V O L U M E 28, NO. 11, N O V E M B E R 1 9 5 6 these materials were solid a t room temperature and the determination of dispersion by conventional methods was rendered virtually impossible. The Eykman function, C = (n2 - l ) / d ( n 0.4), where C is a constant independent of temperature and pressure, has repeatedly been reported to be one of the best approximations to the actual relation between the density and refractive index of organic liquids ( 2 , 3). I n order to investigate the reliability of this function, additional samples of n-hexadecane and casdccahydronaphthalene were prepared in volumes large enough to permit the accurate determination of densities as xyell as refractive indices. These properties were measured over the entire range of temperature from 25" to 100" C. I n the range 25" to 55" C. refractive indices were measured by the method of minimum deviation. Temperature control was achieved using the jacketed hollow prism and air bath described. I t is estimated that these data are accurate to +0.00005, as observations on distilled water at temperatures from 25" t o 55' C. showed an average deviation of ~k0.00003from reliable literature values (IO). In the range 60' to 100" C. the Eykman instrument was used. Densities were determined in duplicate throughout the entire range and are estimated to be accurate to nithin two or three units in the fourth decimal. A summary of the data obtained is given in Table 111. The values of the Eykman function calculated from the data are also given. The standard deviation of both sets of values is about 0.0001. The individual values are scattered randomly about the mean. The mean values were used t o calculate the refractive indices in the fifth column of the table. The average deviation between observed and calculated indices in the interval 25' to 55' C. is less than +O.OOOl. I n this temperature interval the best agreement would be expected, as the average value of the function was derived from the observed indices and densities. However, when the Eykman equation is used to extrapolate to temperatures in the range 65' to 100" C. the agreement between the calculated values and those obtained using the Eykman refractometer is still satisfactory, the average deviation being about two units in the fourth decimal. As further evidence of the consistency of the data it is interesting to note
+
1701
that the refractive index values at high temperature, when fitted by least squares methods to polynominal functions and extrapolated to lower temperatures, agreed with the values obtained by minimum deviation to within two or three units in the fourth decimal. These data indicate that the Eykman equation accurately represents the relationship between refractive index and density for the two liquids examined and that it is entirely satisfactory for converting refractive indices from one temperature to another when accurate densities are available a t both temperatures. Although neither of the instruments used is suitable for routine measurements, it is hoped that this description of their construction and operation will encourage further work of a fundamental nature in the field of high temperature refractometry. ACKNOWLEDGMENT
The authors gratefully acknowledge the assistance of L. G. Bostwick, ill. E. Peterkin, and Richard Williams in obtaining many of the experimental data. LITERATURE CITED
Eykman, J. F., in "Naturkundige Verhandelingen Hollandsche Naatschappij der Wetenschappen," ed. by A. F. Holleman. Series 3, vol. 8, De Erven Loosjes, Haarlem, 1919. Kurta, S.,S., Jr., Amon, S.,Sankin, 9., Ind. Eng. Chem. 42, 174 (1950).
Kurtz, S. S.,Jr., Lipkin, hI. R., J . Am. Chem. Soc. 63, 2158 (1941).
Lipkin, AI. R., Davison, J. 9., Harvey, W.l'., Iiurtz. 9. S.,Jr., I N D . ESG. C H E X . , ANAL.ED.16, 53 (1944). Lipkin, 11.R., Sankin, -4..hIartin, C. C., - 1 s .C'HEM. ~ ~ 20, 598 (1948).
LIair, B. J., Willingham, C. B., Streiff, -i.T., J . Kesearch .Yatl. Bur. Standards 21, 581 (1938).
Martin, C. C., Sankin, A, ANAI..CHEM.25, 206 (1953). Schiessler, R. W., Whitmore, F. C., Ind. Eng. Chem. 47, 1660 (1953).
Tilton, L. W., J . Research .VatZ. Bur. Standards 2 , 909 (1929). Tilton, L. W., Taylor, J. K., Ibid., 20, 419 (1938). RECEIVED for review June 7 ,
1956.
Accepted August 10, 1956.
A Thermistor Temperature Recorder B. M. ZEFFERT and R. R. WITHERSPOON' Chemical Corps Chemical W a r f a r e ~!aboratories,Army Chemical Center,
The use of thermistors for temperature measurement and recording has been described in the literature. The present instrument is an adaptation of thermistors to the automatic continuous recording of temperatures in the range -80" to 32' C. with an accuracy within 0.05'. The span is divided into 11 ranges of 12" each, with 2" overlap on adjacent ranges. Recording of temperature is linear, making use of the fact that the temperatureresistance variation of a thermistor over relatively small intervals (12') can be fitted to the same equation that describes the relationship between the resistance of one arm of a Wheatstone bridge and the unbalance bridge voltage. On each range of the instrument the thermistor is part of a Wheatstone bridge circuit, and the unbalance voltage is fed to a potentiometer recorder. A Leeds & Northrup recorder with a high impedance amplifier (to accommodate the 1-megohm thermistor at - 8 0 ' ) is used. Range selection and range changing are completely automatic.
Md.
A
IjTOhlhTIC temperature recorders are to be desired for many purposes in the fields of science and industry. Platinum resistance thermometers have been made fully automatic ( 2 ) and are commercially available. Recorders that employ thermocouples are similarly in use. Although thermistors have been used for temperature measurement for a number of years, they have not been employed to any great extent a$ the sensing elements of recording thermometers These temperature-sensitive resistance units possess a number of advantages which make them desirable for such work. They are produced in a wide variety of shapes and sizes, so that they are adaptable to many kinds oi work, and have temperature coefficients of resistivity which are many times those of conventional resistance-thermometer materials. Depending on the type of thermistor, they may have low thermal lag, and may be of such resistance values as to make lead errors insignificant. This paper describes an automatic temperature recorder which 1
Present address, National Carbon Co.,Cleveland, Ohio.
ANALYTICAL CHEMISTRY
1702 Table I.
Bridge Constants for Standard Thermistor (Ohms) Trimmer Potentiometers
Range
R,
Rd
2659 2256 3190 2743 2667 2599 2432 2475 2458 2369 2369
1,470 1,900 4,010 5,650 9,260 15,100 25,600 47,500 93,500 168,000 345,000
Rd
60
100 250 250 250 900 900 2,500 2,500 10,000 10.000
Resistor 96.0 2.7 9.0 2.7 3.0 4.4 2.0 4.0 1.2
...
( R , ) ;5.'0
g%z Pot. 3 7 1
2
2 2 2 2 0
2
-
!* "f 9 WEm
I 4
Figure 1.
I
O---i
Tc
Rth
8
Wheatstone bridge circuit for thermistor
employs a thermistor as the sensing element. Most of the temperature-measuring instruments reported to date which employ thermistors are of the manual type ( 3 ) ,and require calibration curves to convert resistance readings to temperatures. .4 thermistor recorder has been described for use in meteorological survey in the range 46" to -12" C. with a reported accuracy within about 0.05' ( 1 ) . The instrument reported here is an adaptation as well as an esteiision and refinement of that design.
DESCRIPTIOS OF INSTRUMENT
The completed instrument is a fully automatic temperature recorder employing a thermistor as the sensitive element,. Eleven separate temperature ranges of 12" each are provided for measurement of t;mperatures from -80" to 32' C. Adjacent, ranges overlap 2 . Temperatures are recorded on a linear scale on the chart of a Leedso& Northrup Speedomax recorder with a maximum error of 0.05 . The linear temperature scale is required t o allow graphic extrapolations of time-temperature data in freezing point measurements, and graphic corrections in calorimetry. .411 electrical components except the recorder unit, limit switches, and the batteries are in one chassis, the bridge unit. All adjustments can be made on the front panel or the chassis of the bridge unit, and the indicator lights are located on the front panel. Thermistor. The thermistor selected for this work is the Western Electric Type 14B, which is recommended by the manufacturer for temperature measurement and control. The thermistor bead is enclosed in the slightly enlarged end of a glass cylinder having two tinned-wire leads brought out axially at t,he opposite end. The glass cylinder is approximat,ely 2 inches long and 0.10 inch in diameter. The thermal time constant of the element when immersed in liquid is about 2 seconds. The thermistor resistance varies from about l i 0 0 ohms at 32" C. t o about 1 megohm a t -80" C. The temperature coefficient is -3.970 per degree a t 25" C., and is larger a t lower temperatures. The resistance a t the highest temperature to be measured is sufficient'ly high to allow the neglect of any errors due to lead resistance, while
at IOK temperatures it is not so great that difficulties due to cupacity effects and induced voltages from other electrical eqiiipinent may not be readily overcome.
It \I as necessary to determine very accurately the resistancetemperature characteristics of the thermistor that wad to be used as the "standard" for all future calculations. The individual thermistor of the selected type (11B)was carefully chosen for reasons discussed below. The calibration was conducted in a special cryostat assembled for this purpose. This cryostat consisted of a large and a small Dewar flask, with the smaller flask mounted inside the larger one. The inner flask was used as the measuring chamber, and contained the thermistor to be calibrated, a platinum resistance thermometer, an electric heater, and a stirrer. Both the inner flask and the space between the flasks were filled with acetone. The temperature of the acetone in the outer chamber was always held several degrees below that of the measuring chamber, t o reduce heat transfer from the surroundings. The heatri m s used to balance small changes in temperature. Temperature calibration points were taken a t approximately 5' intervals from 32" to -80" C. Thermistor resistances mere measured v i t h a 5-decade Rheatstone bridge which had been calibrated at the Sational Bureau of Standards. The bridge was used in conjunction with a Leeds & Northrup 2430C galvanometer. During all calibration measurements the thermistor current was kept sufficiently small to prevent self-heating of more than 0.01' as calculated from the dissipation constant of 5 mtv. per degree for the thermistor. Resistance measurements xere accurate to five significant figures. The chamber temperatures 1% ere determined with the platinuni thermometer and a Mueller bridge, both of whbh had been calibrated. Temperatures were measured to 0.01 . The data obtained were used in calculating the resistances for the measuring circuits as described below. CALCULATION AND SELECTIOh- OF ELECTRICAL COMPONESTS
Thermistors are nonlinear elements, of high negative temperature coefficient, which change resistance approximately according to the equation
where R is the electrical resistance in ohms, II' 1s the absolute temperature in O K., and d and B are constants. Conventional methods of using thermistol s for measuring temperature require the direct determination of resistance (usually in a Wheatstone bridge circuit) and the subsequent conversion to temperature by means of a calibration curve or equation. It is, however, possible to relate the thermistor resistance to temperature by another means which is more conveniently adaptable to automation. I n a TTheatstone bridge circuit, the resistance to be measured may be directly related to the unbalance bridge voltage instead of using a null method with the bridge in balance For the case in which the resirtnnce being measured iq a thermistor, the non-
V O L U M E 2 8 , N O . 11, N O V E M B E R 1 9 5 6
1703
linear temperature vs. resistance characteristics of the element will give a bridge voltage output which is linear with temperature, if sufficiently short, temperature ranges are used and correct bridge constant:: are chosen. Over relat,ively short ranges of temperature, the temperatureresistance relationship of a thermistor may be represented by t
- t,
= C'
-
KKth/(/id
+
(2)
Kth)
where c, K , and Rd are constants chosen to fit the experimental data exactly at three points, tl is the reference temperature, and Rth is the rpsiptance of the thermistor a t temperature t. The output (unt~alancebridge voltage) of a Wheatstone bridge of the type shoir-ri,in Figure 1 may be represented by
E, - E'tr
