i n e e r i n g Labo ra to ry at U . B . C . du r ing the l a s t ten y e a r s . The reasons f o r t h i s s tudy have been ve ry w e l l o u t l i n e d by J . D . L e s l i e i n h i s M . A . S c . T h e s i s . ( 1) . Decahydronapthalene, or d e c a l i n , has been separated i n t o two i somer i c forms by vacuum d i s t i l l - a t i o n f o l l o w e d by repeated c r y s t a l l i z a t i o n s . (2) The p rope r - t i e s of the t r ans isomer have been found to be normal over tne ranges s tud ied but those o f tne c i s isomer have shown a d i s - c o n t i n u i t y around 50° C, s i m i l a r to those of l i q u i d he l ium at the <A p o i n t of 2 . 2 ° K . F o r t h i s reason i t has been suggested tha t the c i s isomer may have a second order phase t r a n s i t i o n around 50° C . A comparison o f the p r o p e r t i e s of c i s d e c a l i n around 50° C w i t h tnose o f l i q u i d he l ium at the A p o i n t of 2 . 2 ° K are g i v e n below, and are con t r a s t ed , where p o s s i b l e , w i t h those of a normal substance at a f i r s t order phase t r a n s i t i o n p o i n t . (1) v a r i a t i o n of P a r t i a l P re s su re w i t h Temperature I f the l o g a r i t h m of the p a r t i a l p ressure i s p l o t t e d aga ins t the r e c i p r o c a l o f the abso lu te temperature, the f o l l o w i n g curves f o r l i q u i d he l ium and c i s d e c a l i n are ob t a ined . (1) J . D . L e s l i e , M . A . S c . T h e s i s , 1941. (2) Angley , P o t k i n s , and Rush, i i . A . S c . T h e s i s , 1942. 2 . (a) L i q u i d he l i um at A p o i n t of 2 . 2 ° K. (1) F i g u r e 1 £a) log p f p err r n r n s . l a of M3:\J  U 0.8 T The s lope of the l o g a r i t h m of the p a r t i a l p ressure curve changes at the t r a n s i t i o n p o i n t . (b) C i s d e c a l i n at 50° u (2) F i g u r e 1 (b) + AO as Lo$ p 0.0 of Hg\J-O.S - ~/.o • ~/.S 25- 3.0 3.^ <40 The s lope o f the l o g a r i t h m of the p a r t i a l p ressure curve changes at 50 C . ( l ) "Phenomena at the Temperature of L i q u i d "Helium" . E . F . B u r t o n , h . Cray-son Smi th , & J . O . W i l l l & m pp.68 (a) C . W . J . Mann, M . A . S c . T h e s i s , 1944. 3 (2) v a r i a t i o n of D e n s i t y w i t h Temperature The graphs below show the v a r i a t i o n of the d e n s i t y w i t h temperature of l i q u i d he l ium at the A p o i n t , c i s d e c a l i n at 50° 0,and a substance undergoing a f i r s t o rder phase t r a n s - i o n change, eg, water b o i l i n g . (a) L i q u i d he l ium at the A p o i n t (1) F i g u r e 2 (-a) O.AS& ' o. / « • O.Z35 0./30 \ <* 1 The d e n s i t y undergoes no change at 2 . 2 ° K but the s lope of the curve changes. (b) C i s d e c a l i n at 50° C (2) F i g u r e 2 (b) oea I , • . i _ tO 30 SO ?0 90 7err»p irr * C (1) B . F . B u r t o n , H.Grayson^Smith , J . O . W i l h e l m , O p . c i t . , . p p . 6 9 (2) C .A.Davenpor te , M . A . S c . T h e s i s , 1938 4 There i s no change i n the d e n s i t y o r any apprec- i a b l e change i n the s lope of d e n s i t y curve at 50° C (c) Water to steam at 100° C F i g u r e 2 (c) An abrupt change i n the d e n s i t y occurs i n a f i r s t o rder phase t r a n s i t i o n . (3) V a r i a t i o n o f Surface Tens ion w i t h Temperature On p l o t t i n g the surface t e n s i o n aga ins t the temp- e r a t u r e , the f o l l o w i n g curves are obta ined f o r he l ium at the f\ p o i n t , and c i s d e c a l i n at 50° C . (a) L i q u i d hel ium, at 2 , 2 ° K ' (1) F i gu re 3 (a) os Surface 7ens/orrQj4 ( l ) E . F . B u r t o n , H.Grayson Smi th , J . O . W i l h e l m , o p . c i t . , pp 76 5 The surface t e n s i o n exper iences no change at the A p o i n t , hut the s lope o f the surface t e n s i o n curve changes, (b) C i s d e c a l i n at 50° C ( l ) F i g u r e 3 (b) 3-7- S u r J a c e T e n s i o n 3 « 2 <Dyn>e& p e r - Cnrr. SS JO 7-5" /OO T e m p , /'rr °C7. C i s d e c a l i n , a l s o , shows no change i n the surface t e n s i o n at 50° but the s lope of the surface t e n s i o n curve changes. (4) V a r i a t i o n of the D i e l e c t r i c Constant w i t h Temperature The graphs shown below g ive the change of the d i e l e c t r i c cons tants w i t h temperature of l i q u i d h e l i u m and c i s d e c a l i n , (a) L i q u i d he l ium at 2 . 2 ° K F i g u r e 4 (a) (2) ( 1 ) C .A.Davenpor te , M . A . S c . T h e s i s , 1938 (2) B . F . B u r t o n , H.Grayson Smi th , J . O . W i l h e l m , o p . c i t . , pp 77 6 The d i e l e c t r i c constant does not change at 2 .2 K a l though the s lope of the d i e l e c t r i c constant curve changes r a t h e r a b r u p t l y . (b) C i s D e c a l i n at 50° C ( l ) F i g u r e 4 (b) £~Of7rA?rr 7*- TO SO SO ~/C*/TT/3. Srr °C. The curve f o r c i s d e c a l i n around 50° C i s ve ry s i m i l a r to tha t f o r l i q u i d h e l i u m at 2 . 2 ° K . (5) V a r i a t i o n of S p e o i f i c Heat with Temperature On p l o t t i n g the s p e c i f i c heat aga ins t temperature the f o l l o w i n g curves, f o r l i q u i d h e l i u m at the A p o i n t and c i s d e c a l i n around 50° C are ob t a ined . These graphs are con t r a s t ed w i t h that o f a substance undergoing a f i r s t o rder phase t r a n s i t i o n , eg, water b o i l i n g ( a ) L i q u i d he l i um at 2 . 2 ° K F i g u r e 5 ( a ) s - ^ , ^ . 3 <Za/s; /per joer- C £ t o (2) AO SCVTT>/?. £.0 /rr rX. s.o (1) B . A . D u n e l l , Masters T h e s i s , 1946. (2) E . F . B u r t o n , H.Grayson Smi th , J . O . W i l h e l m , op. c i t . , pp 75 3 Tne s p e c i f i c heat curve shows a marked d i s c o n t i n - u i t y at the A p o i n t but the s p e c i f i c heat and the s lope of the curve are n e a r l y the same before and a f t e r the break . (b) C i s D e c a l i n around 50° C determined by M i s s Robinson ( l ) u s ing the I so thermal Method. F i g u r e ^5.(b) Spect'f/'c Heart /ocy 'C. •/err AS • /.a • /.7 £.7 **3\ -*7 sa +9 The above curve f o r c i s d e c a l i n shows a marked resemblance w i t h tha t of l i q u i d h e l i u m at the A p o i n t . I t should be noted, however, tha t p r e v i o u s i n v e s t i g a t o r s G . F . Davies ( 2 ) , D . E . M c L e l l a n , ( 3 ) , and H.M.Graham (4) when u s ing tne a d i a b a t i c method obta ined a wavy s p e c i f i c heat curve over tne r eg ion concerned. (c) Water to steam at 100° C. F i g u r e 5 (c) /.o S p e c i e rVea* irr Ch/r. p e r °C. o S *• o . o (1) M.Robinson , M . A . T h e s i s , 1945. (2) G . F . D a v i e s , ' M . A . S c . T h e s i s , 193S. (3) . D . E . M c L e l l a n , M . A . S c . T h e s i s , 1943. (4) H.M.Graham, M . A . S c . T h e s i s , 1944. 8 An abrupt change i n the s p e c i f i c heat occurs d u r i n g the above f i r s t order phase t r a n s i t i o n and the s p e c i f i c heat before and a f t e r the t r a n s i t i o n are not the same. As a c o n c l u s i o n from the p rev ious exper imenta l da ta , i t seems apparent tha t c i s d e c a l i n e x h i b i t s ancmolous behaviour around 50° C and shows i n d i c a t i o n s of hav ing a second-order phase t r a n s i t i o n i n t h i s r e g i o n . 2 . OBJECT OF THE RESEARCH The c h i e f aim of t h i s r e sea rch was to t r y to conf i rm the r e s u l t s , made by p rev ious i n v e s t i g a t o r s , o f the s p e c i f i c heat of c i s d e c a l i n . In p a r t i c u l a r , the anomolous change of the s p e c i f i c heat w i t h temperature around 50° C was to be i n v e s t i g a t e d by the i s o t h e r m a l method. I t was decided to use temperature d i f f e r e n c e s o f . t h e order of one- ten th of a degree to q u a n t i t a t i v e l y determine the shape of the s p e c i f i c heat- temperature curve around the i n d i c a t e d second-order phase t r a n s i t i o n p o i n t , and from the graph to determine the change i n enthalpy or heat content at t h i s p o i n t , 3 . METHODS FOR MEASURING THE SPECIFIC HEAT OF LIQUIDS The A d i a b a t i c and the I so thermal Methods. I n both methods a measured amount of heat i s added to a weighed, amount of the substance i n ques t i on , and the r i s e of temperature i s observed. 9 (a) ADIABATIC METHOD of J . W . W i l l i a m s and F . D a n i e l s ( l ) I n the ad i aba t i c . c a l o r i m e t e r , the substance con- cerned i s p l aced i n a c o n t a i n e r and i s surrounded by a bath l i q u i d . The temperatures o f substance and the r e g i o n sur rounding i t are ma in ta ined the same throughout an a d i a b a t i c s p e c i f i c heat measurement. The s p e c i f i c heat i s then g i v e n by the fo rmula , o =• CP where Cp i s the heat added, -d i s the observed r i s e of temperature Cx> i s the weight of the substance. S ince the temperatures of the substance and the r eg ion surrounding i t are. the same, there i s no heat l o s s by con- d u c t i o n and r a d i a t i o n . The a d i a b a t i c method, however, was not found s a t i s f a c t o r y to f i n d the s p e c i f i c heat i n smal l temperature ranges and hence was not used int. t h i s r e sea rch . (b) ISOTHERMAL METHOD of W.P.White (2) In the i so the rma l method the substance i n ques t ion i s p l aced i n a con ta ine r surrounded by a bath l i q u i d . With t h i s method, however, the substance i n the c o n t a i n e r i s not main ta ined at the same temperature as tha t of the sur rounding ba th . I f the substance i s h o t t e r o r c o l d e r than the r eg ion around i t , i t w i l l . l o s e o r ga in heat r e s p e c t i v e l y by conduc t ion and r a d i a t i o n . When heat i s added to the substance i t w i l l (1) W i l l i a m s J . W . , & D a n i e l s F . , "The S p e c i f i c Heats o f C e r t a i n Organic L i q u i d s at E l e v a t e d T e m p e r a t u r e s " , J . A . C . S . , . v o l . 46, pps . 303-317, 1924. (2) White W . P . , "Some C a l o r i m e t r i c Methods", the P h y s . Review V o l . 31, pp . 545-48, 1910. 10. exper ience a r i s e i n temperature, but t h i s r i s e w i l l not be tne r i s e which "would have r e s u l t e d wi thout heat t r a n s f e r to or from the j a c k e t . Fo r the i so the rma l method, t hen , a c o r r e c t i o n f o r the t r a n s f e r of heat must be a p p l i e d to the formula g iven f o r the a d i a b a t i c type of d e t e r m i n a t i o n . The i so the rma l method depends f o r i t s accuracy on the method used f o r de te rmin ing the heat t r a n s f e r c o r r e c t i o n mentioned above. S ince the substance i n the con ta ine r i s u s u a l l y h o t t e r than the l i q u i d of the j a c k e t , heat i s l o s t to the l i q u i d , and the inc rease i n temperature o f the substance^not as great as i t would be i f no heat were l o s t by i t . The heat t r a n s f e r equat ion then i s u s u a l l y a c o o l i n g c o r r e c t i o n . The method f o r de te rmin ing the c o o l i n g c o r r e c t i o n used i n t h i s research i s the one!, de sc r ibed by W.P.Whi te . (1) Suppose tha t the c o n t a i n e r , h o l d i n g a l i q u i d whose s p e c i f i c heat i s to be measured, i s immersed i n a j a c k e t l i q u i d w i t h both l i q u i d s adequately s t i r r e d so tha t no temperature g rad i en t s e x i s t w i t h i n them. Then a measured amount of heat i s added to the l i q u i d i n the con t a ine r and the temperature o f t h i s l i q u i d i s measured as the heat i s be ing added. S i m i l a r l y when the i n n e r l i q u i d i s c o o l i n g by l o s i n g heat to the j a c k e t l i q u i d , the temperature of the i n n e r l i q u i d i s measured a g a i n . Thezi? on p l o t t i n g a graph w i t h temperatures as o rd ina t e s and t imes as a b s c i s s a , a c o o l i n g curve i s ob ta ined as f o l l o w s (1) I b i d . 1 1 . F i g u r e 6. At time 0 the a d d i t i o n of heat i s smarted. At time A the a d d i t i o n of heat, i s s topped. But the temperature of the l i q u i d con t inued to r i s e because of l a g s i n the h e a t i n g dev ices . ' At t ime 2 the temperature reaches a maximum. Time 4 i s any time l a t e r . Now l e t : ~0<\ be the i nne r l i q u i d temperature at t ime 0 . ' -Q^ be the i nne r l i q u i d temperature at time 2, e t c . A l s o l e t : 77 be t$e time i n t e r v a l from 0 to 2 . 12 7^ be tne t ime i n t e r v a l from 2 to 4 . . <fi be tne temperature d i f f e r e n c e bet-ween the i n n e r l i q u i d and the j a c k e t l i q u i d at t ime T. CO.be the temperature f a l l pe r minute due to the com- bined e f f e c t of evapora t ion and s t i r r i n g . <pm be f $ where ~BCi stands f o r any time i n t e r v a l Tm. I t i s apparent tha t equals the area bounded by the two l i q u i d temperature curves and the two a b s c i s s a forming the boundaries of the time i n t e r v a l Tm. The heat dQ l o s t i n any element of time dT du r ing the experiment because the i n n e r l i q u i d i s h o t t e r than the j a c k e t ": l i q u i d i s g iven by: dQ = C 4> d T ( l ) where C i s a cons tan t . T h i s statement assumes tha t Newton's Law of c o o l i n g h o l d s , tha t i s , i t assumes tha t the ra te of l o s s of heat i s p r o p o r t i o n a l to the temperature d i f f e r e n c e between the two l i q u i d s . Then i n any p e r i o d of time Tm the t o t a l amount of heat l o s t i s or Thus the t o t a l amount o f heat l o s t by the i n n e r to the j a c k e t l i q u i d du r ing a time i n t e r v a l i s p r o p o r t i o n a l to the area bounded on the l e f t and r i g h t by the boundaries of the time i n t e r v a l and on the top and bottom by the two l i q u i d temperature cu rves . 13 Now c o n s i d e r the time i n t e r v a l 7^ The t o t a l l o s s of temperature by the l i q u i d i s g i v e n by -Ok - The l o s s of temperature caused by the combined e f f e c t s of evapora t ion and s t i r r i n g by <^ ^» C a l l the l o s s of temperature caused on ly by the d i f f e r e n c e i n temperature of the j a c k e t and c o n t a i n e r l i q u i d s the d i r e c t temperature l o s s . Then the d i r e c t l o s s i n the i n t e r v a l i s (t% - G+) - ca 7^ (3) Now l e t : <p, be the d i r e c t heat l o s s i n p e r i o d 1 <j£ be the d i r e c t heat l o s s i n p e r i o d 3 Then from the above d i s c u s s i o n i n Equa t ion (2) or g>j_ __ (4) 0s Now l e t : <P, be the d i r e c t temperature l o s s i n p e r i o d 1 ($3 be the d i r e c t temperature l o s s i n p e r i o d 2 (5) 16) Then because i t i s t rue that Now by Equa t ion (3) <?,' = -co 77 (7) Then by. Equa t ion (6) the d i r e c t temperature l o s s i n p e r i o d ( l ) i s g i v e n b y v •<?.'- - . . ( 8 ) 14 Then the t o t a l l o s s of temperature i n the p e r i o d i s g i v e n by and t h i s express ion i s the c o o l i n g c o r r e c t i o n d e s i r e d , and t n i s c o r r e c t i o n i s added to the observed r i s e i n temperature . The r e s u l t i s ^"fr which may be s u b s t i t u t e d i n the exp re s s ion wnich was the formula used to f i n d the s p e c i f i c neat i n the a d i a b a t i c d i s c u s s i o n . To make Equa t ion (9) more convenient to use, some r e - arrangements should be made. R e p l a c i n g - ^ L by ~ * ~ ~ —J or / y- ~ ^ a , Equa t ion (9) becomes T = Q + <*>> ~ ~^~CO^) +cu T, In t h i s research the time i n t e r v a l s 7J and 77 were made of the same l e n g t h so that the f o u r t h term of Equa t ion (10) v a n i s h e s . The areas and <&3 were d e t e m i n d e d from tne graph by a p o l a r p l a n i m e t e r . F o r reasons to be g iven l a t e r ca was taken as z e r o . Hence the s i m p l i f i e d equat ion used i n t h i s research to determine the temperature c o o l i n g c o r r e c t i o n was 77 = ^ -6̂  <2>, ~ - 6L) ••• (ii) 4. APPARATUS. (a) The C a l o r i m e t e r The c a l o r i m e t e r i s s i m i l a r to thavt of W i l l i a m s and D a n i e l s (1) and I s the same one used here by p r e v i o u s workers . " i t i s ve ry adequately dexc r ibed and i l l u s t r a t e d (j-) W i l l i a m s J . F . and D a n i e l s F . , op. c i t . pp . 303/317. 15 „ by D.E . M c L e l l a n i n h i s M . A . S c . T h e s i s . (2) S e v e r a l m o d i f i - c a t i o n s tha t have been made ont the c a l o r i m e t e r A t h i s work was p u b l i s h e d , are l i s t e d below. M i s s M . Robinson i n 1945 added a l e a d weight to the bottom of the cup c o n t a i n e r to reduce, i t s boyancy i n the g l y c e r i n bath and thus p r e v e n t i n g excess pressure on the cup s t i r r e r . She added 5# water to the g l y c e r i n bath to reduce i t s h i g h v i s c o s i t y around 25° C, and i n s e r t e d two t h r e e - b laded p r o p e l l o r s to s t i r t h i s b a t h . She a l so i n s e r t e d a v a r i a b l e t ransformer o'f the type 100-Q to manual ly c o n t r o l the e l e c t r o l y t i c A . C . h e a t i n g of g l y c e r i n b a t h . In t h i s research a 500 v o l t k n i f e hea te r was added f o r r a p i d h e a t i n g of the g l y c e r i n ba th . One of the 3 b laded s t i r r e r s i n con junc t ion w i t h the e l e c t r o l y t i c h e a t i n g kept the bath temperature constant throughout . The maximum d e v i a t i o n between the temperatures of the bath was found by a p l a t i num r e s i s t a n c e thermometer to be 0 . 0 1 ° c . (b) Apparatus f o r Measur ing Temperatures and Energy Inpu t . 11} The temperature of the g l y c e r i n bath was measured by a p l a t inum r e s i s t a n c e thermometer and a M u l l e r B r i d g e . (2) The temperature d i f f e r e n c e between the cup and the bath were measured by a r i v e j u n c t i o n thermopi le made from Leeds and Kor thrup i n s u l a t e d coppe r -cons t an t in thermocouple w i r e . The reason why the new thermopi le was used i s g iven (2.) D . E . M c L e l l a n , o p . c i t . 1 6 . under the s e c t i o n on " C a l i b r a t i o n of Equipment ." (3) In order to get consecu t ive measurements, p f the E . M . P . produced by the thermopi le and the power input to the cup hea t e r , on a U n i v e r s a l Type K Po ten t iome te r , the w i r i n g system was rearranged and i s shown i n the f o l l o w i n g diagram The E . M . P . o f the thermopi le was read by a d j u s t i n g the potent iometer to g i v e zero d e f l e c t i o n on a galvanometer . The e l e c t r i c a l energy to the cup hea te r was taken from a 120 ampere hour storage b a t t e r y , and was c o n t r o l l e d by a r e s i s t a n c e box. The dummy r e s i s t a n c e , whose r e s i s t a n c e was n e a r l y the same as the heater c i r c u i t , was used to d i s - charge the i n i t i a l h i g h vo l t age of the ba t t e ry before s t a r t i n g an experiment. The vo l t age drop across the hea te r was measured on the po ten t iometer , the vo l t age f i r s t be ing reduced to a measurable q u a n t i t y through a v o l t box. The cu r ren t was determined by measuring the vo l t age drop across a s tandard ohm. In both cases the vo l t age was read from the poten t iometer when galvanometer gave a zero d e f l e c t i o n . 17 F i g u r e 7. Diagram f o r Measur ing Power Input to the Cup Heater and Thermopile Reading <3ox Otimm y /Scorer \So/V Sox / Ohrn S+andord: • 6 • VO/T — So/Very Therm OyO*'/e Go/lsorrosTre*/**- 6 6 Galx/orrorrie+vr- ? - \Zott 3oh*ery Cc/o r/eoY/ryg Coii •o Type K -O -o AT 1/orSabfe 6 6 S-/orwdorc/ Ce// 13 19 5. MATERIALS USED (a) C i s D e c a l i n . C i s d e c a l i n was separated from a mix tu re of the c i s and t r ans isomers by r e c t i f y i n g the mix ture at 9 mm. abso lu te pressure i n a Steaman Column ( l ) . The pures t f r a c t i o n o f the c i s isomer so produced had a p u r i t y from 9 9 . 5 - 9 9 . 8 $ . T h i s f r a c t i o n of the c i s d e c a l i n was f u r t h e r p u r i f i e d by s eve ra l c r y s t a l l i z a t i o n s i n a dry i c e ba th , f o l l o w i n g the method used by Seyer and Walker ( 2 ) . The f i n a l product had a constant f r e e z i n g p o i n t of 4 3 . 1 3 ° C, as measured by a P l a t i n u m r e s i s t a n c e thermometer. The r e f r a c t i v e index measured on .a P u l f r i c h t Refractometer was /.*?&/'<s (b) Benzene & Toluene M e r c . " t h i o p i n e freeS" benzene and to luene were used to de termine . the water equ iva l en t o f the c a l o r i m e t e r . 6. CALIBRATION OF THE APPARATUS (a) The Thermopi le . ( l ) Requi red Accuracy . The temperature o f the bath c o u l d be read to 0 . 0 1 ° C on the p l a t inum r e s i s t a n c e thermometer used i n con- j u n c t i o n w i t h a M u l l e r B r i d g e and cou ld be es t imated to 0 .001°C by the c a l i b r a t i o n of a galvonometer s c a l e . The power inpu t to the cup cou ld be measured by the type K poten t iometer to f i v e s i g n i f i c a n t f i g u r e s . Hence i t f o l l o w s , to c a r r y t h i s (1) Ang ley , P o t k i n s and Rush, B . A . S c . T h e s i s , 1942. ——— (2) Seyer and Walker 3 . A . C . S . 6 0 2125, (1938) . 20 f i v e f i g u r e accuracy throughout , the thermopi le must he c a l i b r a t e d 'to g ive f i v e f i g u r e accuracy . (2J Method of Thermopile c a l i b r a t i o n The thermopi le was c a l i b r a t e d u s ing the apparatus shown i n the f o l l o w i n g diagram. F i g u r e 9 \ 21 1. C y l i n d r i c a l copper con t a ine r lagged with, c o t t o n . 2 . Glycer ine .^ "bath 3 . Dewar f l a s k c o n t a i n i n g t r ans d e c a l i n 4 & 8 P l a t i n u m r e s i s t a n c e thermometers connected to M u l l e r B r idges w i t h galvonometers and s c a l e . 5 . Thermopile w i t h l eads going to type K po ten t iomete r . 6. Nicrome r e s i s t a n c e heater f o r hea t ing the Dewar f l a s k . 7. S t i r r e r f o r Dewar f l a s k . 9 . 500 V o l t k n i f e hea te r 1 0 . S t i r r e r f o r ou te r b a t h . 1 1 . Leads to A . C . source to supply e l e c t r o l y t i c heat to the ba th . 1 2 . Copper p l a t e , of same surface area as the c a l o r i m e t e r cup, to ac t as an e l e c t r o d e f o r the e l e c t r o l y t i c h e a t i n g . I n the c a l i b r a t i o n of the the rmopi l e , the g l y c e r i n e ba th was heated to a few degrees above the t r ans d e c a l i n ba th , the temperatures of both baths were evened out , and simultaneous readings of the temperatures of the ou te r and i n n e r ba ths , and the E . M . F . produced by the thermopi le were t aken . The f o l l o w i n g t a b l e was made from the r e s u l t s obta ined by the thermopi le used by M i s s Robinson ( l ) 1.1) M . Robinson, op. c i t . , 1945. 2 2 . TABLE #1 Reading Temp. Temp, o f D i f f e r e n c e Mean Vo l t age VoUfcajg®; No. of batn Dewar i n Temp. Temp Generated Degree 0 j T l a s K °c °c °c °c ^ * • ̂ 7 ° c 1. 26.909 22.997 3.312 24.953 751.3 192.0 2 . 31.563 27.968 3.595 29.766 723.3 201,2 3. 37.860 34.220 3.640 36.040 819.3 225.1 4 . 43.061 39.418 3.643 41.240 838.5 230.2 5. 5-5.374 52.368 3.606 54.171 926.7 257.0 6. 48.552 45.713 2.839 47.132 724.7. 255.3 7 . 52.800 45.542 3.258 51.171 844.5 259.2 8. 80.705 76.570 4.135 78.638 1215.5 294.0 9. •• 69.195 65.659 3.536 67.427 1003.2 283.7 10 . 62.705 58.651 4.054 60.678 1077.0 265.7 1 1 . 31.238 28.905 2.333 30.072 515.4 220.9 12 . 26.403 22.306 4.097 24.354 703.5 171.7 13 . 26.526 21.633 4.893 24.080 854.1 174.6 14 . • 32.159 28.130 4.029 30.144 798.7 198.2 15. 39.144 35.316 3.828 37.230 892.4 233.1 16 . 45.411 41.051 4.360 43.231 1043.9 230 . 4 17 . 51.953 47.569 4.334 49.711, 1104.9 252.0 18, 57,214 53.085 4.129 55.150 1091.2 264.3 19 . . 34.531 33.471 1.108 34.0 27 ai 322.0 290.6 2 0 . 35.872 33.528 2 .344 34.700 5 7 3 . 5 ^ : 244.7 2 1 . 37.150 33.588 3.572 35.374 815.3 228.2 2'2. ,. 39.300 33.698 5.602 36.499 1230.3 219.6 23 . 24. 2 5 . 39.250 39.240 39.240 38.361 38.861 38.771 0.289 0.379 0.469 39.106 39.051 - 39.006 179.6 220.5 247.3 621.4 581.8 527.3 23 From tne da ta g iven i n . t a b l e (1) i t appeared tha t the thermopi le behaved very i r r e g u l a r l y , but seemed to suggest the magnitude of the temperature d i f f e r e n c e between' the l e g s of the thermopi le had a great e f f ec t on the vo l t age gen- erated. . Th i s e f f e c t Was shown bo be t rue by decreas ing the temperature d i f f e r e n c e between the l egs of the thermopi le and i s i l l u s t r a t e d i n the t a b l e , and graph below.. TABLE 2 Reading Temp of Temp of D i f f . i n Mean V o l t V o l t / No Bath Dewar Cup Temp. Temp Generated Degree i n °C i n °C. i n °C iri°C ^ « 7 ° C 1. 39.023 27.702 11.327 33.366 2072 182.9 2 . 39.144 34 ..485 4.659 36.814 974 209.1 3 . 39.. 204 35.548 3.656 37.376 909 248.6 4 . 39.224 36.516 2.708 37.870 763 2 8 U 8 5. 39.254 37.388 1.866 38.321 648 347.3 6 . 39.294 37.997 1.297 38.645 576 444.1 7 . 39.314 38.680 0.634 '38.997 468 738.2 F i g u r e 10 The V a r i a t i o n of E . M . F . per °c w i t h the temperature d i f f e r e n c e between the thermopi le l eg s of the Copper-Copel Thermopile^ . 24 Boo 600 •foo £00 T h i s thermopi le would g ive very e r r a t i c r e s u l t s i n the temperature range of 0 . 1 ° C between the cup and bath temperatures and hence was d i s c a r d e d . A new f i v e j u n c t i o n coppe r -cons t an t in thermopi le was made up from i n s u l a t e d Leeds and Northrup thermocouple w i r e . The thermopi le was t e s t e d s i m i l a r l y to the one desc r ibed above, and the r e s u l t s proved as e r r a t i c . The f o l l o w i n g t ab l e " and graph i l l u s t r a t e t h i s . TABLE 3 Reading Temp, of Temp, of No. Bath Dewar Cup i n \ i n b C . D i f f . i n Mean V o l t . V o l t . Temp. Temp. Generated p e r n i n i n S C . ^cV Deg. °C 1 39.232 24.973 14.259 32.102 2621.6 183.86 2 39.295 30.112 9.183 34.686 1869.4 203.57 3 39.335 34.018 5.317 36.677 1172.3 220.48 4 39.355 35.795 3.560 37.575 845.0 237.36 5 39.355 38.037 1.398 38.696 422.3 302.07 6 39.335 38.990 0.395 39.138 238.3 603.29 25 F i g u r e 11 v a r i a t i o n of E . M . F . per Degree w i t h Temperature D i f f e r e n c e between Legs of Copper -Cons tan t in Thermopi le , 800 /Wt'crovofts 600 4oo '£00 o O £ . 4 - 6 8 /O /£ /•+ Temp. O/fSerena? Be+vee" Legs of Trier-mopi/e /rr ° C- I t was decided t ha t the l a g i n the heat t r a n s f e r through the g l a s s bu lb and s t a n i l a x i n the bulb surrounding the thermopi le l e g caused an i n f i n i t e t ime to be r e q u i r e d f o r the thermopi le to a c q u i r e . t h e cup* temperature. To e l i m i n a t e t h i s i age the g l a s s bu lb was removed from around the thermopi le and d i r e c t contac t between the bath l i q u i d and the thermopi le r e s u l t e d . The thermopi le wi res were spaced and separated from each other by f i n e g l a s s tubes as shown i n F i g u r e 11. As the g l y c e r i n e bath temperature remained very nearby con- s t an t throughout a run the l a g would not a f f e c t the the rmopi le leg i n i t . The g l a s s bu lb was l e f t on t h i s l e g o therwise the e l e c t r o l y t i c bath would i n f l u e n c e the thermopi le r ead ings . 26 Jj'igure 12 C o h s t r u c t i o h of Copper C o n s t a n t i n Thermopile to Reduce Hea t ing Lags eetc^r wire. ~7n ,e/-mo/*'/'e mode o-f ? JZ/rrc+'arrs-, if 7* /n series Leg *rr C<y/» ijgg &a+/r The thermopi le c a l i b r a t i o n was checked w i t h those g i v e n f o r Copper -Cons tan t in i n Leeds and Northrup Thermocouple t a b l e s P . 4 1 . Wi th one l e g o f the thermopi le i n crushed i c e made from d i s t i l l e d water and the o ther i n d i s t i l l e d water the f o l l o w i n g readings were made. TABLE 4 . E . M . F . Produced by Thermopile Water Temp, i n °C 4245.7 4224.8 4088.8 21.30 21.00 20.60 200 200.5 198.6 These r e s u l t s cneck w i t h the va lue of 200^*"/° C found i n the t ab l e f o r a f i v e j u n c t i o n coppe r - cons t an t in thermopi le and t h i s c a l i b r a t i o n was taken as c o r r e c t . 27 (b) Water E q u i v a l e n t of C a l o r i m e t e r . E i g h t i so the rma l runs were made w i t h " M e r c . " to luene "to determine the water equ iva l en t of the c a l o r i m e t e r . The procedure was the same as tha t d e s c r i b e d l a t e r to determine the s p e c i f i c heat of c i s d e c a l i n and a Leeds and Northrup Po ten t iomete r #553553 was used to measure the E . M . F . produced • by the thermocouple. A sample c a l c u l a t i o n i s g i v e n below. Water E q u i v a l e n t Run #4. Average bath temperature Res i s t ance of the l eads Mean temperature of the cup 2 1 . 2 0 ° C = 0.17902 ohms ( l ) S p e c i f i c heat of to luene at 21.76 T o t a l h e a t i n g time To determine the t o t a l heat input Or Vol tage drop through the h e a t A c i r c u i t _ (0.042605) (50) Current th rough ' the hea te r Vol tage drop across the l eads = (0.27076) (0.17902) Vo l t age drop across the s tandard ohm. = (0.27076) (1) Vo l t age drop across hea t e r = (2.13025 - 0.04847- 0.27076) Heat input per second ^=(1.81102) (0.27076) ( i ) I n t e r n a t i o n a l C r i t i c a l Tables P . 115 = 2 1 . 7 6 ° C = 1.671 J o u l e s / gm./°C = 685.5 seconds = 2.13025 V . =^0.27076 a . = 0.04847 V — 0.27076 V » 1.81102 V = 0.490352 Watte 28 T o t a l heat input H = (0.490352) (685.5) = 336.14 J o u l e s To determine the t o t a l temperature r i s e t9i and were taken from the graph & and <&3 were measured from the graph by a p o l a r p l a n i m e t e r . TI e 1.115 - 0.828 & (1.115 - 0.828) (599 - 925) * 0 .186°C 599 T o t a l temperature r i s e ' ^ 1.115 - 0 -h 0.186 = 1 . 3 0 1 ° C To determine the water equ iva len t where t o t a l temperature r i s e = 1 .301° 0 Ww= weight of to luene =^140.23 g S c s p e c i f i c heat of to luene = 1.671 .CP • = 336.14- (140.23) ( l . 6 7 l ) ( l . 3 0 l ) 1.301 = 24.04 j o u l e s j L ° C A summary of the water e q u i v a l e n t s o f the c a l o r i m e t e r i s g iven below i n Table 5 . 29 TABLE 5 Run No. Mean .Temp, of Toluene Water equ iva l en t of C a l o r i m e t e r i n J o u l e s / ° C 1 19.08 19.48 2 19.85 30.16 3 21.68 22.87 4 21.74 24.04 5 21.12 21.32 6 22.84 26.29 7 24.42 27.63 8 24.61 34.13 . A t an average temperature of 21 .92" C the average water equ iva len t i s 25.74 J o u l e s / ° C . T h i s mean r e s u l t was cons idered s a t i s f a c t o r y because any e r r o r s are magni f i ed by hav ing to sub t rac t two q u a n t i t i e s of tne order of 300 to get one of the order of 25. The inc rease of the water equ iva l en t pe r degree was found to be 0.1 j o u l e s f o r 10° C on the b a s i s of a water equ iva len t of 38 j o u l e s ^ 0 C at 30° C (1) The inc rease f o r t h i s c a l o r i m e t e r i B (_1^) ( o . i ) « 0.007 j o u l e s / ° C / ° C (c) The Heat of S t i r r i n g and E v a p o r a t i o n To determine the heat of s t i r r i n g and evapora t ion , cu » tb.e cup c o n t a i n i n g the c i s d e c a l i n was a l lowed to c o o l _whi ie being s t i r r e d w i th no heat s u p p l i e d . A graph as (1) D . E . M c L e l l a n , M . A . S c . T h e s i s , 1943. 30 shown i n f i g u r e 13 wais obta ined . F i g u r e 13 Then the d i r e c t l o s s of temperature i n time 77 i n t ime 7Z = <^> ~ ^ ~ But as shown before on page '3 The d i r e c t temperature l o s s i n 77 i s The d i r e c t temperature l o s s i n ^ i s °^ < ^ > ^ Thus D i r e c t l o s s i n 77 D i r e c t l o s s i n 71 Therefore ^ - &3 - coZ •= co7k) And can be so lved from t h i s equat ion as a l l o ther terms are known. As shown on page 3f f o r the graph of C i s D e c a l i n run #28 the r e s u l t s needed to c a l c u l a t e the heat of s t i r r i n g are as f o l l o w s • = 0.1996, #5 = 0.1520, ^ = r 0.1781 # = 1650, 0± = 746 / / = 17.7 min., ^ == 7.3 minutes 0.1996 - 0.1520 - < a y ( l 7 . 7 ) = 3 i 6 5 Q (0 .1996-0.1781 •746 -tfOc7.3) 31 and GO = 0.00003 ° C / m i n u t e . I n a s i m i l a r manner the heat of s t i r r i n g was found i n three o ther runs and the r e s u l t s are g iven i n Table 6. TABLE 6. C i s D e c a l i n S p e c i f i c Heat of S t i r r i n g Heat Run No, ° C / m i n u t e . 28 0.00003 . 29 0.0003 30 -0 .0007 32 -0.0005 The r e s u l t concluded i s tha t the heat o f s t i r r i n g and evapora t ion i s e i t h e r very smal l p o s i t i v e l y o r n e g a t i v e l y and w i l l , i n l a t e r c o n s i d e r a t i o n s , be taken as ze ro . 7. PROCEDURE FOR DETERMINING THE SPECIFIC HEAT 0? CIS DECALIN Runs 1 - 1 8 i n c l u s i v e were made by adding s u f f i c i e n t heat to r a i s e the temperature o f . t h e c i s d e c a l i n i n the cup by about 1 . 5 ° c . Runs 18 - 36 i n c l u s i v e were made by adding enough heat to r a i s e the c i s d e c a l i n temperature from 0.1 to 0 . 2 ° c * T h e Purpose of the f i r s t 18 runs was to check the r e s u l t s w i t h those of p r ev ious i n v e s t i g a t o r s from 20 - 50° C, Thejj« a few runs were to be taken from 20 - 50° C u s i n g the sma l l e r temperature i n t e r v a l ; i f these r e s u l t s agreed w i t h those made i n the f i r s t runs , the method w o u l i be s a t i s f a c t o r y to explore around the anomoly i n the s p e c i f i c heat curve at '. - 5 0 - 5 0 . 5 ° C. Tne procedure used i n both cases was ve ry s i m i l a r . I n the f i r s t set of runs the g l y c e r i n e bath and the c i s deca l in* the cup were brought to some d e s i r e d temperature, both baths were s t i r r e d and temperatures main ta ined constant f o r approximate ly 15 minutes before s t a r t i n g a run . Then -a measured amount of power was added to the nicrome hea te r i n the c i s d e c a l i n f o r about, 900" seconds. Then the power was shut o f f and the cup was a l lowed to coo l f o r an equal l eng th of t i i e . The temperature of the g l y c e r i n e bath was read c o n t i n u o u s l y i n both p e r i o d s by the p l a t i num Res i s t ance Thermometer #317863, and the E . M . F . of the thermopi le by Leeds and Northrup Po ten t iomete r #634358. • In the second-set of runs the temperatures were main ta ined constant f o r about 1/3 - 1 hour before s t a r t i n g the run . The E . M . P . of the thermopi le was read bo* the Type K U n i v e r s a l Po ten t iome te r . A t y p i c a l set of r e s u l t s i s g iven i n t ab l e 7 f o r c i s d e c a l i n run #28 33 TABLE 7 Time Po ten t iomete r Temp. D i f f , Power-Input Bath i n Heading from B?.th V o l t , Cur ren t Temp. Seconds i n / / K to Cup V o l t s Amps, i n °C - . °C ' . 0 11,15 .0 .0558 34.531 127 14.4 0.072 155 34.528 192 16,5 0.0825 213 34.529 273 34.528 406 34.527 439 0.676475 478 34.528 561 0.085778 592 34.528 687 34.529 735 34.529 830 34.530 885 35.05 0.1752 913 36.5 0.1825 967 37.85 0.1892 986 34.529 1030 POWER OFF 1037 39.4 0.1970 1062 39.6 0.198 34.529 1097 39.45 0.1972 1144 39.4 0.196 34 Time Po ten t iomete r Temp. D i f f . Power-Input Bath i n Heading from Hath V o l t a g e Curren t Te»p i n seconds i n ^ ^ cup °C V o l t s Amps u u 1145 34.529 1227 -34.528 1256 37.85 0.1892 1388 36.45 0.1822 1425 34.530 1563 34.4 0.172 1662 34.530 1690 33.05 0.1652 1800 34.531 1869 34 o 530 1902 31,35 0.1568 1957 34.530 2020 30,5 0.1525 - 2049 34.523 2093 30.1 0.1505 2154 3 4.530 ?.196 0.1478 From t ab l e 7, f i g u r e 14 was drawn f o r c i s d e c a l i n run #28$ 8. SAMPLE CALCULATION of SPECIFIC HEAT of CIS DECALIN - f rom the data of Tab le 7 and f i g u r e 14.* (a) Determin ing Power Input . Vol tage drop across hea te r c i r c u i t = 0.676475 V 35 Turner /rr •StrcorfesCr 36 Cur ren t - th rough the hea te r c i r c u i t =• 0.085778 a Vol tage drop across l e a d s . ^ (0 .085778) (0*17988) =0 .015430 V Vol tage drop across s tandard ohm = 0.085778 Vol tage drop across hea te r = (0.676475 - 0.015430 - 0.085778) = 0 . 5 7 5 2 6 7 V Heat input per second = (0,575267) (0.085778) = 0.049346 Watts T o t a l heat input H = (0.049346) (1030) = 50.826 J o u l e s Determin ing the T o t a l Temperature R i s e . From f i g u r e 1#. ^ = 0.1996 ^ « 0.1520 0t = 1238 <&s = ' 1649 71 0.1996 - 0.1520 + (0.1996-0.1520) (1238-1649) 1649 " - 0.0357 °C T o t a l temperature r i s e — 0.1996 - 0.0596 + 0.0357 = 0.1757 °C . Determining the S p e c i f i c . Heat .of C i s D e c a l i n (coX^&/-y) = /-/ - (Water E q u i v a l e n t ) where CO = weight of c i s d e c a l i n = 146.64 g — t o t a l temperature r i s e =r 0.1757 °C = s p e c i f i c heat of d e c a l i n 3? / - / — heat input -= 50,826 J o u l e s Water E q u i v a l e n t = 25.83 J o u l e s = 1.7961 J o u l e s per gram, pe r degree. ' ; 9 . RESULTS o / s The s p e c i f i c heat of c i s d e c a l i n from 20-50 C §^3 g i v e n i n Table 8 f o r the runs 1-18 i n c l u s i v e . TABLE 8 Run No, Avg. Deca l i n T o t a l Temp S p e c i f i c Heat Temperature R i s e o f D e c a l i n i n °c i n C J o u l e s /gm/°C 1 21.52 1,4716 1.8135 2 27.03 1,5102 1.8021 3 32.66 1.6154 1.7992 4 37,58 1.5185 1.7430 5 25.08 1.6973 1.8191 6 43.67 1.5783 1.7731 7 48.82 1.5931 1.7970 8 28.42 1.5847 1.7999 9 35.64 1.6900 1.8123 10 23.80 1.7674 1.8148 11 30.17 1.3916 1.7902 12 36.78 1.2241 1.8131 1 ? t 4 8 40.79 1.3800 1.8090 39.72 1.2980 1.8321 15 40.51 1.3720 1.8306 16 43.36 1.3004 1.8218 38 Run No. Avg . D e c a l i n T o t a l Temp S p e c i f i c Heat Temperature R i s e o£ D e c a l i n i n °C i n c J o u l e s /gm/°c 17 46,50 1.2457 1.8457 18 48.68 1.2666 1.8565 The s p e c i f i c heat- temperature curve f o r c i s d e c a l i n between ,20°-50°C found by runs 1-18 i n c l u s i v e i s shown i n f i g u r e 1 5 . Fo r comparison, the r e s u l t s of Mead and M c L e l l a n are shown between the same temperature l i m i t s . The r e s u l t s ob ta ined f o r the s p e c i f i c heat of c i s d e c a l i n from runs 18-36 i n c l u s i v e are g iven i n t a b l e 9 . TABLE 9 Run No. Av.ge. D e c a l i n T o t a l Temp S p e c i f i c Heat Temperature of D e c a l i n of D e c a l i n i n °C i n °C i n J o u l e s / gm/°C 19 48,774 0.1502 1.5914 20 R e s u l t s d i s ca rded as b a t t e r y Connect ion l o o s e . 21 48.109 0.1628 1.8987 22 49.602 0.2052 1.9030 23 35.829 0.1928 1.7568 24 49.992 0.2071 1.8311 25 50.123 0.1761 1.6443 26 50.202 0.1825 1.7892 27 30.089 0.1969 1.7391 28 34.657 0,1757 1.7961 29 40.068 0.1871 1.6050 39 N O . S 3 6 , G R A P H P A P E R . S M I T H , D A V I D S O N ft W R I G H T , L T D . 40 Run. No, Avg. .Decalin Temperature i n °C T o t a l Temp of D e c a l i n i n C S p e c i f i c Heat of D e c a l i n i n J o u l e s /gm/°C 30 46.156 0.2350 1.6164 31 49.914 0.1352 1.6559 32 50,000 0.1388 1.6200 33 30.368 0.2253 1.8201 . 34 35.778 0.1543 1.7750 35 42.346 0.1510 1.7324 36 47.927 0.1649 1.5899 The r e s u l t s o f t a b l e 16 are p l o t t e d on s p e c i f i c heat temperature axes hut the p o i n t s are so d ive rgen t tha t a curve through them would b© meaning less . 10 . CONCLUSIONS F i g u r e 14 shows t ha t , i n runs 1-18 u s i n g about 1 . 5 ° C t o t a l temperature r i s e , the s p e c i f i c heat f o l l o w s a f a i r l y - w e l l def ined cu rve . The va lues o f the s p e c i f i c heat' o f c i s d e c a l i n , ' however, are c o n s i d e r a b l y h i g h e r than those found by e i t h e r Mead or M c L e l l a n . F i g u r e 15 shows tha t i n runs 19-36 u s i n g about 0 . 1 ° e t o t a l temperature r i s e the r e s u l t s are not r e p r o d u c i b l e . Hence an accura te graph i s the range of the anomoly of 5 0 . 0 - 5 0 . 5 ° c i s not f e a s i b l e by the method as o u t l i n e d i n t h i s t h e s i s . I t should be noted, however, tha t the readings taken from 5 0 - 5 0 , 5 ° do not i n d i c a t e any abnormally l a r g e change i n the s p e c i f i c heat 41 'J20 sac/ SJ/SXD/^- IS/ fOSW. Z>*f'X!c/g 42 and thus do no t , even q u a l i t a t i v e l y , g ive any evidence of an anomolous s p e c i f i c hea t . I t can be concluded that the i so the rma l method i s s a t i s - f a c t o r y f o r f i n d i n g the s p e c i f i c heat of >a l i q u i d i f a l a r g e t o t a l temperature r i s e i s used, that i s , something over one . degree cen t r ig rade i n the present appara tus . 1 1 . RECOMMENDATIONS ?CR FURTHER WORK o A l i q u i d whose s p e c i f i c heat i s w e l l de f ined from 0-150 C should be used i n the present apparatus to see i f the s p e c i f i c heat can be checked. T h i s method would d e f i n i t e l y show the l i m i t of accuracy o f the present appara tus . The temperature measurements and c o n t r o l should be im- proved . A p l a t i num r e s i s t a n c e thermometer wi thout quar tz cove r ing over the f i l amen t snould be used to measure the bath temperature. T h i s thermometer would e l i m i n a t e temperature l ag s from the bath to r e s i s t a n c e thermometer. The thermopi le should have both j u n c t i o n s exposed to the r e s p e c t i v e l i q u i d s to again a v o i d temperature l a g s . A great improvement i n the present apparatus would r e s u l t i f the thermopi le between the cup and the bath was e l i m i n a t e d . A p l a t i num r e s i s t a n c e thermometer wi thout quar tz c o v e r i n g should be i n s e r t e d i n the cup . Th i s arrangement c o u l d be used to measure the temperature of the cup l i q u i d and a l s o to add tne hea t ing power to the l i q u i d . T h i s p l a t i num r e s i s t a n c e thermometer would e l i m i n a t e the temperature l a g s exper ienced by the present themopi le , I t would a l so s i m p l i f y the apparatus i n the c a l o r i m e t e r cup as the nicrome hea t ing c o i l cou ld be e l i m i n a t e d . BIBLIOGRAPHY Angley , P o t k i n s , and Rush, B . A . S c . T h e s i s , 1942 B u r t o n , E . E . , Grayson Smi th , H . , W i l h e l m , J . O . , "Phenomena of the Temperature of L i q u i d Hel ium" R e i n h o l d . Davenporte, C . H . , "Dete rmina t ion of the P h y s i c a l P r o p e r t i e s of C i s and Trans Decahydronapthalene", M . A . S c . .Thesis 1939. Dav ies , G . i ? . , "The I n v e s t i g a t i o n of the S p e c i f i c Heat of . C i s Decahydronapthalene." , M . A . S c . T h e s i s , 1939. D u n e l l , H . A . , "A Method f o r Measuring the D i e l e c t r i c Constant of L i q u i d s " , M.A.SGV T h e s i s , 1946. Graham, H . M . , "The S p e c i f i c Heat of C i s Decahydronapthalene", M . A . S c . T h e s i s , 1944. I n t e r n a t i o n a l C r i t i c a l Tab le s , V o l . 5, McGraw H i l l Book C o . , New York 1929. L e s l i e , J . D . , "Some S t u d i e s i n L i q u i d V i s c o s i t y w i t h S p e c i a l Reference to the Isomers of Decahydronapthalene", M . A . S c . T h e s i s , 1941. Mann, C .W. , "La ten t Heats of C i s and Trans Decahydronapthalen M . A . S c . T h e s i s , 1944. M c L e l l a n , D . E . , " S p e c i f i c Heat and He at of T r a n s i t i o n of C i s Decahydronapthalene", M . A . S c . T h e s i s , 1943. Robinson, M . , "The Second Order Phase T r a n s i t i o n of C i s Decahydronapthalene"; M . A . T h e s i s , 1945. Seyer , W.F . , and Walker; J . A . C . S . , 60, 1938, pp 2125. Standard Convers ion Tables f o r Leeds and Northrup Thermocouples, P P . 41 Whi te , W . P . , MSome C a l o r i m e t e r i c Methods"; The P h y s i c a l Review, v o l 31, pp 545-548, 1910. W i l l i a m s , J . W . , and D a n i e l s Jb1., "The S p e c i f i c Heats of C e r t a i n Organic L i q u i d s at E l e v a t e d Temperatures"; J . A . C . S . , Vo l 46, pps 903-917, 1924. •

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