INDUSTRIAL A N D ENGINEERING CHEMISTRY
154
Vol. 15, No. 2
Thermal Properties of Various Pigments and of Rubber' By Ira Williams RESEARCH LABORATORIES, FIRESTONS TIRE & RUBBERe o . , AKRON,OHIO
W
I
L E values for The thermal conductivity and diflusivity of rubber may be deterA. The pass B serves to thethermalinsumined by two methods. A method for ihe defermination of the ~ ~ ~ ~ m a f l , $ ~t,Ot lating Power of conductivity of pigments is given and the oalues have been determined pipes and so to give a smalrubbe compounds are for the most common pigments used in rubber compounding. A ler percentage condensation often desired, no adequate method is shown by which fhe thermal conductivity and di$usivity in the Pipes. The steam is table of values is availof any rubber compound may be calculated from an analysis of the able, nor is it possible to stock. such a manner that the steam construct a reliable table assumes a whirling motion for such variable material so the large particles of water as rubber. Practically, the only table containing values by will be deposited on the sides of the chamber and finally blown out through the opening E. The stream used is drawn off which the thermal conductivity or diffusivity might be through the opening F, which is connected as closely as poscalculated is that published by A. A. Somerville.2 This sible to the opening A in Fig. 1. The entire drying apparatus table, besides being rather inaccurate, does not present is constructed of glass and heavily insulated with rubber. the material in a readily usable form, It was with the idea MBTHODOF PROCEDURE of obtaining the data necessary for the calculation of thermal The sample to be studied is calendered conductivities that the following work was undertaken. into a thin uniform sheet which is used to Two separate methods of determination were used, one of cover the outside of the conductivity cell. which gave the conductivity directly, while the second gave The thickness of each piece of material is measured in several places and an values for the diffusivity. Either could then be converted used average thickness determined. The ends into the other through the relation: of the cell and the pipes A, C, and E
tz$:z
' ! ~ ~ ~ ~go;;~ ' ,
Diffusivity k =
conductivity K specific heat X specific gravity
METHOD I - - .. - x
__ *)
A cell method was used for the direct determination of conductivity of the stock examined. This consisted essentially in covering a closed cylindrical vessel with the material t o be studied and measuring the water which collects when steam is passed through the vessel, the temperature of the outside being controlled by immersion in a constant temperature bath.
FIG.~-CONDUCTWITY CELL
APPARATUS The construction of the conductivity cell is shown in Fig. 1. The body of the cell is in the shape of a cylinder with flat ends. The entire apparatus is constructed of thin sheet copper and is 4 in. in diameter by 5 in. high. The pipe A serves to lead in steam which is previously dried, but not superheated. The small opening at B acts as a further safety device to prevent the introduction of any water with the steam, and is open at all times. The steam after entering the cell is allowed to escape through the opening C. To prevent any water from being splashed through this opening, the plate D is introduced. One side of the tube C nearly touches the baffle plate, the purpose being to remove any drops of water which collect on the tube C. A record of the temperature is kept by means of a thermocouple which is led in through the capillary tube E. The junction is brought from the end of the tube and fastened a t F, which is some distance from the end of the tube to avoid any disturbing influence upon the temperature which might be caused by E. During the experiment the cell is immersed to the point X in a thermostat. It is necessary that no water be carried into the yell with the steam. To prevent this, the apparatus shown in Fig. 2 is used. Steam generated at a few ounces pressure is led in a t the opening 1 Presented before the Division of Ruhber Chemistry at the 83rd Meeting of the American Chemical Society, Birmingham, Ala,, April 3 to 7, 1922. 2 Rubber Age, 9 (1921), 131.
(Fig. 1) must also be covered. If the stock is freshly prepared and the cell slightly warmed the stock will adhere firmly to the cell. The length of the stock should also be carefully measured before i t is applied, and when applied the edges should meet to form a smooth joint, in order to prevent a change in dimension of the stock with the corresponding change in thickness. After the coverFIQ. ing has been built up to the desired thickness, the weight of the cell and rubber is taken. This, together with the known weight of the cell, gives the weight of the sample taken. The covered cell is then placed in the thermostat and clamped in such a manner that the level of the water lies a t the line X (Fig. l), and is tilted slightly so that the steam always enters under the water which condenses, The accuracy of the experiment depends largely upon a careful determination of the time-temperature curve covering the first few minutes of the experiment. Therefore, as soon as steam is admitted by opening the stopcock G (Fig. 2), readings should be started and taken a t short intervals until a constant temperature is reached. After the experiment has continued for a known time (10 to 20 min.), the cell is removed and weighed to determine the amount of water collected inside.
A sample data sheet is as follows: CONDUCTIVITYSTOCK P3, LARGECELL, NO.1 Weight of cell Weight of cell rubber.. Area of cell., Specific heat of sample.. Weight of cell rubber water.. Thickness of samde: O.OBO*in. 0 . 0 5 8 in. 0.057 0 . 0 5 9 in. 0.056 in, 0 . 0 5 5 in. Average thickness. .... 0.0573 in. Number of layers used to cover cell.. Thickness of cover..
................................ + ...................... ................................. ....................... + + .............
............ .......................... Time of experiment.. ...........................
12/7/20 466.8 g. 618.8 g. 5 8 3 . 0 sq. cm. 0.502 701.8 g. 0.063 in. 0.055 0 , 0 5 3 in. 2 0.1148 in. or 0.291 cm. 20 min.
Temperatures are shown in Fig. 3. CALCULATION OF WORKING FORMULA FOR CONDUCTIVITY CELL
Steam is condensed inside the cell from two causes-(1) the conduction of heat, and (2) the heat capacity of the material used for constructing the cell and for covering the cell. Let X = water condensed by the cell in changing from the original to the final temperature, M, = the mass of copper,
INDUSTRIAL AND ENGINEERING CHEMISTRY
February, 1923
M, = the mass of the covering, Toand TI = the original and final temperatures, respectively. M, X specific heat Cu X (TI - TO) ThenX = , or substituting latent heat of condensation of water M, X 0.0931(TI - To). in the respective values, X = 537 Let y = water condensed by the material covering the cell.
Here the rise in temperature a t different parts of the stock is unequal. The inside evidently assumed the temperature of the cell, while the outside assumed the temperature of the bath. If we assume the temperature gradient to be a straight
155
(618.8- 466.8) 0.502 (99'2
Y=
537
2 45'5) -
= 3.81g.
We may now substitute in Formula 1, and K =
+
537 [83- (4.35 3.81)]X 0.291 6o 2o 583 52,3 =0.000319cal./sec./cu.cm.
for a difference in temperature of 1O C.
METHOD I1 The second method involves the determination of the diffuline, the temperature rise will be -where T b is the final sivity constant from which conductivity may be calculated. 2 The method follows the work of Williamson and Adams,3 temperature of the bath. This assumption may be made as and consists in measuring the temperature rise at the center long as the covering remains fairly thin, but as the thickness of a cylinder when the surface is subjected to a uniform temperature. The stock to be studied is first calendered increases, the error becomes correspondingly larger. thin and a uniform cylinder obtained by rolling it to the weight of material X specific heat of material TI - Tb desired size. Before rolling the sheet into a cylinder a 2 , thermocouple was placed at the edge so that it would be Theny = -latent heat of condensation of water rolled into the center of the cylinder. The cylinders measor, if we represent weight of material by M, and the specific uring 3/4 to 1 in. in diameter were wrapped in aluminium foil heat by S, and immersed in boiling water. The temperature was recorded by the use of a potentiometer. A sample data sheet is as follows: Y = 537
Ti-Th,
~
STOCKP3
If W, = water condensed by conduction, and W = total water condensed, y). then W, = W -(X cal.through 1sq. cm. in 1see.. But the coefficient of conductivity = fall in temperature per cm. Let A = area of cell, and t = time in minutes during which heat flows.
Time Min. 0 5 9
+
537 w, Then thermal conductivity K =
6Ot A ~
T
-
537 W,I 60 tA T'
1 where I = thickness of covering (material studied), and T = average temperature difference between the bath and cell.
This is obtained from the area between the curves representing temperature of bath against time and temperature of cell against time, by dividing the area so obtained by the length of time over which the experiment extended. If we now substitute the value of W, in the equation above wehave cal./cu. cm./sec. as the expression = 537 (w-(x + 60 tA T for thermal conductivity when using the present apparatus. K
SAMPLE CALCULATION BY FIRST METHOD I n Fig. 3 the line ACD represents the temperature of the cell while the line AB represents the temperature of the thermostat. The area is 1047 degree minutes and the time of the experiment was 20 min. The average temperature difference attained is then - or 52.3' C. This is the value of T. 20 The water condensed by the cell = ,
X = 466.8X
0.0931 X (99.2
- 45.5) = 4.35 g.
537
The water condensed by cover
=
Temperature
c.
Temperature Bath 0
c.
21.3 99.2 51.5 99.2 99.2 77.6 12 88.2 99.2 Diameter of Cylinder, 2 . 4 4 cm. Specific Heat, 0.502 Specific Gravity, 0.92
CALCULATIONS The calculations are quite simple if we make use of Fig. 4, which is taken from data by Williamson and Adams. Here 8 = temperature at the center. eo = original uniform temperature. e, = new surface temperature. t = time in seconds. a = radius of cylinder. k = diffusivity constant.
If we choose the data taken a t 9 min., we have
e- =- el
77.6 - 99.2
=
0.275
21.3 - 99.2 eo- el From Fig. 4 we find the corresponding value of a2
=
0.244
Substituting in the values and solving, we have
and the conductivity will be K = 0.502X 0.92 X 0.000674= 0.000310cal./sec./cu. cm.j0 C.
The corresponding value found by the cell method was 0.000317. A single determination by the cylinder method may vary more than that above if different values of 8 are used in the calculation. For this reason intermediate values of 9 were chosen so that the corresponding value of kt/a2 would fall on the part of Fig. 4 that is most easily read. 8
Phys. Rev., i4 (1919).99.
156
'INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 15, No. 2
CONDUCTIVITY-CELL METHOD (Temperature Range, 45O to loOD C.) Wt. of Cell Wt. of Cell Rubber, and Thickness of and Rubber Water Rubber G. G. Cm.
STOCK
Specific Heat of Stock
P35
0,251
468.5
0.166
20
P3
0.502
466.8
0.291
20
P36
0.385
464.0
0.153
15
P37
0.190
463.9
0.153
10
El
0.383
464.0
0.295
10
Wt. of Cell' G.
Time Mini
466.7 P5
0.422
Frictioned cord 0.418 fabric P61 cured 45 m'in. at 29O C. 0.411 P51 0.411
0.326 I464.0 179.3
0.280
462.1 463.7
0.203 0.123
462.3
0.149 0.142
P53
0.378
P54
0.431
462.2
P651
0.241
462.3
0.138
P56
0.324
462.0
0.140
1
15
Area of the cell is 583 sq. cm. in all cases except that of frictional cord fabric, where the area of the cell
:mp. Rise :grees 50.4 54.8 52.0 52.3 51.9 55.0 54.0 53.3 53.7 54.6 50.8 53.0 52.2 51.4 51.7 51.8 51.6 51.4 56.7 51.6 59.9 57.6 58.9 52.8 51.7 52.2 52.2 52.8 52.8 52.8 52.0 52.3 50.7 51.2 60.8 50.8 is 220.3 s q . cm. Av.
R X 106 0.658 0.663 0.668 0.319 0.319 0.322 0.321 0.399 0.403 0.402 0.968 0.976 0.396 0.408 0.394 0.397 0.368 0.360 0.364 0.361 0.508 0.510 0.507 0.301 0.309 0.297 0.299 0.381 0.390 0.388 0.334 0.340 0,462 0,462 0,387 0.386
CONDUCTIVITY-CYLINDER MZTHOD STOCK
Specific Heat
Specific Gravity
T e m p Bath C.
Diameter Cylinder Cm.
P3
0.502
0.92
99.2
2.440
El
0.383
1.170
99.2
2.080
P35
0.251
2.06
99.2
1.903
P61
0.411
1.082
99.1
1,800
P61
0.411
1.082
99.1
Should the conductivity of a stock be an additive property, as the filler is varied we should obtain a curve of volume per cent plotted against conductivity, which is a straight line between the value for the conductivity of rubber and the value for the pigment used. Since the values for the different pigments are not known, we must obtain the curve by varying the amount of filler in the compound. Once the curves are established as straight lines, the values for the conductiv0 ity of the pigment may be obtained by ow2 extrapolation. That 0 the c u r v e s assume *woe straight lines is shown by Fig. 5. ao w In the following table the values for o woa the conductivity of the different pigments were obtained by extrapolation. The values for the specific heat were taken from the Landolt and Bornstein tables, with the exception of the specific heat of rubber and gas black, which was determined in this laboratory. 4 00,o 0 0016
0014
4
DL10
Time Min.
Temp. Center Cylinder
c.
K X 10'
....
tl!
I!
0
0.316 0.310 0.306
.... .... 0.640
0.407 0.397
0:194
2 .3
1.680
Diffusivity Specific Specific 45OPIQMBNT Gravity Heat 100" C. Zinc oxide.. 5.56 0.125 0,00241 Sulfur.. 2.00 0.175 0.00034 Whiting 2.68 0.201 0.00156 Litharge. 9.25 0.052 0.00106 Lithopone 3.95 0.115 0.00207 2.70 0.209 0.00116 Talc Antimony sulfide'. 3.20 0.085 0.00077 Red oxide , 4.70 0.160 0.00176 Gas black , , 2.00 0.204 0.00164 Blanc fixe.. , 4.35 0.114 0.00157 Dixieclay 2.60 0.200 0.00112 Magnesium carbonate 3.00 0.303 0.00114 Rubber smoked sheet' ale crepe etc., "includin; cured rubber 0.92 0.502 0.00069 Cord fabrics (ap1.50 0.324 0.00168 proximate) 1 Contained 15.6 per cent free sulfur. * Value calculated from determinations made
.. .. .. ........ . . ...... ... . . ... . .. ..... ...... ... . .. .. .. .... . . .... .. .. . ... ....... . ....... . .
... . .
0.293
....
0.314
Conductivity METHODS 08 45ODETERMIlooo C. NATION 0.00166 Cylinder and 0.00012 cell 0.00084 0.00051 0.00094 0.00058 0.00021 0.00132 0.00067 0.00078 0.00058
1
0.00103
]
Cylinder CTgder and
0.00032 0.00082
Cell
on frictioned fabric.
Om06
0
Since thermal conductivity is an additive property and depends upon the volume per cent, the calculation of the value of the conductivity constant is extremely simple. It is only necessary to take the sum of the volume per cent of each material times its conductivity. Let us illustrate with the compound containing smoked sheet, oinc oxide, and gas black. Multiply each per cent (expressed as hundredths) by the conductivity of the corresponding pigment, and take the sum as follows:
INDUSTRIAL A N D ENGINEERING CHEMISTRY
February, 1923 PIGMENT Smoked sheet.. Zinc oxide.. Gas black.. ..................
............... ..................
Volume Per cent 70 15 15
Conductivity 0.00032 0.00166
Conductivity X Volume 0.000224 0.000249
between different determinations, tables of compounds and experimental data are included.
0.00067
0.000100
COMPOUNDS
TOTAL. ......................................
0.000573 No. P3 P5
The total is the conductivity coefficient in calories per cubic centimeter per second. An actual determination of this stock (P50) by the cell method gives the value 0.000572, which is even closer agreement than can be expected in most cases. The diffusivity cannot be calculated in this manner, but must be found by the relation given before, that k = K Taking values from the table above, specific heat x sp. gr. the specific heat of the compound is found as follows:
P35 P36 P37 P51 P52
-
PIGMENT Smoked sheet.. Zinc oxide.. ....... , , Gas black.. .................. TOTAL. ,
157
Per cent by Weight Specific Heat X 0.502 0.365 X 0.125 0.465 X 0.204 0.17 ,
............... ... ...... ............ .....................
...
P53 P54 P55
= 0.183 = 0.058 = 0.035 0.276
The specific heat is then 0.276 cal. per g. per O C. The gravity is found by calculation to be 1-76 and by substitution in the formula, the diffusivity constant k =
0'000573 =: 0.00118 0.276 X 1.76 As an example of the agreement which may be attained
P56
E1
,
PIGMENT Smoked sheet Smoked sheet Gas black Smoked sheet Zinc oxide Smoked sheet Zinc oxide Smoked sheet Zinc oxide Smoked sheet Sulfur Smoked sheet Sulfur Smoked sheet Dixie clay Smoked sheet Dixie clay Smoked sheet Blanc fixe Smoked sheet Blanc fixe Smoked sheet Gas black
Per cent . ... . by Weight 100.0 73.5 26.5 33.5 66.5 69.0 31.0 17.3 82.7 72.3 27.7 51.7 48.3 58.6 41.4
76.1 23.9 33.0 67.0 54.4 45.6 60.6 39.5
Of the two methods described, the cell method probably gives more accurate figures because difficulty is experienced in obtaining a uniform cylinder with the couple exactly in the center. The cylinder method is, however, much more rapid and the results are generally sufficiently accurate for the purpose at hand.
Hard-Rubber Lined Steel Tanks for Transporting Hydrochloric Acid' By F. C. Zeisberg E. I . DU PONTDE NEMOURS & Co., INC.,WILMINGTON, DEL.
Note: Several months after the following paper was read, the with the American Hard N May 24, 1920, a tank in question was opened for inspection and it was found that Rubber Company in regard meeting of handlers thereto, it Was decided to of hydrochloric acid several joints in the hard-rubber lining had opened up. The softWas called by cola B. ask that such a tank be rubber cushion next to the steel was, however, intact, since the built as speedily as possible Dunn, chief inspector of the tank had shown no sign oj leaking. No inspection of the tank had been made since it was first put in seroice; consequentlg, it is and Put into actual service. Bureau of Explosives, to consider specifications for impossible to tell just when the hard rubber jailed. This the du Pont Co., hydrochloric acid tank with the coiiperation of the cars. The necessity for American Hard Rubber action resulted from the classification, according to the GO.,agreed to do. Interstate Commerce Commission Regulations, of hydroOwing to one delay and another, the tank was not actually chloric acid as a dangerous article, which made the Bureau put into service until the fall of 1921. The first shipment of of Explosives responsible for developing specifications for acid was made from our Paulsboro plant on October 5, 1921. containers used in its transportation. At thismeeting a sub- On the hrst trip the tank shifted endwise on the car, but committee was formed, consisting of A. J. Lupfert, General this was remedied by tightening the holding-down bands and Chemical Co.; Otto Rissman, National Zinc Co.; M. M. Neale, providing two wooden end braces. Since that time the tank American Steel and Wire Co.; J. M. Rowland, Hooker Electrochemical Co. ; and Thos. S. Grasselli, Grasselli Chemical Company. This committee held several meetings in 1920, with a view to gathering and correlating the available information on the transportation of hydrochloric acid. At one of these meetings it was decided to have certain companies gather additional information which past expe-P--rience had not developed. Since E. I. du Pont de Nemours & Company had already had under consideration the lining of a steel tank with hard rubber, and had carried on considerable correspondence
0
'
w.
'Received June 9, 1922. Presented before the 14th Semiannual Meeting of the American Institute of Chemical Engineers, Niagara palls, Ont., June 19 to 21, 1922.
Fro. 1
has been in Constant Use for interplant shipments between Paulsboro, Newark, and the Dye Works, without any further
