Oct., 1957
THERMAL CONDUCTIVITIES OF LIQUID NITRATEESTERS
LiPb is -350'; since a pattern of LiPb was obtained at 355", the composition may be inferred to be actually less than 70 atomic % Pb. With the increasing temperature the LiPb patterns were observed to change in a continuous manner from the more complex rhombohedral to the simpler cubic form; evidence for this consists in the blending of the multiple lines on the films into singular ones. An exact temperature for the transition was difficult to estimate; however, some rough qualitative information is available. Patterns photographed at 160" still definitely show the rhombohedral form. At 195" the line splitting is just barely detectable; at 230" the transition to the cubic form seems quite complete. Measurements of cell size were calculated from some of the patterns as a function of temperature. Since the rhombohedral angle is only 1/20 less than a right angle at room temperature, accurate measurements on this changing angle are difficult t o make.
1415
I n Fig. 1, t.he cell constant a and the cell angle a! are plotted as a function of temperature. Since the electrical resistivity measurements are a much more accurate indication of this transition, a curve from the data of Grube and Klaibera for the 65 atom % Pb also has been included. The broken portions of the curves are where precision measurements are not. possible due to the close proximity of the lines in the diffraction pattern. A rough calculation on the thermal expansion coefficientsindicate that they are t o 70'
(%)-I16
x
= -3
10-6/0C.
(rhombohedral or low temp. form)
(%)
230- 366'
= -4.5
x
10-6pC. (cubic or high temp. form)
Acknowledgment.-We wish to express our thanks to Mr. Vernon G. Silveira for photographing and measuring many of the powder patterns.
THE THERMAL CONDUCTIVITIES OF SOME LIQUID NITRATE ESTERS BY D. L. HILDENBRAND~ AND J. A. HAPPE Chemistry Division, U.S. Naval Ordnance Test Station, China Lake, California Received May $1, 1967
A radial heat flow type cell has been used to measure the thermal conductivity of four liquid nitrate esters a t 30 and 70'. The operation of the cell is discussed and data obtained on some representative liquids are compared with the results of previous investigators.
Introduction Tn a study of the combustion of some nitrate esters, the liquid thermal conductivities were needed in order t o compare theoretical and experimental combustion wave temperature distributions. Since there were no reported values for compounds of this type, the measurements described herein were undertaken. Thermal conductivities at 30 and 70' are given for ethyl, npropyl, n-butyl and 2-methoxyethyl nitrates and the operation of a radial heat flow "hot wire" type cell is discussed. Experimental Materials.-The starting materials were Eastman whitelabel ethyl nitrate, City Chemical Corp., n-butyl nitrate and commercial grade samples of n-propyl nitrate and 2-methoxyethyl nitrate obtained from the Ethyl Corp. and Wyandotte Chemicals Gorp., respectively. The n-butyl nitrate was distilled a t reduced pressure through a Vigreux column, while the other materials were distilled through a center rod column a t a reflux ratio of 30 to 1 with the following observed boiling points: ethyl nitrate, 53" (223 mm.); n; propyl nitrate, 39" (49 mm.); 2-methoxyethyl nitrate, 61 (26 mm.). Only center fractions were used. The organic solvents for checking the operation of the cell were Eastman "Spectro grade" or analytical reagent grade materials and were used without further purification. Apparatus.-The thermal conductivity measurements were made with a radial heat flow type cell very similar to that described by Hutchinson.2 I n the present case, how(1) Thermal Laboratory, The Dow Chemical Co., Midland, Michigan. ( 2 ) E. Hutohinson, Trans. Faraday Soc., 41, 87 (1945).
ever, the cell's axial resistance thermometer-heater was a close-wound tungsten helix rather than the "coiled-coil'' electric light bulb filament used by Hutchinson. With the tungsten helix aligned along the axis of a glass tube, the geometrical arrangement resembles very closely that of concentric cylinders, the heat flow attern for which may be readily calculated. Thus the cefi can be used to measure thermal conductivities on an absolute basis and need not be calibrated with a standard liquid as was done by Hutchinsons and others. I n operation, a given electrical power input to the filament establishes a radial temperature difference which can be determined accurately from the change in resistance of the filament. The thermal conductivity of the liquid in the cell may then be calculated from this measured A T , the power input and the cell geometry. The Cell.-A principal advantage of the apparatus used is its simplicity of construction. The glass cell is made from a length of precision bore Pyrex tubing of 1.000 cm. inside diameter and 0.63 mm. wall thickness. The helical resistance thermometer-heater is wound from a 180 cm. length of 2 mil diameter tungsten wire and is spot-welded a t its ends to B & S No. 22 tungsten leads. The helix has a diameter of 1.10 mm., a length of 9.05 cm. and a resistance of about 60 ohms at room temperature. The tungsten leads are sealed through the glass at the ends of the cell, with care taken during this operation to align the helical filament as closely as possible along the central axis of the tube. The dimensions of the cell and helix were determined with a micrometer comparator. Auxiliary Equipment.-Electrical power input to the cell and the corresponding filament resistance are determined by measuring directly the potential drop across the filament and the drop across a standard resistance in series. Heating current is supplied by a group of 120 amp. hr. capacity Edison cells. All of the e.m.f. measurements are read on a calibrated Leeds and Northrup Type K-2 potentiometer in conjunction with a high sensitivity galvanometer. A suitable constant temperature environment for the cell
1416
is provided by a thermostated paraffin oil-bath. Temperature of the bath is controlled by a proportional output device which senseA the unbalance in a thermistor bridge circuit and delivers current to an intermittent heater. The basic circuit for this controller has been described by McFee.8 This arrangement worked very satisfactorily and the bath temperature drift could be held to 0.002" or less a t 30' and to 0.004: or less a t 70" during the 45 minute period that a run was in progress. I n order to obtain temperatures directly from the resistance measurements, the resistance us. temperature relationship of the helical tungsten filament was determined by comparison with a calibrated platinum resistance thermometer. Frequent checks of the filament calibration were made during the course of the measurements. Measurements.-In operation, the liquid filled cell is placed in the thermostated bath and a series of measurements of the filament resistance is made for various power inputs. Experiments have shown that the results are independent of the height of liquid in the tube provided the filament is covered. Ordinarily, at least six different power inputs are made, varying from about 0.0007 to 0.004 cal./ sec. The corresponding temperature differences across the cell range roughly from 0.05 to 0.4" and can be determined to within 0.001". Corrections.-Two principal corrections need to be applied to the data obtained when the cell is operated as described above. These are a correction for heat conducted to the bath through the tungsten lead wires during power input and a correction for the temperature drop across the glass wall. The first of these can be calculated by solving the differential equation describing the temperature distribution along the filament and evaluating the temperature gradient a t the ends. A thorough treatment of the solution of this equation has been given by Gregory and Archer4 for the electrically heated straight wire fixed along the axis of a cylindrical tube. Since this treatment readily can be adapted to the present case, details will not be given here. Maximum value of the correction was less than 0.5%. The temperature drop across the wall of the glass cell may be calculated by referring to the equation describing the heat flow between coaxial cylindrical surfaces with heat gen: erated along the inner cylinder6 2rLKAT &----In ( r h ) where Q is the radial heat flow per unit time over the cylinder length, L , K is the thermal conductivity of the medium between the cylindrical surfaces, A T is the temperature difference between inner and outer surfaces and rz and r1 the radii of outer and inner cylinders, respectively. The cell wall A T can thus be obtained from the corrected power input, the thermal conductivity of Pyrex glass, the wall thickness and the helix length. This correction amounted to about 1% and was independent of temperature over the range investigated.
Results and Discussion A typical set of data obtained on ethyl nitrate a t 30' is given in Table I for purposes of illustration. The table gives the measured heat input, the measured AT across the cell and the final values of these auantities corrected for heat conduction along the-leads and the temperature drop across the glass cell wall. The experimental data were evaluated by referring to eq. 1 and plotting the corrected power inputs against the corresponding temperature differences. Thermal conductivity was then obtained from the slope of the line and the dimensional factors given above. were those Of least squares straight lines through the data. The average deviation of six or more experimental points (3) R. H. McFee. Reu. Sei. Znstr., 88, 52 (1952). (4) R. Gregory and C. T.Archer, Proc. ROWSOC.(London), A l l o t 96 (1926). (5) M. Jakob, "Heat Transfer," New York, N. Y.. 1950, p. 182.
Vol. 61
D. L. HILDENBRAND AND J. A. HAPPE
Vol. I, John Wiley and Sons, Inc.,
TABLE I HEAT INPUTS A N D RADIAL TEMPERATURE DIFFERENCES FOR ETHYLNITRATEAT 30' Q, input cal./sec.
'
ATomeas.,
x 106 696 1153 1300 1610 2395 2765 2818 364n
C.
0.060 .096 .lo4 .132 .202 .226 .234 .298
Q cor., cal./sec. x 106
693 . 1148 1294 1603 2385 2753 2806 3625
AT cor.. OC.
0.059 .095 .lo3 .131 ,200 ,224 .232 .295
from the best straight line was in no case greater than 0.003' and was in most cases 0.002' or less. Because the Q us. AT plots are linear to this order of accuracy, interference due to convective heat transfer would appear t o be absent. Experimental works has indicated that for almost every geometrical arrangement, heat transfer by natural convection is a non-linear function of the temperature difference between hot and cold surfaces. Other reasons for believing that convection is not a complicating factor are (1) the small temperature differences across the cell (0.4' or less) and (2) the absence of any irregular temperature changes such as would be caused by convection currents. Even a t the highest energy inputs, for example, the temperature of the filmanent would remain constant t o within 0.001' over a period of ten minutes or more. It would be very worthwhile, in order to get more information regarding convection, to repeat the measurements with tubes of different diameter to see whether the present results can be reproduced. However, it is not possible t o continue the experimental work a t this time so the results are being written up in their present form. The results obtained on the nitrate esters at 30.0 and 69.5' are given in Table 11. Two independent sets of data were obtained on different samples of each liquid, and the results were reproducible to within 1% or better. It appears that any change in thermal conductivity over the temperature range investigated is within experimental error so that the temperature coefficient must be of the order 0.03% per degree or less. This is in agreement with the magnitude of the temperature coefficient found by Bridgman' for other organic liquids. TABLE I1 THERMAL CONDUCTIVITIES OF SOMENITRATEESTERS Nitrate
Ethyl *Propyl %-Butyl 2-Methoxyethyl
KW
K700
47.8 44.3 41.0 43.6
47.5 44.9 41.1 43.9
cal. cm.-lsec.-' OC.-l X 106
~~~~~i~~~ with otherWork.-In order to pare the results of this research with the results of other investigators, thermal conductivity data were obtained on Some representative organic liquids for which literature values were available. As in the above cases, two independent sets of data were (6) Ref. 5, p. 522-542. (7) P. W. Bridnmsn, Proo.
Am. A c z i . . 4 4 9;L,
51, 1 ; )
(lj
