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The second-order phase transition of cis decahydronaphthalene Robinson, Marian 1945

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f\i S v THE SEC01D-0HDIS PHASE T2AKSITI0K OF CIS DBCAHYBEOMPHTMLISE By Marian Robinson. B.A. A Thesis submitted i n p a r t i a l fulfilment of the Requirements f o r the Degree "of Master Of -Arts In the Department of CHEMISTRY The "University of B r i t i s h Columbia A p r i l s 1945 ACEUGV/LEDGMbUT I t io f7ith pleasure I wish to acknow-ledge the he l p f u l ^suggestions end assistance of Br» Mm F, Soycr a under whoso d i r e c t i o n the pro-soiit investigation "vras carried out» i TABLE OF OOHTEKTS Page Introduction ........ 1 Phase Transitions ..........*«•«.»••.•.«»••.••••»•••••*(•»•• &-Adiabatic Method 14 Isothermal Method ...•••....••.••••••.»••««••»•«««•••«..»»• 15 Apparatus 16 Bath Medium • 17 Bath Heating C i r c u i t 18 Thermocouple 18 Cup Heater C i r c u i t 19 Calibration 21 Operation 21 Adiabatic Method 21 Isothermal Method 21 Cooling Curves »...........<; 22 Heating Curves 23 Calculations 23 Discussion of Results 27 Heating and Cooling Curves 27 Sp e c i f i c Heat Curves ...<. 37 Purity of Compound 38 Bibliography LIST OF ILLUSTRATIONS Figure Page 1 Vapour Pressure of Cis Decahydronaphthalene 2 2 Surface Tension of Cis Decahydronaphthalene 2 3 Verdet Constant of Cis Decahydronaphthalene 3 4 Density of Cis Decahydronaphthalene 3 5 First-order Phase Transitions 5 6 P-T diagram 5 7 Second-order phase Transitions 7 8 Specific Heat Curve-Second-order t r a n s i t i o n 7 9 S p e c i f i c Heat of Ammonium Chloride 9 10 S p e c i f i c Heat of Potassium Di-hydrogen Phosphate 9 11 Density curve of Helium 10 12 S p e c i f i c Heat Curve of Helium 10 13 P-T Diagram of two phases 12 14 Cali b r a t i o n of Thermopile 20 15 Isothermal Temperature Ri3e i n Time . 25 H6 Heating and Cooling Curves 31 17 Heating and Cooling Curves 36 18 Sp e c i f i c Heat Curves - Adiabatic Method 41 19 S p e c i f i c Heat Curves - Isothermal Method 43 20 Average S p e c i f i c Heat Curve - Isothermal Method 44 IHTRODUCTIOII The physical properties of c i s decahydro-naphthalene have been studied extensively in this labor-atory. The .evidence obtained from, measurements of vapour pressure (figure 1), surface tension (figure 2), and v i s c o s i t y suggest the presence of a t r a n s i t i o n point i n the l i q u i d state. Dr. II. D. Smith and his assistants found evidence j.'or a Verdet constant change with temperat-ure i n the v i c i n i t y of 50°C, (figure 3). Smith, Barton'^ and Zotov found differences in the Raman effect of the isomer at temperatures above and belov; 50®C. Surface tension measurements indicate i t takes place at 50°C. i 0.2 3ino« no discontinuity was foi<nd in the density curve ( f i r u r e 4) has been suggested the t r a n s i t i o n i s of a second-order. It i s the bject of the present research to deter nine the nature of the t r a n s i t i o n from studies of the s p e c i f i c heat curves. Phase Transitions In a f i r s t - o r d e r phase t r a n s i t i o n at constant temp-erature and pressure there i s , accompanying the transformation, a jump i n entropy associated with the latent heat and a jump i n the s p e c i f i c volume. The thermodynamic potential or Gibb's function, g, i s the aame for the two phases, but the f i r s t - o r d e r derivatives of the Gibb's function change discontinously. In mathematical terms, Thus, i f for an ordinary transformation, the Gibb's function entropy, s p e c i f i c heat and volume are plotted as a function of the temperature with p constant, the results are as shovni i n (figure 5)., If i n a PT diagram (figure G) AB i s a l i n e along which a transformation of the f i r s t - o r d e r takes place, then for the f i r s t - o r d e r t r a n s i t i o n , a v/here^is the heat of transformation and F'IRST ORDER P H A S E TRANSITIONS "TE M P T E M P FIO. 5 to -6-Let x be a quantity which does not change in passing from ono side to the other of AB i n (figure G) and l e t ^ p and A t be corresponding changes i n p and T i n passing along t h i s curve. Then - m i Let x = g and we then obtain tho Clausius-Clapeyron Equation dt = Tfy-T/J In a second-order phase trs^nsition, on the other hand, there i s no change i n entropy or volume at the t r a n s i t i o n point. The f i r s t - o r d e r derivative of the Gib'o's function changes continuously as. the substance passes from one phase to the other (figure 7). As' can be seen, there i s no step i n the curve but a discontinuity i n slope at the transformation point. S i m i l a r l y the thermal .Measurements shew no latent "neat but a oharp discontinuity i n s p e c i f i c heat (figure 8). , The following processes are generally regarded by physicists as second-order phase t r a n s i t i o n s : _ 1: A ferro-magnetic metal such as iron and n i c k e l becomes paramagnetic at the Curie point. 2: A super-conducting metal becomes an ordinary conductor at a d e f i n i t e t r a n s i t i o n point. S E C O N D ORDER 7-PHASE 1~R/\NS IT I ONS T E M p. ' T e p. " TE M P FIG. 7 IT EM P FIG. 8 -8-3J Tho ammonium chloride e f f e c t . The s p e c i f i c heat of NH CI as compared with HaCl i s shown i n (figure 9). The sharp maximum at 243° K. represents tho c r i t i c a l temperature of a co-operative adsorption of energy which commences at much lower temperatures and i s not accompanied by a change i n c r y s t a l structure. I t has been shown that i n t h i s and similar cases tho anomalous s p e c i f i c heat i s due to a t r a n s i t i o n from a state i n which tho molecules merely l i b r a t e (wobble) about f i x e d orientations to a state i n which they are p r a c t i c a l l y i n free rotation. This ia again a co-operative phenomena, since a p a r t i c u l a r molecule be-comes more froe to rotate when i t s neighbors are already i n rotation for then the f i e l d produced by theia approaches more c l o s e l y to opher-i c a l symmetry and the tendency to orientation i s reduced,, 4: The anonoly observed i n the heat capacity of potassium dihydrogen phosphate at the Curie temperature . This ia shown i n (figure 10). From the experimental entropy value for t h i c change and from studies of KH AsO. and KH.H P0., Stephenson and Hooley conclude that the hydrogen bonds i n these "crystals are responsible f or the t r a n s i t i o n . 5 s Liquid Ee2 becomes Liquid Eel ai; various temp-eratureo and pressures, for example, the •«point where T = 2.19°K and P = 38,65 mm. At t h i s point the density of Hel i s the same as He2. In p l o t t i n g the density curve vs. temperature (figure 11), there i s seen to be a discontinuity but no step at the Vpoint. S i m i l a r l y the thermal measurements show no latent heat but a sharp discontinuity i n the s p e c i f i c heat curve, (figure 12). For a transformation of tho second-order, 7* - 7' - a But i n a l l these processes the quantities, s p e c i f i c heat and density show discontinous changes during the phase t r a n s i t i o n . i t follows that a second-order t r a n s i t i o n i s characterized by changes i n the second-ordor derivatives of the Gibb's Function. Also If then x i s a quantity which does not change i n passing from one form to the other and l e t A p an., a t be the corresponding changes i n p and t in passing along the curve div-iding the two states then: Let x = s and x = v -12-These are the assumptions on which Ehrenfest rind Von Laue have based th e i r work. Epstein suggests the assumption goes too f a r when they d i f f e r e n t i a t e the equation g^ -g = 0, t h i s implying that contact exists along the whole l i n e (or a f i n i t e part: of i t ) of the intersection of the surfaces g ^and g. There i s nothing in the experimental observations to j u s t i f y t h i s assump-t i o n . T h e o r e t i c a l ^ i t i s also a remote case, It is a far :r.ore common occurence that the two surfaces are i n contact i n a singular point, that i s , the equation £ x - g ; s 0 i s s a t i s f i e d i n just one point, whose co-ordinates we w i l l denote as p o ,T0 . We now wish to f i n d what ta'-res place at p^ *--*- dp, T d^Fand i t i s seen that transformations are possible i f not i n the point p o T 0 i t s e l f , i n it£ immediate v i c i n i t y as i s i l l u s t r a t e d i n the (p,T) diagram of (figure 13). h- 1 5 r There are two l i n e s in which the phases (1) and (2) can co-oxist and they intersect at a singular point p„T 6. Yfhen the substance i s cooled at a pressure exactly coinciding with that of the intersection (dotted l i n e AB), no transformation takes place. If i t i s cooled at a s l i g h t l y d i f f e r e n t pressure A'B' i t is transformed f i r s t from phase -13= (2) into phaso ( l ) and at a lower temperature back into (2) again. Some of the experimentally measured anomalies present features com-patible with t h i s picture: as the temperature i s changed the s p e c i f i c heat jumps discontinuously and, at a s l i g h t l y lower temperature jumps back to the i n i t i a l value. Since no discontinuity was found in tho density curve of c i s decahydronaphthalene, any t r a n s i t i o n which ta'ces place must necessarily be a second-order phase t r a n s i t i o n . ^e have shown that: that i s the s p e c i f i c heat curve i s a f i r s t - o r d e r derivative of the entropy curve. Since, i n a second-order t r a n s i t i o n , the slope of the entropy curve changes at the t r a n s i t i o n point, the s p e c i f i c heat curve should be discontinuous at the t r a n s i t i o n point. It i s t h i s d i s -continuity we are endeavoring to detect. If we could possibly obtain a heating rate low enough to bring about t r a n s i t i o n without r a i s i n g the temperature and without other effects taking place the s p e c i f i c heat curve would -14-appoar as follows j 7 That i s we would got some readings with no temperature r i s e at a l l or i n f i n i t e s p e c i f i c heat. P r a c t i c a l l y tho curve would be of the forms T TJhen the heat of t r a n s i t i o n i s very small compared to the s p e c i f i c heat, the curve would have the forms T It i s t h i s l a t t e r form of s p e c i f i c heat curve which i s expected f o r c i s de c c ahydronaphth alene, •\ The Adiabatic Method and Errors Involved; " ' - Tho adiabatic method i s considered the most accurate for long experiments as were carried out here i n the f i r s t part of the work. By reducing the value of the thermal leakage to a minimum t h i s method reduces errors i n i t s measurements and inconstancies i n i t s values due to convection, evaporation, rad i a t i o n , s o l i d conduction and evapor-ation. By t h i s , lags are made nearly constant over the whole experimental period and errors due to lags are reduced accordingly. -15-Dxpc-rimental c a l i b r a t i o n eliminates the systematic errors of the calorimeter. The v a r i a t i o n i n these offsets therefor e e are r e a l l y tho errors. I t has been calculated that the heat roquirod for the evaporation to maintain saturation i s below 0.1% of the s p e c i f i c heatj, so any variations i n t h i s amount would bo n e g l i g i b l e . The s t i r r i n g motor has a constant rate cf 75 r.p.m. which produces a temperature r i s e of not more than 0.0035°C per ciin. at a temperature of 50*0, This in equivalent to an energy input of 0. )05 watts. Applying a correction for fchio amount i n the calculations again gives the dcairod accuraoy. The accuraoy of measurement of energy input was shown to be O.ZBft, as can bo shown below. The current input of 0.12 onps end the voltage from the v o l t box of 0.195 volta can be measured to 0.00001 v o l t s giving O.OOSvo and 0.005$ precision respectively. Time intervals of 6000 seconds accurate to one second and temperature intervals of 2° accurate to 0.0005° giving 0.02^ and 0.25?prccisions respectively. This insures on accuracy of 0.20;& onsrgy input. It w i l l bo seen that temperature measurements i n -volve the greatest error an the temperature i n t e r v a l s are reduced to obtain greater s e n s i t i v i t y . The Isothermal ''othodt sihilo the adiabatic method lias been proven the best for protracted oxporixaonts, i t i s not always the most accurate mothed i f the experiment can be conducted as short runs. The apparatus wan roarrunged therefore so that the isothermal method could b© used. -16= Since the heating rate i s proportional to the thermal head we have V = K if where V a Rate of temperature change i n calorimeter K r. Thermal leakage modulus (j> n Thermal head The temperature loss formula i s , therefore, rrj = 7T ~ K T if> In the adiabatic method since 1^ i s zero, errors caused by temperature loss are consequently reduced to a minimum9 But i f <^can be accurately determined, the error i n determining tho temperature loss i s caused then only i n E f a i l i n g to remain constant. After each experimental period, i n a c a l i b r a t i o n period the rate of cooling was redetermined* Consequently these errors are reduced to an order compatible with the adiabatic method when the same heating rate was used. Apparatus; The apparatus used i n t h i s investigation i s tho 1 8 some as that used by Head and McLollan and i s adequately described i n t h e i r theses. A b r i e f resume w i l l be given here and any changes p a r t i c u l a r l y noted. The Calorimeter i s the same as used by previous workers and was constructed s i m i l a r l y to "Williams and Daniels. It consisted of a thih-walled spun copper cup holding the c i s -17-docahydronaphthalene , t h i s cup being sot i n a large c y l i n d r i c a l copper container, 8 cm i n diameter and 12 cm high. To the bottom of the container, 650 gms of lead were soldered to lessen the buoyancy pressure on the s t i r r i n g shaft during operation. The inside cup was f i t t e d with a grooved f i b r e r i n g , a copper sluve running from tho groove to the l i d * The l i d contains openings for necessary heating and measuring equipment, v i z , thermopile, heating c o i l leads and shaft for the s t i r r e r . Attached to the l i d with rubber cement was a t h i n washer of neoprene rubber. The other side cf the washer was coated with rubber cement and the l i d immediately screwed t i g h t l y i n place. Bath Medium: The bath i s s t i r r e d by tiro high speed shafts, each equipped with several three bladed p r o p e l l o r 3 . It has been found i n previous work: that the use of glycerine for a bath medium below temperatures of approximately 40°C involved too large temperature gradients i n the bath. D i f f i c u l t y due to i t s leakage into the calorimeter and i t s high vapour pressure was ex-perienced using water. From vapour pressure vs. v i s c o s i t y curves, a 95fa aquoous glycerol solution was considered s a t i s f a c t o r y . Adding 5% water to the glycerino lowers the v i s c o s i t y at 25°C from 945 c e n t i -poises to 366 centipoises. Temperature gradients i n tho bath f o r t h i s v i s c o s i t y and at 25°C did not exceed 0,01°C. This was considered s a t i s f a c t o r y . -18= The vapour pressure at t h i c temperature and con-centration was 2.4 m. and no d i f f i c u l t i e s were experienced with thio vapour pressure Bath. Heating C i r c u i t ; Tho e l e c t r o l y t i c both boating c i r c u i t was modifled to give hotter temperature control. An adjustable transformer (vari&c Type 100 Q) woe i n s t a l l e d i n place of several variable resistances. An arcaoterwaa also placed i n the c i r c u i t . A current of O.Go arap. was r e -quired at 50° G i n tho adiubatic method when tho cup was heated with an input of Oei watts. A current of 0.45 amps was required to koop the bath temperature constant at 50°C. outor bath, heator was used only to bring tho bath up to the temperature of the experiment and then only the e l e c t r o l y t i c hontor was usod. Use of the photoelectric c e l l end relay f o r c o n t r o l l -ing bath temperatures was also discontinued as better contol was ob-tained with manual operation of tho transformer. Theraocouplo: A new thermopile was constructed of -^ 33 B and S gauge copper wire and #30 B and S copol wire, f i v e couples being used i n each junction. The wires were twisted together four times, soldered and each junction insulated with g l y p t a l varnish. The thermopile wan calibrated using two baths*, 10°C apart i n temperature. The temp-eratures of tho baths were measured with two platinum resistance thermometer;;. -1S-The results given below are plotted i n (figure 14) Table I Temperature D i f . °C. E.M.F.<^<?C. 62-52 208.0 55-45 206.0 52-42 205.0 32-22 201.5 With a l l junctions at the same temperature, the e.m.f. set up was l ^ v corresponding to 0.005°G. This small temperature d i f f e c -onoe may have been due to i r r e g u l a r i t i e s i n the bath and the temperature was considered constant. Cup Eeater C i r c u i t ; The e l e c t r i c a l energy was supplied from 120 amperehour lead storage battery, the quantity being controlled by a rheostat of nichrome wire i n the battery c i r c u i t . The voltage drop across the heater was measured by a Type K Universal Potentiometer', f i r s t being reduced to a measurable quantity through a volt-box. The current i s calculated from the voltage drop across a one ohm standard resistance. From the e.m.f. indicated by the potentiometer the voltage drop across the leads and across tho standard resistance must be subtracted to give the voltage drop across the heater i t s e l f . The resistance of the loads was measured. Results were as follows: 24°C - 0.1795 ohms. 50°C - 0.1828 ohms. The resistance varies l i n e a r l y with temperature between these points. -21= Calibration; The ca i c r i n e t a r had been previously calibrated with B toluene . The water equivalent waa found '„o be 58.0 joclos t- 0.1 j o u l e s / 10°C. Operation; S p e c i f i c Heat Doterainat.ions Adiabatic I'othodg The sample (150g - 160g) was placed i n the oup, the calorimeter assombled and placed i n tho bath. A l l leads wero connected and the battery current passed through the dummy boater. The bath and cup \7ere both raised to 40°C and f i e i r temperatures equalised. "Khen steady conditions noro maintained, the current »as switched to the - cup heater and roadinf,3 of tine and temperature token at regular i n -t e r v a l s . Chocks were made as often as possible on voltage end current input. A heating rate of 0.1 watts was used. iGQthornal Method; The apparatus was assembled as for the adiabatic method. A two-way switch was insortod in the thermopile galvanometer c i r c u i t , the other h a l f of the switch being connooted to tho o.suf. terminals of the potentiometer. The galvanometer scale was calibrated for various temperature differences as measured by the potentiometer. It was found a temperature difference of 0.2°C (40.1 -^v from the thermopile at 50°C) deflected the 3cale 24.5 cm. This value was checked p e r i o d i c a l l y throughout tho runs varying not more than 0=5 ess. -22-Tho leads from the thermopile were disconnected from the potentiometer and the leads from the cup-heater c i r c u i t were re-connected. The bath and calorimeter were brought to the desired temperature using the cup-heater, e l e c t r o l y t i c bath heater and outer heater. While current was flowing through the cup-heater several determinations of voltage and current were made. The current was switched to the dummy heater when hob i n use. After steady cond-i t i o n s had been maintained f o r a short; period, the cup heater and stopwatch were switched on simultaneously. A current reading was taken and the cup-heater switched o f f j a f t e r 45 seconds. To ensure complete e q u i l i b r i um of the l i q u i d , before each determination the calorimeter was held constant at the i n i t i a l temperature f o r an hour. The approximate temperature r i s e used i n f i r s t and second runs were 0.2°C and 0.02°C respectively. Operation (Continued): Cooling Curves: Apparatus i s assembled as for a s p e c i f i c heat run with the exception of connecting the thermopile leads to the potentiometer instead of to the galvanometer. Sine© no measurements of power input to the cup are needed, these leads may be disconnected from the potent-iometer and the heating c o i l used only f o r obtaining the desired temp-eratures . Then one adjusts the cup and bath temperatures using the heating c o i l i n the cup and the e l e c t o l y t i c bath heater f o r the bath. The decalin should be approximately 53°C and the bath 50°C. V/hen the desifced bath temperature i s reached, i t i s kept constant by -23-adjusting the heat input to the e l e c t r o l y t i c bath heater to a low value. During the cooling, simultaneous readings of time and thermo-couple e.m.f. are taken at 2-3 minutes i n t e r v a l s , one junctions of tfXe thermopile being i n the bath and the other i n the decc&in. The e.m.f. i s determined to the nearest-^v, i . e . 0.005°C, so i s of the same order of accuracy as the platinum resistance thermometer. Readings are continued u n t i l the decoclin has approached within 0.1° of the bath temperature. Heating Curves: The procedure f o r obtaining the heating curves i s almost exactly the same as for the cooling curve but the bath i s now at a temperature greater than 50°C and the decalin below 50°C. To avoid hysteresis e f f e c t s , i t was avoided using the heating c o i l to bring i t to a temperature where readings could be started but to do thi s by heat transfer from the bath. In t h i s way, no part of the de-c o l i n w i l l have been heated above 50°C before readings are commenced. It should be noted that heat input to the bath equals heat l o s t to surroundings plus heat l o s t to decqlin whereas f o r the cooling curve, heat input equals heat l o s t to the surroundings minus heat gained from the decalin. Calculations: For the adiabatic runs the method of ca l c u l a t i o n of sp e c i f i o heat values was the same as that used by McLellan. For the isothermal runs the temperature r i s e must be calculated before the s p e c i f i c heat can be determined. -24-A sample set of readings i s given i n Table II : Table II Resistance (R) Current (Amp.) 3.0537 0.49343 Scale me (Sec.) Reading 92 16 126 20 139 21 156 22 189 23 250 24 351 24 436 23 536 22 645 21 778 20 876 19 1011 18 1135 17 1290 16 The scale readings were converted to temperatures, a graph of temperature vs time was plotted (figure 15). By interpolation back to zero time the true r i s e i n temperature was found. This method was not very accurate, however, and the following S calculations were used, as given by White. -26-We have: * ^ - the temperature r i s e due to heat that stays i n the calorimeter. <fj = the temperature loss due to heat l o s t . Therefore: =Atf'the temperature change corresponding to the t o t a l measured quantity of heat. * Assume the cooling of the calorimeter, that i s , a l l change not due d i r e c t l y to the measured heat, has the formula: nj - uj-f X.dj = heat of s t i r r i n g ^ = thermal leakiness if = thermal heat The observed rate of cooling i s given i n the formula : - ^ z K if The proportional part of t h i s rate for the experimental period i s : fa - t^)£c * ^ x = average thermal head i n experimental period. = average thermal head i n c a l i b r a t i o n period. Therefore the t o t a l rate of cooling for the experimental period i s : h 4* '3 Formula f o r temoer&ture loss ^ = [*>+ But since ^ i s approximately equal to ^ i t i s advantageous to substitute and with t h i s quantity we obtain the true temperature r i s e using ^ = A6 . Tthen the true temperature r i s e has been determined the s p e c i f i c heat i s calculated as for the adiabatic method. Discussion &£ ?^§M%fc§: Heating and Cooling Curves: The heating and cooling curves were obtained to see i f a change of slope could be noted i n the region of t r a n s i t i o n . The results are necessarily q u a l i t a t i v e because of i n s u f f i c i e n t knowledge of the thermal leakage modulua of the calorimeter. This quantity must be known accurately to determine s p e c i f i c heats. The time-thermocouple e.m.f. measurements from which were calculated temperature differences are given i n tables 3,4,5. Tho logarithm of the temperature difference i s plotted vs time. A s can be seen figures 16, 17 b, show d e f i n i t e breaks i n the region varying between 50.29°C - 50.4°c. Figure 17 a, shows no break. This was possibly due to contamination of the decolin through leakage of the calorimeter or perhaps the more rapid rate of heating and cooling has mashed the effeot of the t r a n s i t i o n . The pl o t t i n g of log<a.t vs time i s based on Hewton's Law of Cooling. Over a short i n t e r v a l of time dd a quantity of heat passes through the walls 6T the calorimeter from the bath* -28= According to Hewtons Law of cooling fL® * K (t -t) T ; h e r e t f a= bath temperature t = decahydronaphthalene temperature K » i n s t a n t A l l the heat i s used i n r a i s i n g the temperature of the calorimeter and i t s contents. Therefore: dQ a u) Cp dt -t- Wdt Where U) s yrater equivalent of the decalin Cp = s p e c i f i c heat of the decalin W " water equivalent of the calorimeter dt = r i s e i n temperature Combining these two equations we obtain: KclB - J t (^ Cpjt^Oj^ /•1 it Over a temperature range of only a few degrees C^ and V/ may be con-sidered constant. tr Therefore: KB = _ [ (uJCprU/J^ - *) Therefore: ^ 0 = JL~>(ty-t) * S i m i l a r l y f o r a cooling curve: JL~(t-tb) A normal logarithmic cooling curve should be a straight l i n e . Any i r r e g u l a r i t i e s i n cooling would sho1.? by a change i n the slope of the l i n e . -29-= Table I II Heating and Cooling Curves - Run $1. Weight of sample - 151.809 g. Heating Curve Cooling Curve Temperature of Bath - 50.86°C. Temperature of Bath - 49.9 ° c Transition Temperature a 50.39 ° c Transition Temperature - 50.29 Ime (sec.) Log T Time (sec.) Log T 0 0.6946 0 0.3927 321 0.6646 187 0.3434 678 0.5289 418 0.2923 960 0.4609 565 0.2695 1356 0.3S17 733 0.2253 1788 0.2577 912 0.1818 2172 0.1673 1122 0.1367 2613 0.05311 1343 0.0864 3007 -0.0555 1626 0.0334 3458 -0.1662 1915 -0.0306 3812 -0.2291 2258 -0.1057 3979 -0.2696 2528 -0.1637 4110 -0.3098 2850 -0.2299 4245 -0.3565 3200 -0.3098 4440 -0.4089 3435 -0.3556 4616 -0.4559 3690 -0.4067 4832 -0.5376 3965 -0.4647 5004 -0.6108 4360 -0.5317 -30' Table I II (Continued) Time (sec.) 5303 5677 6137 6612 Log T -0.7077 -0.8327 -1.0078 -1.3010 Time (sec.) 4900 5436 6074 7456 Log T -0.6108 -0.7077 -0.8327 -0.0088 -32= Table 17 Heating and Cooling Curves - Run 7/2. Weight of sample = 151.280 Heating Curve Cooling Curves Temperature of Bath = 51.63^ Temperature of Bath = 48.765° c ime (sec.) Log T Time (sec.) Log T 0 0.9025 0 0.7513 370 0.8041 354 0.6590 759 0.7033 766 0.5599 1148 0.6042 1053 0.4900 1380 0.5478 1143 0.4683 1610 0.4900 1243 0.4456 1818 0.4578 1350 0.4232 2024. 0.3892 1438 0.3979 2208 0.3444 1555 0.3711 2420 0.2923 1678 0.3424 2617 0.2465 1802 0.3139 2830 0.1975 1930 0.2810 3005 0.1523 2077 0.2455 3211 0.1038 2230 0.2095 3430 0.0531 2407 0.1673 3680 -0.0088 2572 0.1206 3904 -0.0696 2790 0.1719 4177 -0.1331 3038 c o i r * 4385 -0.1721 3322 -0.0540 -33-Table 17 (Continued) Time (DOC.) Log T Timo (sec.) Log T 4590 -0.2306 3640 -0.1337 4763 -0.2484 4054 -0.2299 4998 -0.3279 4680 -0.3904 5157 -0.3556 5350 -0.4920 5417 -0.4295 5662 -0.4647 5960 -0.5467 6265 -0.6118 6580 -0.7077 7123 -0.8321 7900 -0.0088 Table V Heating and Cooling Curves - Bun #3 Weight of *>anple - 151.280 Heating Curve Cooling Curve Temperature of ^ ath = 50.86 °C Temperature of Bath = 49.9°C Transition T e mperature = 50.1 °£ Transition temperature 50.4 '£ ime (sec.) Log T Time (sec.) Log T 0 0.6902 0 0.4456 197 0.6355 212 0.4065 462 0.5821 419 0.3617 670 0.5353 636 0.3139 1206 0.4150 896 0.2577 1375 0.3802 1160 0.2014 1581 0.3345 1452 0.1367 1915 0.2577 1685 0.0864 2262 0.1818 1947 0.0334 2516 0.1206 2137 -0,0088 2850 0.0531 2370 -0.0545 3036 0.0128 2608 • -0.1051 3234 -0.0S11 2870 -0.1637 3460 -0.0794 3173 -0.2306 5790 -0.1487 3364 -0.2692 4070 -0.2132 3735 -0.3316 4227 -0.2487 4020 -0.3798 Table V (Continued) Time (sec.) Log T Time ( Sec.) Log T 4324 -0.2684 4131 -0.4087 4522 -0.3188 4390 -0.4647 4700 -0.3556 4793 -0.5327 4977 * -0.4067 5200 -0.6108 5254 -0.4647 5700 -0.7077 5573 -0.5327 6383 -0.8177 5918 -0.6106 6337 -0.7077 6948 -0.8794 -57-Sp e c i f i c Heat Curves; It has been shown that the s p e c i f i c heat xsurve should be of the form given i n (figure 8). The results obtained by the adiabatic method are given i n table VI. The curves (figure 8) have only a small change i n slope at the t r a n s i t i o n point. The reasons f o r t h i s may be as followsj 1. The heat of t r a n s i t i o n for c i s decahydronaphthalene i s small compared with the s p e c i f i c heat. That i s ( C f a - ~ C P) dt - d hi where ^~Pa~ - measured s p e c i f i c heat Cp s r e a l s p e c i f i c heat d hi - d i f f e r e n t i a l heat of t r a n s i t i o n 2. The t r a n s i t i o n requires a f i n i t e time and the r a t i o heat input being used i n the t r a n s i t i o n to that used i n r a i s i n g the temperature i s influenced by the heating rate, that i s , i t probalby r e -quires a de f i n i t e heat input for a d e f i n i t e time to e f f e c t the trans-action so that a greater heat input would mean a greater proportion of heat being U3ed to raise the temperature. 3. Tho higher the heating rate the higher the temp-erature gradient between the c o i l and the bulk of the l i q u i d . This en-ables the t r a n s i t i o n to take place at a s l i g h t l y lower bulk temperature 6f tho l i q u i d . For a heating rate of 0.8 watts the temperature gradient between the heating c o i l and the decolin was calculated to bo 0.3°C. At the heating rate of 0.1 watts used here t h i s e f f e c t would be p r a c t i c a l l y n e g l i g i b l e . -38-Therefore i t oan be seen, the lower the heating rate, the more de f i n i t e should be the change i n the slope of the curve. At very low heating rates, however, the errors of the experiment, heat of s t i r r i n g , temperature measurements, become appreciable. The curve obtained i n (figure 18 b ) shows no discontinuity i n the region of 50°C. This was due to impurities which had leaked into the decolin during the experiment. The results from the isothermal runs are given i n table 7. The curves, plotted i n (figure tL9) a d e f i n i t e break at 50.2°C. show In obtaining (figure 19 bj^aivery low temperature r i s e was used,approximately 0.02°C. Since the l i m i t of accuraoy i n co n t r o l -l i n g the temperature of the bath i s 0.005°C, and tho temperature r i s e per minute due to heat of s t i r t i n g i s 0.0005°C, then i t can be seen errors w i l l be appreciable. This accounts f o r the i r r e g u l a r i t i e s i n the curve. Quantitatively the results are, therefore, unreliable but q u a l i t a t i v e l y they show the discontinuity quite d e f i n i t e l y . A smooth curve, obtained by averaging these results i s shown i n (figure 20.) From the area under the curve the latent heat was calculated to be 0.737 calories per mole. Its very small value probably accounts for the d i f f i c u l t i e s experienced i n detecting i t s presence. Purity of the Compound: The c i s and trans isomers of decahydronaphthalene were se-parated by vacuum d i s t i l l a t i o n i n a Stedman column of commercial docolin from the Eastman Kodak Co. The c i s isomer was then r e p u r i f i e d by three r e c r y s t a l l i z a t i o n s u n t i l a constant freezing point of -43.67°C tras obtained. -39= Table VI Specific Boat Determinations - Adiabatic Method. Run #3 Run #1 Specific Temperature Heat Run #2 Specific Temperature Heat 45.394 45.85 46.453 47.208 47.811 48.313 48.815 49.318 49.821 50.323 50.847 51.329 51.833 52.335 53.342 53.703 1.7834 1.7774 1.7795 1.7751 1.7884 1.7903 1.7880 1.7886 1.7858 1.7923 1.7911 1.7924 1.8047 1.8130 1.7930 1.8036 44.701 45.198 45.801 46.303 46.805 47.308 47.811 48.213 48.565 48.866 49.118 49.369 49.770 50.323 51.329 51.832 52.336 52.839 53.343 53.847 54.350 1.7942 1.7950 1.7959 1.7988 1.8048 1.8128 1.8156 1.8176 1.8187 1.8209 1.8221 1.8207 1.8216 1.8239 1.8295 1.8288 1.8303 1.8304 1.8297 1.8351 1.8360 Temperature 43.792 44.294 44.796 45.299 45.801 46.303 46.806 47.308 47.811 48.314 48.816 49.167 49.367 49.569 49.970 50.170 50.374 50.626 50.928 51.229 51.480 Specific Heat 1.7795 1.7943 1.7915 1.7869 1.7901 1.7937 1.7976 1.8019 1.8042 1.8029 1.8036 1.8077 1.8153 1.8181 1.8151 1.8165 1.8197 1.8197 1.8172 1.8105 1.8139 S p e c i f i c emperature Heat Table Vx (contJ.nued) Specific Temperature Heat 54.853 55.355 55.859 56.362 56.865 57.220 1.8480 1.8525 1.8527 1.8584 1.8555 1.8541 Spec i f i c Temperature Heat 51.832 52.355 52.839 53.344. 53.796 54.249 54.792 1.8166 1.8191 1.8247 1.8280 1.8500 1.8379 1.8395 SPECIFIC ME/\T- JOULES'/GM Tabic VII Specific Heat Determination - Isothermal Method. Run #1 Run #2 'emperaturo Spocific Heat Temperature Specific 47.3 1.8122 49.9 1.821 47.6 1.8128 49.5 1.809 47.8 1.8484 50.0 1.815 48.0 1.8166 50.05 1.839 48.2 1.8056 50.11 1.908 48.6 1.82000 50.15 1.907 48.8 1.8240 50.20 2.728 49.2 1.8135 50.25 2.164 49.6 1.8025 50.31 1.870 49,6 1.8190 50.40 1.771 50.0 1.8294 50.51 1.771 50.2 1.9030 50.63 1.834 50.4 1.8854 50.70 1.834 50.6 1.6641 50.80 1.709 50.8 1.7856 50.9 1.833 51.2 1.8081 51.0 1.833 51.6 1.8115 51.12 1.833 51.8 1.8298 51.22 1.833 52.0 1.8221 51.3 1.832 51.35 1.832 51.4 1.832 51.45 1.766 51.55 1.831 51.59 1.831 Bibliography 1. E.F. Burton, H. Grayson-Sraith and J.O. Y/ilhelm, Phenomena at the Temperature of Liquid Helium. 2. A.R. Ubbelohdo, An introduction to Modern Thermodynamical P r i n c i p l e s . 3. J.K. Roberts, Heat and Thermodynamics. 4. Paul S. Epstein, Textbook of Thermodynamics. 5. Walter P. White, The Modern Calorimeter. 6. Zemansky , Heat and Thermodynamics, Second E d i t i o n . 7. B. R. Mead, M. A. Sc. Thesis, 1940. 8. D. E. McL9llan, M. A. Sc. Thesis, 1943 e 9. H. M. Graham, M. A. Sc. Thesis, 1944. 10. Morel Watson and Yip, B. A. Sc. Thesis, 1940. 11. J . Chem. Phjrsics, 7, 1019 (1939). 12. J . Chem. S o c , 127, 1421, (1925). Bibliography Continued. 13. J . Am. Chem. S o c , 46, 903, (1924). 14. J . Am. Chem. S o c , 37, 1719, (1915). 15. J . Am. Chem. S o c , 59, 2726, (1937). 16. J . Am. Chem. S o c , 66, 1397, (1944). 17. J . R e i l l y , T7.IJ. Rae, T.S. Wheeler, Physico- Chemical Methods. 16. R. R. McLeod, M. A. Thesic, 1944. 19. II. Barton, ' M.A. Thesic, 1943. 20. G. Zotov, M.A. Thesis, 1941. 21. Davenport, M.A. Sc. Thesis, 1939. 

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