Specific Heats of Some Hydrocarbon Solutions Citation Backus, Harrison Stout (1935) Specific Heats of Some Hydrocarbon Solutions. Master's thesis, California Institute of Technology. doi:10.7907/r6xy-6p78. https://resolver.caltech.edu/CaltechTHESIS:10222024-211548740 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Chemical Engineering) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Lacey, William Noble (advisor) Sage, Bruce H. (advisor) Thesis Committee: Unknown, Unknown Defense Date: 1 January 1935 Funders: Funding Agency Grant Number American Petroleum Institute UNSPECIFIED Record Number: CaltechTHESIS:10222024-211548740 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10222024-211548740 DOI: 10.7907/r6xy-6p78 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16809 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 22 Oct 2024 22:52 Last Modified: 22 Oct 2024 23:33 Thesis Files PDF - Final Version See Usage Policy. 12MB Repository Staff Only: item control page

SPECIFIC HEATS OF SOME HYDROCARBON SOLUTIONS Thesis by Harrison S. Backus In Partial Fulfillment ot th$ Requirements for the Degree of Master of Science California Institute of Technology Pasadena, Californla 1935 Introduction Hydrocarbons as they oeeur in nature are in general very complex mixtures. If one wishes to discover the ba.s1e relations governing their physical behavior, it 1S obviously beet to study firs t the Simple and work through to the complex. However, even a study of all the individ- ual ehemieal eomponents in natural hydrocarbon mixtures bould be inadequate , if one's aim is to use the results of such studies in aiding the petroleum industry. ledge of the behavior of mixtures is desired. Know- Consequently, in the American Petroleum Institute Project No. 37, those mixtures h ave been studi ed which would yield resul te capable of immediate application and also useful in more fundamental inv·e st1gat1ons of hydrocarbon behavior. The type of work which 1s reported here represents one phase of those studies. The specific heat data are only a part of those required to make up a complete picture of the thermodynamic behavior of given mixtures. However, specific heat values for subatances, apart from any other thermodynamic consid erations, are of direct value. Consequently, an examination of them may be of interest. It is the purpose of this thesis to set forth the experimental methods and results of studies on a few eompa.r ativ ely simp le mi xtures _. Only the speeifl~ heat of the liquid phase is d.e termined by the method here discussed. In the work of Project N.o. 37, emphasis is placed on studies of mixtures of oil and gas under various conditions 2 of pressure and temperature. The pressures go as high as 3000 pounds per square ineh .. In a specific heat calor- imeter, then, the bomb to hold the samplec must be able to wi thstanel this pressure .• Earlier work ha.d: been done using a calorimeter now discarded!. It eons1.sted of a steel bomb on a heat .. inS-u- lating mounting which eould be rotated( for agitating the contents)-· all eontained in a double ... walled jacket, having circulating pil 1.n the walls which was kept auto- matically at the same temperature as that of the surface of the bomb. After considerable work on developing the technique of -0peration of this apparatus, the er;J?or ill results was reduced t -o , at best, 1 .. 5 f.; and generally a bout 5 t -0 8 %a The main source of inaecuraey lay 1n the fa.et that the heat capac·1 ty of the bomb was about -fi,fe times that of the contents. 'Thus, the specif le heat capae:t ty ·o f the eon tents was ealcula ted from the diff ere nee of _two large quantities . Also the oscillation of the bomb to agitate the eontents ea.used forced convection o-f the air in the jacket,. and: any slight inequa.11 ty of tempe!rature _of jacket and bomb caused an appreciable heat transfer .. On the basis of experience obtained in the operation of this first ealorlm-etel', a new one was d-e sigtied am built .. The -essential changes made were to make a new bomb of hirrh strength and low heat capac'it.y, and to enclose this bomb in a highly eva.euated chamber. Also a. different type of insu- lating mounting for the bomb was used . The fer.mer mounting consisted essentially of a micarta. collar holdi!'.ig the bomb, supported by trunnions going through the walls ·of the jacket. 3 The steel backing for the micarta had considerable hea t capacity, and the surface of micarta. in contact with the bomb was. excessive. As .a result., there was a slow flow of hea t which made the time te reach eonstant temperature so long that ethe:r e:rrer.s became appreciable.. The new bomb is supportea: in wire-wheel fashion by th:ree pairs · or fine piano wires 1n a light steel ring which ts carried. on the It is designed for working pres$ures VP to about 600 pl;ltinds pe~ square inch, and its heat capacity is about one fi:fth to one half that of the contents. Since its working pressure limit is only 600 pounds~ the range of su'bstaneee and mixtures studied was correspondingly llmi ted. In v'iew ef the su:ecess in the use .o f speola1 .s teel alleys ·1.n the construction of the new light bomb, it seems feasible to build one to withstand 3000 pounds per square .inch, ard •thus to extend the range of study . With the present 1ns t:rument an aceuraey o.f 1 • to 1. 5% ls obtained! for the spec1t"ie heat·s of most systems . A considerable number of systems have been studied, but, for . reasons given below, 011ly two are reported here~ • ria ~tures Cb:osen for study Two series of mixtures have been eh.o sen 9',S subjects for this report. The first is a series of liquid mixt ures of propane and crystal oil, the latte:t> being a heavy , highly-refined, stable hydrooa.r·b on oil. The seco·nd series eonsists of liquid mixtures .o f n-<lrutane a nd crystal oil. These two were chosen for twa reas.ons. F irst, the pressure 4 range for these systems 1s suitable for the li p:ht bomb. Second, there have been de t ermined previously in this laboratory all the necessary supplementary isothermal data for converting the obServed: values of s pecific heat at constant volume to specific heat at constant pressure. M:ater .i als The propane used was obtained from t he l?h1lga.s Company. They ma.de a special analysis of th:ts· 'Tot of propane and .reported: Mone $tha.ne Propane Iaobutane 100% No,n e The normal butane was obtained from the same source. A $:pecial analysis of it showed; Isobutane N-butane Isopentane The crystal oil is a highly refined wtter-white 011. It wtis chosen for this and other studies becaus e it fulfilled the de·s ired conditions of a liquid. of rather high viscosity with a narrow range of polling point and compos ition.. It. is stable with respect to time and temperature, that is, meaBurements of its properties are reproducible 1n Spite of heating w:t thin the experimental range and in spite ·o f long s t and1ng.. l\.lso, its vapor pressur:e is not e.ppre-c1able wi thln the r ange stud1ed. follows: Some of 1 ta proper-t ies are as F FIGURE I G· 5 Sp. gr. •• Q/39 • 20 ( 100 F ). 0.8665 Gravity 0 A.P.I. {60°F ) 29.1 Viscosity at 200° F 40.5 - millipoises Aver . Molecular weight 337~5 Method a nd Apparatus The general method of measurement is conventional. A weighed sample of the subStanee to be studied is placed in a bomb. form. The bomb is shaken until its temperature is uni- A known amount of hea t is added electrically, and the correapond1,ng rise :ln t€ mp eratur E is observed. From thEse data a value of the specific heat at constant volume may be calculated. In figure 1 is shown a diagramat1c cross section of the calorimeter. The bomb ( B) is supported by three fine ste-e l piano wires fastened to the ring ( A). This X'ing is carried on trunnion bearings (D, H), allowing the whole . 0 bomb assembly to be os c11lated. through a.bout 90 . The space surrounding the bomb, within the j a cket (F) is pumped down to a vacuum of 10- 5 t o 10- 3 mm of mercury. The oscillation of the bomb is effected by means of the extendetl shaft ( H) . On the end of this shaft is fastened a steel bar or armature. It is free to rotate with the shaft within the flat cylindrical chamber shown. chamber is evacuated also. This latter Ou tside of th1B chamber is mounted an oscillating electromagnet ( G) . With the e,id of the magnetic coupling between the magnet and the steel armature, one is enable to get mechanical agitation in the 6 bomb, without any direct coupling through packing glan1s which would make difficult the atta:tnr.nent of high vacuum. The interior of the jacket is chromium plated, and the surface of the bomb is nickel plated in order to minimize radie.tion heat transfer clue to momentary differences in temperature. By maintaining the vacuum at or below 10- 3 mm of mercury, hea t transfer by conducti on and convection is reduced. to the position of a mi.now factor. The whole jacket ( F) is s1..irrounded by circulating oil kept automa t- ically at the proper temperature. The oil bath consists of a double walled can in which baffles are provided so as to giv ca,symmetrical flow of oil over the whole outer surfacB of the jacket (f). The electric heater for this oil is located within the circulating pump., so tha t no local 0 hot spots r' oceur in the bath. The temperature of this bath is so regulated that the inner surface of the jacket ( F) is at a.11 times during the run within about o.02°F of the surface of the bomb. When this condition existed, the eonve11tiona.l calorimeter curves were not drawn, for it was found tha t the temperature of the bomb would neither rise nor fall by more than o.02°F in an hour. This automatic control of surface temperatures de pended upon a. thermocouple device. One thermoceupl€ junction was placed on the outer surface of the Jacket ( F), and the other in series with 1 t was placed on the outer surface of th'e bom'h. The went two leads fr om this couple to a high-sensitivity galva nometer, the llght-beam of which actua.te'1 a photo-electric cell. It was this cell which, through relays, controlled the heaters A C FIGURE 2 7 in tne oil bath. 'Thus, whenever the tem{;lera.tu1"e of the bomb was rising during the measured energy input, the thE'rmoeoupl€ control would eaus e the oil bath to heat at exactly the same rate as the bomb. When the energy input c.eased, the bath temperature would become constant as soon as did that of the bomb. As a fina l aJ.d in ma. :l n t aJ.nir.rg t emperature stability, the whol e calorim-e ter wa.s set in an a ir thermostat which wns kept within :; 0 of the bomb temperature. Th1 8 gave the control system a chance to regulate over a much narr.o wer varie.tion. r ange. A detail d iagriun of the bomb is Shown in Figure 2. two bell ends (A, B) anrl The th € cylindric a l body ( C) were ground from bar stock of a s pecial high tensile strength steel alloy (90,000 l bs / s q. 111. tensile strength ). When f :ina.lly ready for assembly, the thre ads of the three parts were tinned , and during assembly, t he whole wa.s s weated together. In order to avoid leakS, no electrical leads were bushed through the walls of the bomb. The electric heater for g1 ving the measured enerrt.y input to the bomb was enclosed in a spiral of stainless steel tubing ( P), and. this went through the wall at a soldered joint. The thermocouple for the accurate measurement of the ' temperature of bomb and contents sas Emeas Ed in the deep well ( E), which extended into t he bomb about a third of its length. 'l'he samples of oil and gas were intro-: l ucE'..-0. through the connection and diaphram valve shown at the top~ ·The whole bomb assembly wei gh ed about 250 grams, having; a volume of 8 about 160 ce. The mass of sample was obtained by wei ghing the bomb before and after filling. Becaus e of the lightness of the bomb, errors in this operation were inappreciable. As mentioned above, the temperature of the bomb was measured by thermocouple. This w,zs a coppe:r-constantin couple, and , to eliminate stray e .m .f . 's, the oons tantin wire was all one piece from hot to cold junction. junction was in an agitated ice bath. The cold The couple wa.s cali bra ted by i mmersing a cali bra.t Pd mercury th ermometer in the surroundi ng oil bath, and meas uring the thermocouple e.m.f. af ter the s ystem had been stead y for a considerable time. This method assumed t ha t the bomb a nd ·ba th were at the same temperature, a nd this as s m,1ption seemed to be born out by observatio n . At any :rate, any g iven point on the calibrat ion curve should be a ccura te to a bout O ..o4°F, and a smooth curve drawn t hrough all t he points should allcnv one to calculate temperature ris es somewha t more accurately .. (') The usual temperature rise was about 10 F, and so the error 1n this measurement may be about 0.2%. The potent- iometer used in this work ws.s similar to the Wolfe type instrument, a nd it had been calibrated against a Bureau of S tandards instrument. One could measure tem-peratu:r'€ 0 . variations e asily down to 0.005 F with the cold junction at 32°F. The energy input to the bomb was de termined by mea- suring power input a nd time of input. The ti me of input was standardized at 20 minutes a nd was mea.s ur ed by a. counter U Cf) 0.98 1.00 1.02 100 I 0 1 I FIGURE 3 DEG. TEMPERATURE 0 160 0 140 120 0 F 180 - 9 run by a synchronous clock motor. The wattage was determined several times during a run by measuring the dir€ct curre nt voltage at the terminals of the bomb and. the current flowing. A device was arranged so that the watts input was essentially constant during the 20 minutes, and so no integration was necessary to arrive at a total energy value. These voltage and current values were determined by the use of a Leeds and Northrop Student Potentiometer and were probably accurate to about 0.1%. The heat capacity calibration of the bomb itself was carried out with the bomb filled with hydrogen a t one a tmosphere. Here some difficulty was experi enced in attaining equilibrium between the main mass of t he bomb and the thermocouple. After several tries 1 a sat i s'factory calibration curve we. s obtained. To ch eck it, how ever, a run wa.s made on the specific heat of wi:i.ter. of t his run are s hml\Tn in Figure 3. The results The calibration that was finally used in s ubs e guent calculatio r:s may 'be in error · by as much as 3%.. The resultant effect on the SpEcific heat calculated for the contents, was an error of 1.5 to o . 6%. Thus, the factor which contr'.'tbutes most to t he experimental errors 1s the unc ertainty in the heat capacity of t he bomb. This error would make al l the values wrong by s ome abs olute amount. If there were no other appreeiable errors, the experi menta l data would s till lie on smooth curves. Since the y do not, it is Evident tho.t there must l,e other contributing factor s ~ They probably arise fro m the technique of opera tion . After the bomb has been 10 standing at equilibrium fo~ half an hour, with the photo- el€ctr1c control working perfectly, one suidenly turned on the hea t to the bomb. The sudden flow of heat to the surface caused the control to hunt, and because of the natural lag in flow of oil to the control junction, the hunting was sometimes disastrous. The same trou ble aros e when th€ .hEat input. was cut off. Various methods of oper- ation were tried to overcome thls d ifficulty, an:1 by care it cou1r.'l lare:ely be eliminated. However, it is nearly c ertain that this was the chief cause of s cc9, ttering error in the earl1er runs. One other effect which shou ld be not e,:!. concerns the nature of the contents of the bomb. For very fluid sub- stance [; E! uch a.a li c!uid propane, after a g iven heat input had been c ompleted,the bomb and contents reached their final equilibrium temperature very quicltly, s a y within Six minutE>S. On the other hand~ for viscous substances, like thE crystal oil used here, the temp ere.tur e would a pproach its fina l value in a s lov,, as ymptotlc na.nner, sometimes taking; a.s lone as forty minutes to r each a satisfg,ctory ste ady state. S ince t he viscosity of the s e mixtures de cr€aS ed cons idE:-re.bly w1 th temperature, one mi ght expect grea.tE-r consistency of values a t the highcc t emperatures. Fxr)e-rimen t ally this Vi .""!, S f ound generally to be the case . As a m.at te;r of s t andar5. technique, however 1 the bomb was allov.•ed to sta nd f or about forty minut es after the t wenty mi nu t es hea ting. i.' h iS r;av e more compl ete assuranc e of the atta.ln.rnent of equ ilibrium. I N- BUTANE IN CRYSTAL OIL 100 140 180 0. 7 > U 0.6 0.5 PROPANE IN CRYSTAL OIL 100 140 TEM P ER ATUR[ 180 °F DIRECT EXPERIMENTAL DATA SPECIFIC HEAT AT CONSTANT F I G U RE 4 VOLUME ll The specific heat as calculated directly from the above m€asurements is a specific heat at cormtant ·volume. However, it is not Cv for the liquid 1n the bomb. In a bomb of this type there must always be some gas space: a.nd consequently t.wo phases in equil1br1um. Thus, whenever the bomb is heated, some of the more volatile component. will pass out of the liquid phase, and: the heat absorbed in this vaporizBct1on will a:ppE>ar to increase the specific heat of the contents. The larger the gas space pres e:nt, the greater will be the magnitude of this effect. Thus, for every c1if:f.€re:nt smnple, Cv as measured will be different. For this !'68,Bon, no direct ex · :- erimE'mtal data have been t abulated.. An i.dea of the accuracy of t h e Geasuremex:r~r: J may be gained from a.n examination of Figure 4. From the ·smoothed curves shown, values have been taken and converted to l!:l"peciflc heats for the liquid in the concien,'=3ed region. at . a pressure Ol'1ly 1nfin1 tcs1mally erea.ter than tlw.t at which thE, flrst trace of e;as is 11 be.rated from the liquid phase ( the bubble point). It 1s the purpose of this section to indicate the opera,U.ons by which thrse conversions were macle. •All the data for them were obtaine::1 from pressure-volume-temper- a ture data for the substance in question. First let us consider the case 6f' a pure compound., such as butane, since itn treatment is somewhat different from tha t of a mixture. For the heat abSorbed by vapor(1) ization, the following correction is made • 12 ½X2-L1x1 AT i- (rLx) mean { I) , c.:r is Cv in the two phase region but corrected for vapor1za.t1on Lis the latent heat. o:f Yaporization xis the quality o:r fraction of mass ln the gas phase 4 Tis the rise in temperature of the run 1n ·questton 1 and 2 r ef1:r to values at T1 and T?, the ini tie,1 and . final temperatures for the run L may be calculatE:d f'rom vapor pressure data and the Clapeyron equation. X: the qualrty, may be evaluated from a consideration of the apec1f1c volumes of the two phases and the specific volume of the system in the bomb. For this 1 t may shown from a simple balance of masses and volumrs tha,t x= v1rv1 Vg -VJ. Vb is the sp. vol. of the system in the bomb v1 iS the Sp. vol. of the 11qu:td ( II) Vg 1s the sp. vol. of thE vapor All these and the following corrections are best made by calculating a few correction terms and pJ. otting them against temperature and using the curve for correcting all values across the temperature range for that particular substance., Next the heat capacity of the gas phase must be considered. When vaporization has been accounted for, we may write for the specific heat of the two phase system w 0.9 z <i Q_ cs 0 a: Q_ 0 -::) 0.8 CV UNCORRECTED a _J LL 0 I- 0.7 <i w I u LL u 0.6 w Q_ (f) 100 140 180 TEMPERATURE °F FIGURE 5 13 -... C-Cg:x ( III) 1-x where x ls quality. 'Fihen the boml:i 1a nearly full, x is very low, and t;he cofi."ection is almost neglig1 ble. A very rou__'sh guess at the value for Cg,,the specific heat of the gas, will suffice. ~!lb.en this cor1°eetion has been applied, we have the a peeific heat of t h e 'liquid under saturation, usua lly written C8 • This qu antity i s cl escri becl simply as ( 1/w) (dQ/d'I) under- L'Ubble point cond1 tiona when in infin1 ... tcsimal tut cons t ant amou nt of gas phafle iS pres ent. convert from thls to Op for t he To liquid just above bubble (!) poi nt pressure, we wlll use t he rela.tion ( IV) where L :ls t he l a tent he nt of vaporization V fF; vl is th E Sp. vol. of the vapor la the sp. vol. of' the liquid. The partial derivative iB the thermal expans 1 o·n. of the liquid as constant pressure, and may be evalua too: by tak1ng slopes on the curve of saturation volume vs T fo-r the saturated liquid~ This convers ion term is of quite appr<:M. a. ble magnitude, a n<l care is necess ary in EfValuating i t .. Ar idea of the size of thes e corre ction.S may be gainc-d f rom Fi pure 5. In it are sh own for the case of - propa ne:. (1) Cv , s pecific hE=a t a.t cons tant volume as experi menta lly l-4 determineo., before any eorrection terms have been applied. It 1s to be not€-d t.ha.t this is not the Ctr for the liquid at the bubble poi nt. (2) Cs, the specific heGt of the liquid at the bubble po:lnt as defined: above. (3) • CP , the speeifie he,at .at constant pressure for the eonclensed liquid at a pressure just a bove bubble point pressure~ The fact the the Cv and C8 curves cro:1s each othe:t' ts uriusua:t. but 1s read ily explained. Ordinarily, by reason of vapori- zati on, tbe apparent specific heat Cv is greater than the specific he 0t undE= I' saturation condition,g ,G:;. ·Ho~rever, 0 with p1"opan€ ,. 1n the upper temperature ranp;e, the liqu id is expanding so fast with rise in temperature that the vapor spa ee is actually decreasing.. A c.aleulation of t he quality x by the eque.tion ( II) r::tven above for it, Would show that the qualtty was decreasing with tempera.tm:•e ri se in this range. This means tha t with this ri s e, some pl'opane is condensed. Heat evolution attends this proces s, and. SQ the appe,rent specif:Le hea t Cv is lower tbe..n C8 , mes.nine: tl:lat the aurves rm.is t cross somewhere 1n th e higher tempera~ure range .. The reason for the increasing correction for CP may be sse-n from rquat:ton (JV) used above, written 1n a different form: (-H) {V) sat As tl1e critica l point of propane ls approac':-:ied, the derivative (o v/"<, T)P finity, and so for the liquid 1s approaching in... (CP - C8 ) is likewise approa ching infinity. 15 .At first glanee, also, i t may seem strange that Cv is greater than Gp in the lower temperature range. It is not correct, however, to make this comparison. The Cv Shown, it will be remembered, 1s the experimental value for the system 1n a different state than that f .or which Cp is shown. From an inspection of Equation (VIII) given below, it may be seen that Cv, the specific heat of the liquid on the single :phase s:tde of the bubble polnt, 1s a curve lyinr; continuously below Ca by an m.a.ount equal to T( tJp/ ~T)v (dv/c1T) 8 a.tn , where Urn (op/ o T}v ls for the liquid on the stngle phase side of the bu'bt•l e point. This term for condensed liquids at constant Yo1umc is! of course, quite 1~.r~e as compared w1 th the same der:tvative in the two pha~ie region, and the correction would p::c-o'ha.bly throw the Cv curve co!1Siderably below the C8 curve. At all e 1rents, the three curves ( Cp, CE ar.d Cv) for the single phase system at bubble polnt would lie one above thf.~ other with no crossing over. For mixtures, the calculation is slightly different. l!'o take care of the two phase corrections, we may use the convenlent equation: (VI) By its use we may convert the obs crve1 Cv to thE Cv when o:nly an infinitesimal En.nou:'t of gas phase is present. For mor::j t of the mixturE:S s tuclied, the volume of gas space in the bomb was cor:1paratively small, and the fraction of the gas-e ous comp onent which \\'as in the gas phase was also small. Consequently, the composition of t he liquid phase differs only very slie-.htly from that of the system as a whole. i~,; A conmequence of t his is that the prei'.l s ure exist- 1n the bomb was only Slightly less than the bubble point pres sure for that mixture. Now, sine,e the pressure remains essentially constant as the volume is cha nged , their derivatives against t emperatu1"e Will also be confJtant. Also (_..a:_o/ ~ ~) v will be clos ely equa l to (d 2p/dT 2 ) 8 atn· From a plot of bubble point pressures against temperature, fo1· t he given mixture, one obtains the first d er i vative (dp/dT\~ a t n a nd from a plot of this against temperature, one obta ins the des1l"cd second del"1vat1ve. Now, s ince this der:Lva tive docs not change apnreciabley with volume , we may write t be equa tion as S ince t h e volume is being d. eereas cd fr om bomb v olu:.,YJ.e to bubl1l e p a i nt volu:mE , Cv f or t he l i qu i d j u st on t h e two phas e s i de of t h e bubble po int will be s mall er t..rian the obs srv ed c,,.. I-laving obta i ned CV for t he liquid Juo t on t he two phas e s ide of .t he bu bbl e p oint, we maJ use t wo thermody- namic :rela tions to convert to Cp for the l iqui 1 jus t on the one ph2s e side. T. (_c)1') . ( d 1-;) .• CP ~P dT satn (VII) (VIII) 11 Since we are now dealing with the system Still in two phases, with only a minute amount of gas phtis e, 1 t is quite closely true that ~) ( 0 i. 1:: P (dv) satn • aT a:nd ?fi th the.:.: e equa lities. holc11ng, we may E:limina te C3 and Wl'i te Cp C V + 2T ( dv) dt • satri (d ~ } (t Jl.) • cf'f/satn The volume der:1.va.tiVE·S may be obta ined from Slopes on a plot of bubble point liquid volumes vs temperature for the mixture. The prrssure c1or1vat:tve is 1i1rcv:1s e obtained from a bubble po:tnt p:t•essure va temperature plot One must be watchful 1-n the use of equations such as the s e to make a clear distinction between px•operties on the one phan e sid e and one t,.11.e t wo phf'.S e sid e of the bubble p oint. T'Jost o:f the properties, Buch r-:s CP :1nd Cv- a. nd these derivatives: undergo c1iscont.inu1 tier~ as the bounde,1--;y is cronsed. Ho".:ever, Cs is a property wh:lch has s ignif1c ance only on the bounda,ry, but the concept is still valid at infinit rsimrll dist :,_nces on either 8ic1.e of the boundary. It. j_B for t h is re a.son that spec1flc hea ts were converted from Cv for the t wo phe.se s ,yste m throup:h Cs to I. 0 l------+------+-----+---+--r-----7 0.91---------4------+------+--+-------t----------i z 0.8 1 - - - - - - 1 - - - - - - - + - - - - - - - l - + - - - - - - - - - l f - ? ' ' - - - - - - - , 0 I- <{ 0::: 160°F :::) I- <{ 1/) 1- o.7 l - - - - - - 1 - - - - - - - + - ~ l - - - - + - , . - L . _ - - - - - l f - - - - ; , , " L . _ - - - i <{ u Q. 0.5 20 MASS 40 PERCENT OF PROPANE 60 80 IN PROPANE- CRYSTAL FIGURE 6 OIL 0.9r--------+------+------+-----+----------1 0 .8r--------+-- ----+------+-----+----------1 z 0 0. 7 - - -- - - + - - - ---+------+-----+----,,', I- <! 0: :::::, I- <! en u Q. 20 40 60 80 MASS PERCENT OF BUTANE IN BUTANE-CRYSTAL OIL FIGURE 7 18 C-u for the liquid one the one phase Side of the boundary. ii. numeric-a l ex.ampl-e ., carrying theHe cal·c ul!1tions out for one specific case, is given in an append.ix. In Figures 6 and 7 .are shown the results of the studies on the systems propane-cryr1tal oil and n-butanecrJ1S tal oil respectively. 111e experimental points are not shown, since all the pointi1 lrty on the Hmooth•.lrawn curves Shown for the butane system, and lilrewise far the propane system with one e:xcept1011. The mixture containing 13.lilti propane was systematically low by 1 to 3%. This a~ems almost, E>vident from a rough inspection of the plot of the original data (figure 4). However, in spite of this one poor set of data, the remaining material is complete enough so that a very satisfactory curve again.qt composition may be drawn. In Tables 1 and 2 are recorded values taken from these smooth curves. The value for pure propane at 190 oFis not shown because experiment.el d.ata did not extend to this temperature, nor near enough to it to make an cxt1"apolation warranted. The final overall maximum. error in thene figures is estimated to be 1.5%. lf'able l Propan-e-Cryst.£>,1 oil System SPFCIFIC BFAT AT CO'.NSTA:NT PFYSStJRj, F OR THI BOBBLE': POINT 1JQ,UID I-;:e.ss percent of Propane in· the mixture Temp Op ot O,o 20% 40% 60. dp 80;t 100% 70 0.442 0.l~61 0.500 0.536 0.575 0.617 100 o.4-62 o.489 0.526 0.567 0.612 0.661 130 o.482 0.512 0.560 o.617 0.679 0.746 160 0.502 0. ·538 0,.60~ 0.689 0.785 o.886 190 0.523 0.576 0.667 0.815 Table 2 -- - .. N... butane--Cr_ystal Oil Sys tem S :?FCH'IC HFAT AT COTu"ZTArTT PRFSSUR1f FOR THE BUBBLF PO INT L IGrJID Maas °F percent of Butane i ne the nixture ot I 20% 40~l c1. .• I~ 6o 80;f. 100% "'(0 O.lf.l~~ O.lr.61 O.ll83 n ~05 -_, • ::> 0.530 0.564 100 o.1:t-62 o.4-79 o.4-98 0. 51.9 0.550 0.601 130 o.48~ o.498 0.517 0.538 o.. 511i 0.611-1 160 0.502 0.521 0.541 0.5611- 0.605 o.699 190 0.523 o. 54.5 0.567 0.595 o.6 1+5 0.758 Temp 20 Discuss 10.n It 1s evident from Figures 6 and 7 tha t the specific heats of the components cannot be considered as additive. If they were, these curves would be straight lines across the whole range of composition. At the lower temperatures th€y seem to approach th.is eondi ti on, but the dep::1,rture is rapid for any appr eciable .r ise above 70°D'. nevertheless, regular in their behavior... fi1e y are, 1 ro 1:nvest:tgate 1 the possibilities of this regularity, recourse is made to 4 a quantity called the partial specific heat capa city} ) This heat capacity is a property of a component in a mix-t;,ur-e whi ch plays a role thermod ynamically identi ca.l w:lth the corresponding heat capacity of the s ame component when in the pure state. It is defined by the relation (t;lt - C1 This says that t '.: e parti !J.l s pecific heo.t capacity 'c1 of component 1 in a m.ixt u:c e :ls defined as the rate 9f incrsase of he r,t cap.:~ci ty of t he mixture wl th t he acU.i tion of co:!lponent 1, thE: amounts of t he cmn: ·,oncnfs bd.l1f'; , for the purpo, e of this work, conB idered on a mass barns. are There correspondlng expressions for the other conrponents of the mixture. ~~hese derivat:lves, in the ca5e of t h E:, mix- tures studiec1 here, rn.ay be obtn. ined d ire ctl;f from the cornpo □ i tion diagrams, ·:.- 1e;urc;s 6 and 7 w The 1n~thod u sed is call ed the "method of intercepts II and is desc.:t~ibcd. else- ,,,,, I _,,,_,,,190°F / / / / / 0.8 / / / / f<( w I ---- / ,,/ o.6 ~ t:=:--G::: ~ PROPANE / 160°F ~ ~- 130°F 100°F L--- 70°F 0 u ._ ___ 190°F ----- zC~60°F w Q. (f) 70°F _l 0.4 ' ~ .. '- ---- .......... ~ ", '--- 100~130°F <( f- CRYSTAL OIL 0:: <( Q. 0.2 ~ ','\ '\ \ \ \ \ \ ------- \ \ 20 40 60 MASS PERCENT PROPANE FIGURE 8 80 o.sL- - -+-------+----+-------t-- - - , I l suTANE ~~ 0.6 t~~~~~1;;;;;;;~;;;;~~~~~~~~~~~=~=-1 70°F 1-~----+-----t----- u L.... U 0.41--- ----l------+- - - - + -- -----'~-l;::---- ------i w Q. CRYSTAL OIL U) _J <r ~ 0.21---- ---l-- - - - - +----+-----t--7"""""'~ ~ 0.01-------+---------l-----+--------t----tt 20 40 60 80 MASS PERCENT BUTANE FIGURE 9 21 (4) where . The results of a determination of such partia l heat capacities for the propane and the butane mixtures. a.re shown in Figures 8 and 9. The lower family of curves in each figure gives the partial specific heats of crystal 011, while the upper family 1s for propane and butane respectively. Since hydreea.rbons are relatively nonpolar subSta.nces, we might see how these quantities compare with those for the ease when the mixtures behave as perfeet solutio?}S. In the latter case, the heat capacities would be strictly additive, and the derivative given above would be constant across the whole composition range, merely by definition of the additivity of properties. It will be noted that 1n the butane crystal oil system, the partial specific hen. ts of both butane and crystal oil are practically constant up to about fifty mass percent butane. This means that within this range and for a given temperature, the specific heats of all the possible mixtures might be calculated a value for the constant partial for butane and one for arystal oil. Such 1s not the cas e for the propane-crystal oil system. The partial specific heats are cha nging even in rather dilute concentrations of propane. For propane, however, the regularity lies on the other side of .the diagram. Here the partial specif i c heat for propane 1s quite constant from 100% down to 50%, while the corresponding quantities for crystal oil increas e by about 2 to · 4% in this range. Stnce these mixtures behave as perfect solutions within certa in ranges, with respect to the property of 22 heat capacity, one might sus pect that perhaps they also obeyed: the laws of perfect solutions with. respect to other properties. There is some evidence, based: on data obta ined in this l a bot'atory, thfl t the partial specific volumes f or the butane-crystal oil system show the same cha.racterie t 1cs as have been pointed out for the partial specific hea t s for this system. In order to see whether these curves fulfill certa in conditions required of all partial quantities, one may u se the relation (XI) ( 4) where N1 and N2 are masB fractions of the components 1 and. 2 respectively. In very dilute solutions of com~ ponent 2, N2 approaches zero. approa ches zero. Then the ratio N2/N1 also This means that either the derivative ( o C1,/ ~ N2 ) is approaching zero, or that the other derivative is approaching infinity. For the ca.f, e of heat capacities, the former holds. That this d eriva tive iS a.pnroe.. ching zero means that in mixtures with hi r:h concentration of component 1, the change in the parti al specific hea.t of component l with che.nge in concentration is approaching zero, 1.e., the curve comes in to zero concentra tion horizontally. This iS clearly the ca::, e for mix- tur es low in butane, where the partial for . cr.Ystal oil is quite flat. Als o for propane mixtures low in crystal oil 23 the partial for propane is quite flat. For mixtures low in propane, the crystal oil partial is reasonably flat near zero, but for the la.st case--mixtures high in butane, this ia so far from true that one is led to suspect that the ab$olute values for butane specific heat are a little too high. If such is the ease, then a r ~construction of curves ,using slightly lower ·values for butane, would change-the slopes so much that the range in which the partials are constant would probably be extended considerably beyond fifty percent. Corresponding to the case of simple add1ttv1ty, the equation in the case when partial quantities are used 1s (X!I) where N indicates the mass fraction of the component; C the appropriate partial speci_fic heat; and C the re- sultant specific heat of the mixture. By the use of this equation and. data such as presented 1n Figures 8 a nd 19, one is enabled to calculate the specific heat of any mixture in the system. Of course, the same thing eould be done by direct reading off of Figures 6 and 7 , but for the case of butane, the equation permits the evaluation of specific heats for mixtures up to 50% butane without the use of any graph at all. In the following Table 3 are listed the partial Spee1fie heats of the components for mixtures of butane and crystal oil, the values being those which are constant for all mixtures up te 50% butane. 24 Table 3 Partial Specific Heats Temp °F N-butane cp Cr;v.:stal o l l cp 70 0.44 0.54 100 O.l~6 0.555 130 0.48 0.57 160 0 .. 50 0.60 190 0.52 o.635 For any concentration with the range, mere substitution of these values in the equation ( XII) will give the specific heat o-f' the mixture to within about 2°fo. It 1s interesting to speculate on the us e of such obs €rv-ud partial quantities in other hydrocarbon mixtures. For instr: m ce, it is quite w:1.V:in the :realm of poHsibility that the part1 e.l specific h€at of butane or pro \1ane in crysta l oil 1s approximately the s a me a n tha t when they are dissolved in some other heavy hydroc,irbon oil. The possibility of such a ge neraliza tion would be interesting to invest igate. It sho uld be said that interpreta. tlo:r of the :o e partial specific heat diagrams must be made with caution. In diagrams li ke Figur es 6 and 7, whenever the r a te of curvature is high, the tane;E nts which are constructed on them for evaluating the partial quantities a.re necessarily rather in:.'l ccur0.te. But, for the most part, the accuracy is 25 sufficient to warrant such conclus1ons as have »sen drawn here. F or the benefit of anyone who mi ght w1 s h to use the data here pr es ented , a final remar1r should be mad e conc erning Cp It was defined as the specific hea t a t con- sta nt pressure for the liquid as a pres sure jus t above bubble point pres sure. This reference state was chosen because it was considered as the least arbitrary of the possible choices. Values of CP calcula ted for this state also havE· the advantage that t hey are usable as values of CP for the liquid in que s tion at pressures a. great deal h1gh€r than the bubble point pressure. The error made in using the values at higher pres sures may be corrected. or estimated by the equation ( XI I I) Thus, for propane, a r a ther hl 0hly expansive liquid, at 100°F an increa s e of 200 pounds per square inch a bove the vapor pressure decreases the s pecific heat from o.661 to O.65. This is an extreme case , however, and the general diffsrence for ·natural heavy hydrocarbo n mixtures is much less. For n- butane, the next bee.vier member , t h :in in- cre c1se in pressure a t 100°F will caus e the Sp E,cif:i. c heat to drop only from O.6O1 to 0 .598. Consequently , it ma y be s een that the values listed e.re quite usabl e over a wide range of pressurs above bubbl e poJnt pressure . 26 Summary The specif io heats of two se.ries of liquid hl7dro- carbon mlxtures have been determined. Th~ components of one series were propane and crystal, a heavy, highly refined oil. The component.q of the second series were n•butane and crystal oil. The measurements were ma.de as specific heats at constant volume for two phase mixtures, and thes~ were converted to specific heats at con,.catant pressure for the liquid. The results show that the specific heats of the components a.re not additive 1n the mixtures. Ho.w ever, by the use of the concept of partial specific heat~, decided regularities in the two series were made apparent. On the basis of them, it was made possible to iniicate a simple method for calculating the specific hea.ts of butane-crystal oil mixtures. 27 Apoondix Typical Numerical Caleula.tion The case ohoaen 1a the mixture of propane and crystal oil., containing 73.33 mass% propane Because of space limitations, the graphs which were used 1n these calculations cannot be shown, but the manner of thtir use will be indicated. Calculat1on of specific heat at constant vol. for the system as it ex1atr1 1n the bomb One point: 6.084 volts voltage across the hea ter current time Q.: energy input ,;;F~It ~ 0.2680 amps 20 min. 32.6! watt-min. or l.856Btu 0 Mean. T:: 101.5 F -- 0. 1637 Btu/°F Heat capacity of . the bomb taken fr om a da11brat1on curve at 101 •:Jr::Op. : Cbomb-=- O• 0843 Btu/OF · Heat capacity of contents =-0.1637-0 .. 0843 • =0 .. 0794 Btu/OF Mass of contents -; 61 .. 182 gram, 0.-1349 1 b C : V 0,.0724 = 0,5886 0.1349 at 101.sO,F Conversion of Cv to Cv just on the two phase B1de of the bubble point. The relation 1s Now (M}., ( ~ ~• ), :: T ( do~~l and (if}sJ-are quite nearly equal 1n the two phas e region, and as was noted in the -: 11scus0ion, this derivative doe$ not vary appreciably with volume 1n the range of volumES considered. And . so v1 e may write .28 From a graph of bubble point pressures va c.ompos1 t1on are obta.lned values for the 73. 33% mixture at a These a re shown in column II series of t cmpe.r atures. below. A plot of thes e against temperature gives a smooth curve on which tangents may be drawn, g1v1ng(j-~~own in column III. . In a similar manner, on a plot or'(j{} againat T, one obtains the second derivative shown in coltunn IV II l r·f p ~ IV IIJ V (Ii~>ft T'R Ti (:~J tt/i..,. VI ~J -.ff/4: vn: (vi,....b -V51t) V!II IX (V~J-) JtT(j~I' 1--, Cf•t.s,;J 70 123 1.80 l .661t•l 530 .02495 J>l724 .1517 0281 100 187 2.34 2.00 560 .02723 Pl496 .1676 0310 130 267 2 .. 98 2.38·· 590 .03038 .0118J .1672 0310 160 367 3.79 ? -· 94·· 620 .03425 .00794 .1447 0268 190 502 4187 4.,00·- 650 .04025 00194 .0501~ .... 0093 . . ·- · 1 • • From a. graph of saturation volumes against compos1.t1on are obtained values for the 73.33% mixture at a series. of temperatures-, shown in column VI Mass of sample - 61.182 gm; 0.1349 lb. Volume of bomb-:; 16L.2cc::. 0.005692 cu.ft~. .: Sp vol pf contents .. 005692+C.1349::; O. 04219 ft.1 /1 b/ Subtracting from this the s aturation volumes , we obtain column VII.. Mult1ply111..g the values for(~), T and (V-Vs,J-J all together gives the d€S1red correction terrn,column VIII. To convert th1e term to heat units, we convert to foot- 29 pounds and then to Btu. Thus for the term at 70.0 0.1517x144+777.6 ~ 0.0281 Cv - Cv sat-::. Conversion from Ov on the two phase side of the bubble po1nt to CP on the one phase side. _ C Cp - The relation 1s -+ .2. V T ( ~\ (d(] <J(J~t .,,.,,. We alre ady have values for (dp/dT)sat, and also values for Vsat fol? the liquid. One plots Vsat against temper- ature and takea derivatives .. : shown in column III below. II I IV III r:fl~t (;{)JJ" T"F ;"~ VI V zr(#J.if) c,-c., c-ft 1~ /°F ,, -7 0 1.80 6 •75 X lo·S- 530 0.1288 0.0239 100 2.34 8.80 .. 560 .2306 .0427 130 2 .. 98 11.37 .. 590 .3998 .011+0 160 3.79 15.54 620 . 7303 • •. 1352 190 4.,87 27.05 650 1.7126 ---- - - . .3171 The next operation is simply to multiply the fou~ quantities together ')._x Ti(';}-;-) 'f (#). Again, , ~- ~ .convert tqis term to heat units, we multiply by 144/777t 6• values are shown in column VI .. Thus for 70°, 1. 80x6. 75xlo~ 5x530x2 = o .1288 • and 0.1288.x 144/777.6 = 0.0239:: CP - Ov Apr,ly1ng these correc t ions to one cas e: For 70° , the smoothed ,a-0,lue fo.r Cv uncorrected is 0.568. Cv 6 at = 0. 568 - 0 •028 ::= O. 540 Cp ~ o. 540 + 0.,024 ::; 0.564. References (1) Bureau of Stamards Paper No. 313 ( t) A convenient listing of the r: e general functions is given in Perry --,.Chemical Engine,e rs' Handbook11 McGraw-Hill ( 4) Lewis and Randall n Thermodynami ca 0 MeG:raw-H1ll Acknt1>wledgement • The author wiahes to thank the Arneriean Petroleum Institute and its individual members for their generous sponsorship or this research. For bis ei.ear-s1ghted advice and instruct.ion 1n conn:eet1on with this project, the author extends an admiring appr0cie.tion to :Or. w. I<J. Lacey. To Dr. B. H. Sage, for constant gu1danc€ in the rugged domain of thermodynamics and friendly coop€rat1on in work, all my thanJrs.