ANALYTICAL CHEMISTRY
938 These calibrations have been carried out in t h e following way: Pressures exceeding 1 mm. of mercury were read directly on a proper mercury-filled U-manometer (which was, however, badly attacked when the gas was bromine). From these readings an Alphatron gage (6) was also calibrated, and this manometer, because of its linear range at lower pressures, could be used as the reference below 1 mm. of mercury.
Table 11. Tracer Hydrogen Coal gas Methane Carbon dioxide Methanol Ethyl alcohol Ethvl ether Acetone
Leak Hunting
Gas or Air Saturated with Vapor 2.7 1.8 1.8 1.3 1.1
Liquid
..
.. ..
T h e tests described here have been performed with a n artificiaI leak in a borosilicate glass capillary which was exposed t o gases or liquids. T h e evacuation was performed by means of a molecular pump, giving a pressure inside the manifold of 5 X lo-” mm. of mercury. A conventional and a feed-back manometer were used, and there was no significant difference in behavior, except for t h e much greater speed of t h e latter, which facilitates t h e work. Table I1 gives the relative increases of t h e readings, t h e deflections of the meter pointer being given in terms of the air pressure scale. Here, 1.0 means no increase (sensitivity). These results agree roughly with those recently reported by Blears and Leck (2). T h e feed-back manometer has an additional and very outstanding advantage in that it remains very sensitive u p to atmospheric pressure on tracers such as hydrogen and coal gas.
‘16 7
...
2.7 1.4
14 16
Figure 11 clearly shows that the solvents that are most frequently used in vacuum techniques all have molecular conductivities which far exceed that of air, and often that of hydrogen too. Their molar conductivities are, however, smaller, and the range of pressure covered b y the manometer is more limited upward, because of the smaller mean free path of these compounds, if compared u-ith air. T h e curve for water vapor coincides below 0.05 mm. of mercury with that for hydrogen ( 5 ) )and boron trifluoride and carbon tetrachloride coincide belox 0.2 mm. of mercury. When dealing with vapors, the feed-back manometer thus cannot really do more than the Alphatron does, but it was found that its stability was better-for example, on water vapor-and, except that it lacks a linear calibration curve, it is a convenient substitute for the latter gage. Leak Hunting. Single-tubed manometers, where no differential action with a tracer gas or liquid can be used, are by no means very effective in leak hunting. However, circumstances often arise in which the best must be done with the gage that happens t o be available, and efforts have therefore been made t o find suitable tracers.
ACKNOWLEDGMENT
The writer is indebted to the editor and t o the publisher of Applied Scientific Research, Delft, Holland, for permission to take over material from his previous articles. LITERATURE CITED
(1) Blasco, E., and Miranda, L.,Rea. Sci. Instruments, 21, 494 (1950). ( 2 ) Blears, J., and Leck, J. H., J . Sci. Instruments, Suppl. 1 (Vacuum Physics), 20 (1951). (3) Dardel, G. v., and Ubisch, H. v., Tek. Tid. (Stockholm), 82, 203 (1952). (4) Daynes, H. A., “Gas -4nalysis by Measurement of Thermal Conductivity,” London, Cambridge University Press, 1933. ( 5 ) Dunoyer, L., SCAD, 136 Rue du ThBatre, Paris (15e),personal communication. (6) Dushman, S., “Scientific Foundations of Vacuum Technique,” Chap. 6, Xew York, John Wiley & Sons, 1949. (7) Farkas. 9., and Melville, H. TV., “Experimental Methods in Gas Reactions,” London, Cambridge University Press, 1939. (8) Kenty, C., and Reuter, F. TT., Jr., Rev. Sci. Instruments, 18, 918 (1947). (9) hlinter, C. C., ANAL.CHEM.,19,464 (1947). (10) Spangenberg, K. R., “Vacuum Tubes,” p. 768, New York, McGraw-Hill Book Co., 1948. (11) Ubisch, H. v.,Applied Sci. Research, A2, 364, 403 (1951). (12) Ubisch, H. v., Nature (London), 151, 927 (1948). (13) Weber, S., Ann. Physik, 54,325, esp. 338 (1917). RECEIVED for review April 24, 1951. Accepted March 19. 1952.
Measuring Specific Heat of liquids at High Temperatures Small Sample Apparatus NORMAN H. SPEAR‘, John B. Pierce Foundation, .Vew Haven, Conn.
A
DEFIR’ITE need for specific heat data in the temperature range of 100’ to 300’ C. arose during the experimental development of engine coolants and other heat-transfer liquids. Knowledge of moderately accurate specific heat values for smallvolume chemical fractions in this temperature range was helpful in evaluation of the heat-transfer characteristics of the experimental liquids. Extrapolation of low temperature specific heat curves was not considered satisfactory, and review of the literature showed relatively few experimental values, and these generally not in good agreement. This is caused, in part, by the general lack of elaborate apparatus needed for entropy and enthalpy curves, when this approach is used, and the inherent difficulties of pressure, evaporation, and surface coefficients when direct measurement methods are used. Solution of the problem required the development of a relatively 1
Present address, Colt’s Nanufarturing Co., Hartford, Conn.
simple calorimeter which x-as capable of measuring specific heat of nonmetallic liquids a t constant pressure in the 100’ to 300” C. temperature range while utilizing liquid volumes on the order of 50 ml. The calorimeter was required to minimize difficulties encountered in direct measurement methods and yield values x i t h an accuracy better than 5%. The liquids mentioned in this paper are experimental heat transfer agents developed by the Pierce Foundation. PRINCIPLE OF THE &IETHOD
Review of the basic methods of direct measurement of specific heats and the difficulties in selecting a method ( 3 , 4)led to the selection of the thermal leakage method employing differential rates of heating and cooling for this work. This method was chosen in preference to the method of mixtures in view of the small volume requirement and the high precision of all measurements
V O L U M E 2 4 , NO. 6, J U N E 1 9 5 2
939
A small-sample calorimeter using twin radiation tubes was developed in order to measure accurately at high temperatures specific heats of new heat-transfer liquids currently under development. No available instruments fulfill these requisites. The calorimeter is readily calibrated, has a temperature range to over 300" C., and measures with an accuracy better than 5% on samples of approximately 35 ml. Specific heat for one liquid is reported and data are compared with data on another liquid which was available for measurement by conventional methods. The apparatus is unique in its incorporation of modern laboratory techniques, which eliminate previous difficulties in use of the method.
Thus, if the specific heat of one liquid is known, the specific heat of others may be computed by Equation 1. Equation 1 is considered the basic equation for this test. It assumes only that the rate of heat loss or gain from each vessel is equal, and this should be true, regardless of the mode of heat transfer. -is Xewton's cooling Ian was not used in the final derivation, the equation is not subject to the approximation of this law. If evaporation occurs, it is necessary to modify the basic equation to e4 f C A J f A - EA = _---___ CB f C B J f B (2) tA
Figure 1.
Schematic Diagram of Apparatus
is
n here EA and EB are evaporation rates affecting the heating or cooling rates, In work on experimental liquids, the latent heats of evaporation which are needed t o evaluate EA and EB are often unknown and may be obtained only by direct measurement or computation from Trouton's rule or the Clapeyron-Clausius equation. I n older to eliminate this difficulty, two heating-type tests may be iun on the same liquid, but with samples of different masses, under the same thermal conditions. Under these conditionq, and because the evaporative surface areas are the same, it follo\m that the evaporations are equal and may be eliminated fiom the basic equation for the two tests. The thermal leakage method of measuring specific heats has been in disuse until recently. Regnault, a h o did some of the early work with this method, found it unsatisfactory for granulated solids, and although he used it for measurements of liquids, he doubted its usefulness because of the differences in film coefficients a t the interface between the liquids and the apparatus. Smith (2) has used the method rrcently to obtain data on brass
required by t,he iiietliod of mixtures under such restriction. The electrical input method was not used because oi complications in precise measurenic.nt of the electrical input when applied in con.junction wit,h the magnetic stirring technique employed to reduce surface film coefficients. The measurement of specific heat by thermal leakage has been revie\\-ed by Cork ( I ) . Briefly, it, consists of heating or cooling like vessels, one containing a reference standard liquid and the ot,her a liquid of unknown specific heat, toward the temperature of a surrounding constant temperature. The differential rates of thermal exchange are compared by the equation
where thermal capacity Of vesse! %nd associated apparatus, calories er u. CA = specific heat of liquigcontents of vessel, caloriee per gram per O C. MA = mass of liquid contents, grams t.4 = time of heating or cooling, seconds, etc.
CA
=
I.
Figure 2.
Cooling Data from Typical Twin Radiant Specific Heat Test
ANALYTICAL CHEMISTRY
940 alloys, and the Centra] Scientific CO.,Chicago, I]]., uses it to ~if the liquids ~ in ~ each demonstrate a radiation method. H vessel are stirred vigorously, so that their Reynolds numbers are high, the previous difficulties experienced from film coefficient differences are minimized. This is possible because the liquids tested Of the same and Of equal thermal conductivities. APPARATUS
The apparatus used had to comply with four restrictions: (1) small sample technique, (2) measurement of C, and not C, over a wide temperature range, (3) simplicity for duplication, and (4) a relatively fast test. The basic parts of the calorimeter are shown in Figure 1.
tions, substituting one specific heat value in the fundamental equation, for the specific heat of the other liquid. ~Values ~ and solving ~ well , within realized were the accuracy required, and read-
ily repeatable Over the entire test range.
Tm,o factors of mechanical heat were considered, Conductive heat losses were not through the stirring because there was no mechanical bond, but friction had to be considered, with respect to both the liquid and the sample tube. The friction by collision of the magnets with the walls of the sample tubes was indicated by a random noise, and it was assumed that the rotating magnets actually were lifted from the botLom of
1
The entire apparatus is designed t'o give siniul. taneous heating or cooling curves for a test and a reference liquid, contained in identical sample tubes. These sample tubes, B , are 29/52 inch in outside diameter and 6.5 inches long, and are made of No. 26 gage yellow brass. The bottom is closed with a plug inch thick, while the topis capped n i t h a tight-fitting one-piece cap of the same gage. The sample tubes and caps are nickel plated and highly polished to reduce the rate of heat transfer. Each tube is centrally suspended by rigid thermal insulation, F , in air i n identical light bronze cylinders, G, 2 inches in diameter by 8.5 inches long, the concentric cylinders thus formed being held in similar position in a heat-resist,ant frame. The bottoms of the cylinders are closed with bronze plates and the tops are closed with similar plates with an opening suitable for the sample tubes. These openings are covered with bronze disks during the test, so t.he entire area of the sample tubes radiates to or from the same temperature. The inner surface of the bronze cylinders and t'he disks are painted F~~~~~3, with engine black paint to give a constant surface condition. The bronze cylinders are suspended in their frame in an aluminum kettle, 9 inches in diameter, which also contains a constant temperature bath controlled to iz0.5' C. This bath is stirred by electrical stirrers and is filled so the liquid level is almost at' the top of the bronze cylinders. The kettle and cylinders are thermally shortened and the entire apparatus is lagged with cork and asbestos insulation. Air is supplied to an air-driven magnetic mixer which is located directly beneat'h each cylinder, a t constant pressure through a reducing valve, so the stirring speed is always constant. The magnetic mixers rotate small borosilicate glassjacketed bar magnets, D , which are located inside the sample t,ubes and thereby stir the test' and reference liquids. This prevents temperature gradients from developing wit'hin the liquids during tests, and provides fluid motion at such a rate that a high Reynolds number is assured and the differences in thermal gradients due to different film coefficients are made negligible. Thermocouple wires enter through two small insulated holes, E , in each sample tube cap and through the supporting piece over each cylinder. These small apertures separate the wires, so that the recorded e.1n.f. is indicative only of t,he temperature a t the junction, C, and assure atmospheric pressure at all times but restrict evaporation. For tests employing cooling techniques. a small oven is used t o preheat the sample tubes sufficiently abovc the temperature of the constant temperahre bath.
1
2
6
5
Heating Data from Typical Twin Radiant Specific Heat Test
C.ALIBRATION
The S o . 30 gage iron-constantan t,hermocouples used in these t,ests were calibrated at, 0" and 300" C. against the most precise thermometers avftilable and \vere matched against each ot'her, giving like e.m.f. s throughout this range. The precision thermometers were accurate to 0.5" C. The thermocouple cold junctions were kept in an ice bottle at 0" C. The potentiometer was of the null indication type and \\-as zero-balanced against a standard cell every fifth minute during the tests. The heat capacities of the bar magnets, sample tubes, and caps were calculated hy mass determinations arid accurate knowledge of the specific heats of the components. These calihrat'ions were verified by ralibration t'ests, which consisted of heating or cooling standard liquids of known specific heat in each t,ube under identical condi-
I 0
100
200
i 300
I1 a00
500
TEMPERATURE ---OF
Figure 4.
Engineering Specific Heat Curves
030 600
94 1
V O L U M E 24, NO. 6, J U N E 1 9 5 2 the tubes by stirring currents and hit the walls only because the magnets "float" from side to side. Calibration tests were run to determine the temperature rise above bat,h temperature realized from stirring in comparison t o unstirred. Results showed t h a t the temperature rise was so small t h a t i t was negligible over the short time intervals of test runs. Also, assuming constant and like speed of stirring, the actual energy gained would be equal for each sample, and consequently would cancel o u t from each side of the basic equation. Variations from differences in physical properties other than C, of the sample liquids were considered negligible. An additional test was run to determine esactly the precision involved when totally different heat capacities were used in each sample tube. This test was run with approximately 50 ml. of ivater in one sample tube and 20 ml. of water in the other tube. The results were within the prescribed accuracy of the test, but ahowed t h a t more accurate results were obtainable with matched hrat capacities. Irit,erchange of sample tuhes from one cylinder to the other to determine if the assumed slight deviations from actual concent,ricity were significant revealed no perceptible errors, and interchange of liquids in t,he sample tubes showed that the emissivity of each tube was the same. T h e standard liquid used for comparison was distilled water for temperatures below 100" C. and tetraaryl silicate, a special heattransfer liquid, for higher temperatures. The specific heat of this "standard" liquid had been determined previously b y a convrntiorial method over the entire temperature range. Artual specific heat values used were talcell from an equation of C, z's. temperature which was derived statistically from the data. . l c ~ u r a c yof this standard was easily within 1yo. Water was used to measure the values of specific heat of toluene, benzene, and tetraaryl silicate in preliminary t e s t s T h e wsulting calibrations showed a n accuracy of 1%.
RESULTS
The specific heat at constant pressure of isopropyl phenol silicate was measured by this method a t approximately 50" C. intervals between 50" and 250" C., and the data were statistically fitted t o an equation of C, us. temperature for purposes of liquid thermal characteristic evaluation. Bt least three determinations were made at all points, and at least four deterniinations were made for the heating-type tests in which appreciable rvaporation occurred. Typical cooling and heating test data are presented in Figures 2 and 3. I t may be noted in Figure 2 that t'he data arr s u f f i h i t for calculation of C, from the basic test equation. T h k is not possihlr for data given in Figure 3, because i t is necessary to eliminate thcs evaporative effect by combining tests. Resultant values at the high temperat,ures were lower than expected because the evaporation eliminated a highly volatile and low density liquid componrnt. a t approximately 200" C., and thereby left a liquid of higher molecular weight. I t was determined previously that increase i n molecular weight was synonymous with der1 in this particular chemical family. Figure 4 is a graph of the specific heat curve for iioprop1.l phenol silicate derived from this st,udy in comparison u-it,h the curve for tetraaryl silicate. D a t a were converted from metric to English units for purposes of engineering usefulness. The a(*curacy of the isopropyl phenol silicate derivrtf curve is within 1 in the loa- range and 2% in the high range. Experimental d a t a are helieved to have an accuracy within 5%. CONCLUSION
The t,ePt and apparatus were developed for use during a time when only small volumes of esperimental liquids were available, but, in view of the accuracy realized and the subsequent value of the data obtained, the method is believed to be an advancemrnt. in specific heat measurement of liquids a t high temperatures.
T E S T PROCEDURES
LITERATURE CITED
Test temperature was est,ablished at 25" C. above or below the bath temperahre, and the sample tubes and liquids were preheated or chilled to 75" C. above or below the bath temperature, to permit a constant thermal exchange over the range of Z!C 10" C. from the test temperature. Temperature measurements were rec,ortied on each liquid, on alternate minutes, over the approsimate 60" C. range. Th(. highly polished sample tuhes were handled only with ahsorbent cotston a t all times to prevent heat leaks through partial 1)lac.k h d i e s . Stethoscopic determinatiori of positive stirrer :ic,tiori was found satiqfactory.
(1) Cork, hl. J.,
"Heat," 2nd ed., Ken, York. John \Vilex 6- Sons,
1942. (2) Smith, C. S., Trans. Am. I n s f . Mining M e t . Engrs.. 137, 236-44
(1940). (3) Spear, S . H., .4STM Bull., S o . 168,79 (1950); TP 207. (4) Spear, S.H.. "Measurement and Significance of Specific Heat of Thermal Insulating Materials," presented a t .I.S.T.JI. spring
meeting, Symposium on Thermal Insulating JIaterials, Cincinnati, March 7,1951. RECFJVED for revipw Soveinher 0 , 19.51. Accepted IIari,Ii 19. 19.52.
Procedures in Ice Calorimetry H. T. SPENGLEK Carbide and Carbon Chemicals Co., Union Carbide and Carbon Corp., South Charleston, W . V a . i simple Bunsen ice calorimeter and bath were designed for the rapid and reasonablj precise deterniination of enthalpy and related thermal data. Contrasted to the elaborate power-measuring equipment required for an electrical calorimeter, this apparatus requires no auxiliarl equipment other than an analltical balance. In addition to the determination of heats of fusion, heats of reaction, and enthalpies above 0" C., which have pretiously been determined b) the methods of ice calorimetrj , this instrument has been applied to the determination of heats of vaporization at 0" C. and enthalpies a t temperatures down to - i 7 ' C. Because of its simplicity, versatility, and ease of operation, a calorimeter of this type should find many uses where data of moderate precision are required.
T
HE isothermal-type calorimeter wing the volumetric. change and heat of transformation (fusion) of thp i(-e&water a t 0" C. to measure thermal effec't? b v w ti wribed h>- Robert Bunsen in 1870 ( 1 ) . Since that time severa! 6, 7 , 14) have brought out LTarious motlifications other workers (4, and applications of t,his instrument. Thr, latest ani1 most rrfineii design is t,hat of Ginnings and Corrucvini (.il, n.ho ]lave applied their apparatus to obtaining enthalpieP in th(8 teniperature range 0" to 900" c. The so-called ice calorimeter i,c particularly uFeful i n thc determination of small and veq. s ] ~ \ \ -heat efferti;. Artirlcs covering the following applications have appeared in the lit Property Enthaliiies ah0X.e 'O C. Heat of adsorption Heat of fusion
Reference
(4) (12)
(a)
Propel ty Reference FIrnt of solution (6) Heat of radioactive decay (76) Heat of reaction (7)
