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Heat capacity of cis and trans decahydronaphthalene Mead, Bruce Ronald 1940

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I HEAT CAPACITY OF CIS AND TRANS DEC AHYDRONAPHTHALENE By: Bruce Ronald Mead, 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 of MASTER OF APPLIED SCIENCE i n the Department of CHEMICAL ENGINEERING APRIL, 1940 TABLE OF CONTENTS Preface lag© Adiabatic and non-adiabatic methods 1 Design of Calorimeter 2 A i r gap . 3 Lag errors 3 Diagram • 4 Construction 5 Heater . . . 5 Sleeve • 6 Cup and S t i r r i n g • • • 7-8 The Calorimeter .....<*.... 7 S t i r r i n g Heat , 8 Thermopile • 8 E l i m i n a t i o n 9 Adiabatic Control 10 E l e c t r i c a l Measurement 11 Procedure and operation 12 Ca l c u l a t i o n s 13 Check Method 14 Water Equivalent 14 The General Assembly 14 Graphs .... 15 Conclusions 16 Method f o r Heat of T r a n s i t i o n . 16 Bibliography PREFACE For several years i n these l a b o r a t o r i e s work has been c a r r i e d out on the p h y s i c a l p r o p e r t i e s of isomers of decahydronaphthalene. A method has been developed f o r pre-paring the c i s and trans isomers of very high p u r i t y i n quantity. The purpose of t h i s i n v e s t i g a t i o n i s to determine the heat capacity i n the temperature regions i n which known changes take place i n other p h y s i c a l p r o p e r t i e s . Accordingly, u s i n g the experience gained from s i m i l a r measurements by G-.F. Davies here i n 1938-39? i t was thought advisable to con-s t r u c t a new a d i a b a t i c c a l o r i m e t e r . I t i s with pleasure that acknowledgment i s made f o r the h e l p f u l suggestions and assistance of Dr. W.F. Seyer, under whose d i r e c t i o n the present i n v e s t i g a t i o n was c a r r i e d out. 00O00 HEAT CAPACITY OF CIS AMD TRAMS DECAHYDRONAPHTHALENE GENERAL : Adiabatic and Non-Adiabatic Methods-The ad i a b a t i c method of calorimetry i s p a r t i c u l a r l y u s e f u l here since i t i s the change of heat capacity with temperature that i s des i r e d . A non-adiabatic method would not f u r n i s h the desired accuracy. To determine heat capacity at a d e f i n i t e temperature, the terminal temperatures must be close and even small errors i n the thermal head, because of di f f e r e n c e s i n r a t e of heat l o s s between the l i q u i d used f o r c a l i b r a t i o n and the d e c a l i n , would be an appreciable part of the whole. Even i f these errors were n e g l i g i b l e , convection and evaporation err o r s are not; or i f the time (T) were short enough to eliminate the lags i n a t t a i n i n g •'•temperature e q u i l i b r i u m , more than moderate accuracy i s unattainable i n determining terminal temperatures. Further, a great deal of time would be required f o r a number of experiments. An almost equal number of c a l i -b r a t i o n experiments would be required since the X-period c h a r a c t e r i s t i c s change with the temperature-time p a t t e r n . With the a d i a b a t i c method, one sample over the whole temperature range s u f f i c e s since the terminal temperature of one temperature range i s the i n i t i a l temperature of the second temperature range. Further, a method of c a l c u l a t i o n given l a t e r enables heat capacity to be c a l c u l a t e d at mean temperatures d i f f e r i n g by f r a c t i o n s of a degree. 2 I f cp - thermal head V = r a t e of temperature change i n calorimeter K = thermal leakage constant Then V - K<^ , or i f ^ z temperature l o s s °l = VT = cp KT Here <f i s diminished. The error i n measuring <$> i s u s u a l l y l e s s than the e r r o r i n a d j u s t i n g jacket temperatures. The small values of £ p however, lessen the errors from inconstancies i n K, which are f a r more serious, e s p e c i a l l y those due to evaporation and convection. These inconstancies may be considered as v a r i a t i o n s i n l a g which give r i s e to absolute e r r o r s . Where p o s s i b l e , lags are made constant. This d i s p l a c e s the value by the amount occ u r r i n g during the l a g (usually n e g l i g i b l e ) but w i l l not introduce an absolute e r r o r . The a d i a b a t i c method makes p o s s i b l e a c o n s t r u c t i o n which diminishes thermal leakiness (K), notably i n convection and evaporation e f f e c t s , and with that, e r r o r s from v a r i a t i o n i n l a g s . Hence i t i s generally regarded as the best method f o r the type of pr o t r a c t e d experiments necessary here, DESIGN: The design of the calorimeter was s t a r t e d with c o n s i d e r a t i o n of the thermal leakage constant K.. The most p r a c t i c a l values to which e r r o r s should be reduced was taken as that required f o r an o v e r a l l probable e r r o r of 1 per raille. Each i n d i v i d u a l e r r o r should, as a working r u l e , be reduced to about one tenth of t h i s value. This was r e a l i z e d to be too 3 small f o r evaporation e r r o r s i n t h i s p a r t i c u l a r series of experiments, but e l i m i n a t i o n of other errors was desired to be c e r t a i n to help i n f i n d i n g remaining sources of e r r o r . F u l l advantage was taken of a reduction i n the convection and con-duction f a c t o r s i n K by use of a wide a i r gap of 20 mms. This was planned to make p r o v i s i o n f o r departures from ad i a b a t i c c o n t r o l necessary to increase the accuracy of determining t e r m i n a l temperatures by stepwise operation of the. bath, and to make p r o v i s i o n f o r slow rate of temperature r i s e to f u r t h e r m i t i g a t e against the l a g i n the e l e c t r i c thermometer. AIR GAP; *From tables i n White ( 5 }, i t i s shown that.the airgap may s a f e l y be 24 mm. with the a d i a b a t i c method lessening, convection. This reduces K to about 0 . 0 0 1 2 . In any case, an a i r t i g h t sleeve was to be used to lessen the large, vapouriza-t i o n l o s s and so a gap of 20 mms. was decided. The sleeve increases K by approximately 1/3 when using a f i b r e r i n g around the cup and t h i s r a i s e s K to approximately 0 . 0 0 1 6 . This value of K and a 5° head i s s u f f i c i e n t f o r 1 per m i l l e accuracy and the head, i n stepwise a d i a b a t i c operation, i s of the order of l / 5°C. Thus by usi n g a wide airgap to counteract the e f f e c t of the sleeve, the large e r r o r due to vap o u r i z a t i o n may be r e -duced to l i m i t s of allowable e r r o r , under favourable c o n d i t i o n s . LAG ERRORS I There i s a change i n c e r t a i n lags because of changes i n visffiosity at 50°C and at 110°C, with r e s u l t a n t e f f e c t s on temperature e q u i l i b r i u m and on s t i r r i n g heat. E r r o r s because of such changes i n l a g are inherent i n t h i s method. They are n e g l i g i b l e unless the v a r i a b i l i t y i s greater than about 30%, which i s u n l i k e l y f o r the observed changes i n v i s c o s i t y . For adiabatic operation, l a g determines the length of time f o r which c o n t r o l i s not as good as the accuracy of the thermometer. The. thermal head thus allowed to be set up and the length of i t s duration j o i n t l y determine the s i z e of e r r o r f o r the value of K of the calorimeter. Considered i n d i v i d u a l l y , and f o r stepwise operation, n e g l i g i b l e errors r e s u l t from e f f e c t s of s o l i d conduction i n wires and sleeve using c o n d u c t i v i t y c o e f f i c i e n t s and data on wires ( lfe3), a i r convection, a i r con-duction, d i f f u s i o n due to concentration gradient set up by changes i n s a t u r a t i o n value, and from r a d i a t i o n . CONSTRUCTION I > The c o n s t r u c t i o n was, i n general, s i m i l a r to the calorimeter of Richards & Daniels & Davies, and the f o l l o w i n g a l t e r a t i o n s were necessary to improve the accuracy when opera-t i n g up to 150°C. The r e s u l t s of the numerous changes t r i e d are described i n d e t a i l . The weight ofthe calorimeter was reduced as much as p o s s i b l e throughout the c o n s t r u c t i o n . This was done to increase the s e n s i t i v i t y i n temperature d i s t r i b u t i o n and to reduce the time of l a g i n maintaining a d i a b a t i c c o n d i t i o n s . The e r r o r s caused by v a r i a t i o n i n lag,caused by v a r i a t i o n of water eo xuivalent with change i n s p e c i f i c heats of the materials of the calorimeter, were reduced by t h i s means. HEATERs The heater was constructed of drawn t h i n walled glass tubing,to eliminate d i f f i c u l t i e s encountered using mica, and of nichrome wire. The wire s i z e was as large as p o s s i b l e f o r the r e s i s t a n c e necessary (15 ) to give greater surface i n both diameter and length. However, there must be a temperature gradient between wire and l i q u i d s u f f i c i e n t to give a f a i r heating r a t e on 6 v o l t s . Tentative c a l c u l a t i o n s i n d i c a t e d #26 nichrome wire to be s u i t a b l e . The l e a d - i n wires were f i r s t put i n a glass fork of such a shape , | ^ < ^ running through the bath f o r about 20 cms. to eliminate the temperature gradient and conduction errors along the wires. Connection was through mercury w e l l s to platinum wires sealed i n the t i p s , which were soldered to the ends of the heater wire. This method was abandoned because of d i f f i c u l t y i n preventing leaks and the f a c t that breakage would change the calorimeter c h a r a c t e r i s t i c s , Insulated wires were brought i n through a copper pipe and a ground glass j o i n t made to the pipe with the contacts as before. This was to prevent any contamination of the d e c a l i n with rubber i n s u l a t i o n m a t e r i a l . .SLEEVE; The sleeve was made l a r g e r than the cup and f i t t e d i n t o the l i d with a tapered brass-to-brass s l i p f i t . The bottom of the sleeve was covered w i t h a wide washer cut from sheet dental dam rubber. The cup was then pushed up and p u l l e d down forming a t i g h t j o i n t of t h i s nature This method was abandoned f o r runs over 90° using d e c a l i n , because of p o r o c i t y and s w e l l i n g , but was s a t i s f a c t o r y i n runs using benzene and toluene up to 70°. This made necessary a new determination of the water equivalent. A machine f i t was put on a f i b r e r i n g and dr i v e n on to the cup with a hammer. The groove i s covered w i t h a narrow 3 mm. sheet rubber washer and the sleeve forced i n t o i t t i g h t l y . This remedied the tro u b l e w i t h the sleeve and made i t t i g h t . * waole suspension 7 i s held up to the l i d by a spring stand covered with a small asbestos top. An a i r cap necessary to prevent free convection and a vent pipe necessary to release pressure were i n s t a l l e d as shown. CUP AND STIRRING-: The cup was made as l i g h t as possible and with a spun bottom to eliminate dead spaces. The s t i r r i n g was accom-p l i s h e d with two sharp-edged, w e l l shaped, moderately pitched p r o p e l l e r s , since i t was i m p r a c t i c a l to i n s t a l the s t i r r i n g tube required for best r e s u l t s . The apparatus i n the cup pre-vented a s w i r l i n g around of the l i q u i d to a large extent and, with the moderate p i t c h on the p r o p e l l o r s , provided good s t i r r i n g . The shaft was held between asbestos jaws i n a chuck reducing any heat c o n d u c t i v i t y i n case a temperature gradient were set up. In determining the r a t e of s t i r r i n g , c a l c u l a t i o n s show that the heat of s t i r r i n g i s of secondary importance and the temperature e q u a l i z a t i o n throughout the l i q u i d of f i r s t importance. • I. ; • ' The Calorimeter• STIRRING- HEAT; 3 Accordingly, f o r running slowly the heat recommendation of White was followed: that the s t i r r i n g heat he not over 0 . 0 0 1 0 per minute f o r very constant s t i r r i n g , or 0 .0001G per minute to he n e g l i g i b l e altogether. A high speed synchronous motor, geared down to 150 r.p.m., was used. With i t the very constant heating rate was 0 . 0 0 0 5 0 per minute. On t h i s b a s i s , the motor gave about the maximum permissible amount of s t i r r i n g . Thermopile The thermel was constructed on a frame of #36 B & S copper wire and #30 B & S constantan wire. Five couples were used to each thermopile. The ends of the wires were bared of i n s u l a t i o n , c a r e f u l l y cleaned, and at each j u n c t i o n twisted together four times. As f a r as p o s s i b l e each j u n c t i o n was made the same. Since the zinc c h l o r i d e i n usual fluxes forms i n t e r -mediate compounds and p o s s i b l y impairs the accuracy, powdered r o s i n was dusted on to each j o i n t . The ends were then dipped r a p i d l y i n t o a puddle of molten solder and so covered with a t h i n l a y e r . To the eye these j o i n t s appeared i d e n t i c a l . They were then dipped into rubber d i s s o l v e d i n a mixture of carbon d i s u l p h i d e and benzene and d r i e d i n an oven overnight at 100° to replace the i n s u l a t i o n . The two thermels were then enclosed i n glass j ^ j tubes by p u t t i n g a glass bump on the i n s i d e bottom of the L 7 and using the n a t u r a l spring of the wires to get them around the corners. The ends of the tubes were drawn down and blown out u n t i l the glass was as t h i n as p r a c t i c a b l e . The leads were taken o f f through the glass tube passing through the bath and prevented from breakage at the top by passing them through a' s p l i t cork pushed i n t o the end of the tubes. About 0- . 5 g . of l i g h t o i l were placed i n each l e g around the junctions to give a quicker response.' The two thermels were balanced against each other f o r temperature i n t e r v a l s of GC—~ room temperature and room temperature -~100C. In each case the .deflection on the galvanometer scale showed d e f l e c t i o n s of 1- 2 m i l l i m e t e r s at 1 metre distance, i n d i c a t i n g about 0.8 microvolts set up. For these thermels the p o t e n t i a l set up i s 5 x 40 « 200 /" per degree ( 19 ) and t h i s corresponds to a temperature d i f f e r e n c e of .005°C. This temperature d i f f e r e n c e might w e l l have been due to i r r e g u l a r i t i e s of temperature d i s t r i b u t i o n i n the baths and the thermels were considered exact. E l i m i n a t i o n of Leaks Considerable d i f f i c u l t y was experienced with le a k s . Various types of packing were t r i e d , and those described below r e s u l t e d i n a p e r f e c t l y t i g h t l i d . The copper tube box f o r the l e a d - i n wires was made p e r f e c t l y t i g h t with the standard gasoline pipe brass c o l l a r . Boxes that were not used were sealed w i t h two c a r e f u l l y f i l e d s o f t t i n metal d i s k s and screwed down. The heater stand box was treated i n the same way, the t i n washers covering the f l a r e d end of 1" of copper pipe to which was joined the glass heater stand as shown i n the drawing. A t i n washer was c a r e f u l l y f i l e d f o r the thermel with a feather-edged hole s l i g h t l y smaller than the g l a s s . The glass was pushed through and the j o i n t packed below the washer with asbestos cord. The whole was screwed down t i g h t l y . The 10 t h i n shoulder on the l i d and large diameter r e s u l t e d i n the rubber washer being squashed out of the space. To make the l i d t i g h t the threads were l u b r i c a t e d with white lead so as to turn r e a d i l y and the l i d screwed down to w i t h i n 1 mm or. so of the shoulder. Tight e l a s t i c bands were sprung i n t o the gap and a f i n a l t w i s t made the j o i n t t i g h t . A d i a batic Control The a d i a b a t i c c o n t r o l was improved i n several ways. The bath d i d not pass enough current to maintain good c o n t r o l over 80° and a t o t a l of 45 g. of ferrous c h l o r i d e were required. The c o i l heater around, the bath was used to o f f s e t losses to the atmosphere. A powerful a i r - c o o l e d three-speed s t i r r i n g motor was used i n top speed f o r d r i v i n g a shaft with three, tfaree-bladed, properly shaped ( 3 ) p r o p e l l o r s . Since quicker temperature changes r e s u l t from vigorous s t i r r i n g i n short wide paths of a small quantity of g l y c e r i n e , the quantity was kept the same. A p a r t i t i o n was put i n the bath separating i t at about l / 4 of the diameter i n t o two compartments so that a l l p a r t s of the bath were covered by one current. Cotton i n s u l a -t i o n was placed i n the outer can to a i d i n maintaining higher temperatures. With t h i s arrangement, a d i a b a t i c c o n t r o l could be maintained' below about 45°C to w i t h i n .Q3°C correspond-i n g to 1 .5 cms on the thermel s c a l e . Above 50° the a d i a b a t i c c o n t r o l could be maintained to w i t h i n 0.; cms to 0 . 1 cms at higher temperatures, t h i s l a s t being the l i m i t of accuracy of the thermels and corresponding to 0 ,005°C. 11 E l e c t r i c a l Measurements The e l e c t r i c a l power f o r heating the cup was obtained from two 120 ampere-hour capacity lead storage b a t t e r i e s i n p a r a l l e l . In the l a t e r runs these b a t t e r i e s were steady i n voltage over a run to w i t h i n 0.0001 . The i n i t i a l high voltage of the b a t t e r i e s was allowed to drop to a constant value by discharging through a dummy re s i s t a n c e of 20 ohms fo r about one-half hour p r i o r to commencing readings. This voltage was adjusted by means of a length of nichrome wire which could be v a r i a b l y put i n s e r i e s by a s l i d i n g connection. A v o l t box and a nul type K U n i v e r s a l potentiometer were used to measure the voltage drop across the heater c o i l . A new and constant Weston c e l l , c e r t i f i e d from the U.S. Bureau of Stand-ards, was used i n the measurements of voltage and current. The current was measured by a p o t e n t i a l drop across a c e r t i f i e d 1 ohm r e s i s t a n c e . The current dropped o f f l i n e a r l y with increase i n temperature and allowance was made f o r t h i s i n c a l c u l a t i o n s by t a k i n g readings as convenient and i n t e r p o l a t i n g f o r the average value i n the i n t e r v a l being used. Timing was made with an accurate stop watch. A platinum r e s i s t a n c e thermometer, placed i n the adi a b a t i c bath to avoid conduction losses along the wires from the cup, was used to determine temperature i n t e r v a l s . A graph of R vs T shows a s t r a i g h t l i n e r e l a t i o n and gave a conversion f a c t o r of 1.0180. Fortunately (since they could not be made) cor r e c t i o n s using N, R 7, and N_ were not necessary f o r such d i f f e r e n c e s . The mean of the R. i n t e r v a l was read o f f the same graph as the temperature f o r that value of the heat capacity. Here again, the corrections were unnecessary since f o r absolute value of temperature a sample c a l c u l a t i o n at room temperature r e s u l t e d i n a f a c t o r of 1 , 0 1 8 3 . Factors f o r higher temperatures were obtained from a graph of R vs T drawn by c o r r e c t i n g f o r N, R z, and N z, keeping the bath temperature constant by means of the thermel. Procedure and Operation The sample was put i n the cup, covered with a watch gl a s s , and weighed to w i t h i n 10 m i l l i g r a m s . The dummy heater was then put i n t o operation while the apparatus was being assembled. The current was then changed over to the cup heater and a d i a b a t i c c o n t r o l was commenced. Several readings of current and voltage were taken to make sure the source \ma constant. In operation i t was found that l a g i n the c o i l heater was too- great to give a d i a b a t i c c o n t r o l properly, and so i t was used continuously to o f f s e t l o s s of heat to the surroundings and the e l e c t r o l y t i c heater put i n or taken out to maintain a d i a b a t i c c o n d i t i o n s . The apparatus was run f o r ten minutes before readings were s t a r t e d to allow steady conditions to be set up. Stepwise operation of the bath i n steps required to give a 15-20 second time to take the temperature was t r i e d . The steps were about 3/40°- r i s e due to s t i r r i n g = «015° 2 about 1 cm on thermel s c a l e . The l a g i n the thermel was about l / 3 the l a g of the thermometer. Since the change was i n the same d i r e c t i o n at the same rat e of heating each time, the r e s u l t i n g e r r o r was very low i n determining temperatures. In operation the v a r i a t i o n i n water equivalent more than o f f s e t t h i s gain. The stepwise operation could not be c o n t r o l l e d s a t i s f a c t o r i l y 13 over 100°C as the c o i l heater was i n s u f f i c i e n t to compensate f u l l y f o r loss of heat to the surroundings. An i n s u l a t i o n the e n t i r e depth of the cans, instead of r e l y i n g on a r i n g of cotton at the top and the a i r gap, was added. This improved the c o n t r o l m a t e r i a l l y . Accordingly, i t was necessary to res o r t to the procedure of making the l a g i n the e l e c t r i c thermometer as nearly constant as p o s s i b l e . This was done i n two ways. F i r s t l y , the rate of heating was n e c e s s a r i l y r e -duced from about 1 .8 w to h a l f t h i s value, doubling the running time. Second, the heating r a t e of the bath was adjusted to the heating rate of the cup f o r at l e a s t 15 seconds before the reading was taken. Since the thermel and thermometer both l a g the change, the d i f f e r e n c e i n l a g was not over 15 seconds. The thermometer was st a r t e d from about the same place on the scale i n i t s swing past zero. The time when the shadow passed zero was taken. This operation gave r e s i s t a n c e agreement to one d i v i s i o n on the l a s t d i a l f o r equal times i n the same region and so was taken as having reduced the e r r o r i n temperature measurement s u f f i c i e n t l y . Readings were taken at successive i n t e r v a l s of from 1-3 degrees. Voltage and current were checked as often as convenient. A method f o r f i n d i n g wrong readings and errors i n c a l c u l a t i o n was developed and used i n regions of t r a n s i t i o n . A sample of the readings taken from the calorimeter and method of c a l c u l a t i n g heat capacity f o l l o w . 14 T R 1. 00 :00 2.79890 2. 5:40 2.81400 3. 7:00 2.81700 4. 12:34 2.83080 5. 16:26 2.84060 6. 19:55 2.84830 V I 3.222 .4667 3.222 .4665 Check Method Now suppose a s u i t a b l e i n t e r v a l 3 - 5 degrees^ depending on how r a p i d the change i s a t t a i n e d with readings 1 and 4. Then 2 - 5 and 3 - 6 and 4 - 7 are taken. Thus^ each reading i s used twice and coupled with one before and one a f t e r . I n d i v i d u a l errors are so located since each of the before and a f t e r readings i s coupled with others. This method was used when a good set of readings was obtained and was very u s e f u l i n l o c a t i n g thermometer l a g e r r o r s and d i s c a r d i n g those readings. General Assembly -The water equivalent was, f o r benzene, 9 3 . 5 j/g/C,* for toluene, 94.0 j/g/C. 16 CONCLUSIONS With the temperature gradient e x i s t i n g "between the l i q u i d and heater wire, the h o t t e r surfa.ce of the wire would a f f e c t any i r r e v e r s i b l e change at a lower indi c a t e d tempera-ture than was a c t u a l l y r e q u i r e d . A contrast of temperatures of t r a n s i t i o n with the abrupt changes i n surface tension and v i s c o s i t y i n d i c a t e s that the change may not go i n the reverse d i r e c t i o n as r e a d i l y , and hence the heat of t r a n s i t i o n by t h i s method appears to s t a r t to be required f o r transformation i n each case at somewhat lower temperatures. Method f o r Determining Heat of T r a n s i t i o n at One Temperature I f the t r a n s i t i o n takes place at one temperature, as seems to be the case from s t a t i c measurements and v i s c o s i t y changes, ad i a b a t i c conditions should be set up fo r s l i g h t l y below that temperature and the heat input required to e f f e c t the change to s l i g h t l y above that temperature determined. A c o r r e c t i o n must then be applied f o r the energy required to r a i s e the temperature, as i n present experiments, i f s p e c i f i c , heat i s assumed constant. The present apparatus could be r e a d i l y adapted f o r such measurements u s i n g a thermo regulator i n the bath and the thermel i n d i c a t o r i f the rate of heat input were very low. The e l e c t r i c a l equipment i s of such p r e c i s i o n that such measurements are po s s i b l e with accuracy. This method eliminates the c h i e f e r r o r s i n the adi a b a t i c method used f o r t h i s purpose; namely, the l a g i n the e l e c t r i c thermometer, s a t u r a t i o n changes, and heat of vap o u r i z a t i o n . The above i s p o s s i b l e , f o r example, since the change in d i c a t e d at 110° i n both c i s and trans forms from s t a t i c measurements seem to s t a r t here at about 90° ( i . e . when wire i s ' 110°) and are completely f i n i s h e d when the body of l i q u i d i s at 110°. BIBLIOGRAPHY 1. f. P. White Phys. Rev. 1910 — pg 670 2. N. S. Osborne Bui. Bur. Stds. 1918-19 pg 14-135 3. W. P. White — The Modern Calorimeter 4 . J . Dickinson Bui. Bur. Stds. Vol . 11 1915 pg 229 et seq. Vol. 9 1913 • pg 43 " " 5. U.S. Bur. Stds. Bui. 12 1915 pg Yj-JJ 6. Bui. Bur. Stds. Vol. 9 1912 pg 7 7. Bui. Bur. Stds. Vol. 11 1914 pg 132 -8. J . Franklin Inst. 172 1911 pg 559 9- J. Am. Chem. Soc. Vol. 11 1914 10 .J. Am. Chem. Soc. Vol. 1 1915 11. Ann. Ent. Soc. Am. Vol. 20 1927 pg 513-21 12. ?/. P. White — Phys. Rev. 1910 pg 155 et seq., pg 545 et seq. 13 • B. 15. Spence Phys. Rev. 1910 pg ^ 66 14. T. F. Wall E l e c t r i c i a n Vol .100 1928 -- pg 297-9 15. W. P. '.Vhite — - Phys. Rev. 1910 pg 562 16. Daniel R. S t u l l - — J. Am. Chem. Soc. Vol. 59 1957 pg 2726-35 17. Giauque & Wiebe • J. Am. Chem. Soc. 1928 pg. 50-101 18. P. N. Pavlov J. Gen. Chem. (U.S.S.R.) 7, 1957 — pg 2442-7 19. Thermel — Phys. Rev. 1910 — - Vol. 51 — pg 145 20. J . Williams & F. Daniels J. Am. Chem. Soc. 1924, Vol.46 pg 904 21. G. F. Davies Sp e c i f i c Heat of Cis Decahydronaphthalene 1959 

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