Peter J. Reilly and Loren G. Hepler
Jnversty of .ethorage Lernbr age, A oerta, Canada
II
Temperature Measurements with Positive Temperature Coefficient Thermistors
Temperature measurements have played and continue to play an important role in chemistry, with resistance thermometry one of thc most widely used methods. Until less than a generation ago, metal wire resistors (platinum, copper, or nickel) were the only common resistance elements used in resistance thermometry. Then development of negative temperature coefficient thermistors provided useful nonmetallic resintance elements. Still more recent development of positive temperature coefficient thermistors offers new opportunities for making ternperaturc memurements with increased sensitivity or of making measurements of any given sensitivity with simpler and less expensive instrumentation. A convenient measure of the sensitivity of a resistance element to be used in resistance thermometry is its percentage change in resistance per degree change in temperature. Values of this quantity (100 dR/RdT) for typical resistance elements at 25'C are summarized in the table. These figures show that the new positive temperature coefficient thermistors offer sensitivity -65, -50, -33, and -5 times as large as platinum, copper, nickel and negative temperature coefficient thermistors. Therest of this paper is devoted to discusby Pennsylvania Electronics Technology, Inc.' and supplied to us by John Herring & Co. Ltd.2 Resistance-temperature characteristics of positive temperature coefficient thermistors are illustrated in Figure 1, with the -20" interval that is most useful for resistance thermometry marked by vertical lines. This useful range for temperature measurement varies from about -15" to about 190°C for dierent thermistors. Our test measurements have been made near 25'C with PET-T34 H15 thermistors having resistance -7800 ohms at 25°C. Pennsylvania. Electronics Technology, Inc., 1397 Frey Road, Pitt,shurgh,Pennsylvania 15235. 2 John Herring & Ca. Ltd., 3468 Dundas Street West, Toronto 5, Ontario, Canada. 1
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journal of Chemical Education
Figure 1. Typicol resistance-temperature curve far o positive temperature coefficient thermistor. The useful range for rendlive ternperdure meowremen1 or control extends over about 20' for each thermirar, with different thermistorshaving useful ranges from about - 15' to about 1 90PC.
We have found sensitivity of -6 X 10W4 deg/ohm with a positive temperature coefficicntthermistor in a Wheatstone bridge. With a decade resistance box (0-1000 ohms in 0.1 ohm steps) in the variable arm and a good null detector it is therefore possible to obtain deg, with useful temperature sensitivity of -6 X range -0.6". Percentage Resistance Change Per Degree for Typical Resistance Elements at 2 5 ' C
Resistance Element
100 dRIRdT (%Id%)
Platinum CODD~~
el
Negative temperature coefficient l:hwmist,or ....-...... ~~
Positive temoerature coefficient thermistoG
20
Values of 100 dRlRdT are smaller than 20y0/deg at lower temperatures and larger at higher temperatures. Values a: high and as 67%/deg and 100%/deg have been observed at -95 -120°C.
Figure 2. Schomotis diagram of the M d e r transposed bridge circuit in which RT, RF, and Rv represent the temperoture sensitive element, matching fired resistor, ond a variable retistor t h d is adjusted occodonally to maintoin constant total current through the bridge. At conrtont current, which is monitored by means of potential Vs, the bridge potentid VI i= proportionol to the temperature.
The Maier transposed bridge circuit may also be used for precise temperature measurements, with advantages for calorimetry3 and cryoscopy.' I n our most recent Maier bridge circuit (Fig. 2) potential measurements have been made with a Leeds and Northrup K3 potentiometer and Keithley 155 null detector. Temperature deg/pV with sensitivities are as follows: 4 X copper, 4 X deg/pV with negative temperature coefficient thermistors, and 8 X 10-Weg/pV with new positive temperature coefficient thermistors. The Maier bridge operates with constant total current, but we have used lead cells with approximately constant voltage. It has therefore been necessary to monitor the bridge current by measuring V2 a t regular intervals with subsequent adjustment of R, as required to maintain constant current. Operation can be simplified by using a constant current power supply, which also adds to the expense. A simple modification of the Maier circuit is illustrated in Figure 3. To analyze this circuit we begin 3 0 ' H ~W. ~ F., ~ , Wu, C. H., AND HEPLER,L. G., J. CHEM. EDUC., 38,512 (1961). 4 A ~ ~J. C., ~ MILLERO, ~ ~ ~ F. 1J., GOLDBERG, ~ , R . N., AND HEPLER, L. G., J . Phys. Chem., 70,319 (1966).
Figure 3. Schematic diagram of modifled Maier tronrpessd bridge circuit' This circuit leads to V r / V 1 proportional to temperoture and is therefore most conveniently wed with o constant voltage power supply ro that VI is then proportional to the temperature.
with an expression for RT of a thermistor (positive or negative temperature coefficient) in the usual exponential form for a small range of temperature near To RT = ROexp[B(T - To)/TaT]g Roexp[BAT/Taa] (1) We assume that both thermistors are identical and choose both fixed resistors represented by RX.to have resistances equal to Ro. The potential difference VI is given by V,
=
VJl
- exp(BAT/T,Q)]/[l + exp(BAT/TOa)]
For T near Towe use exp x T E To
1
+ x and obtain
+ (2To1/B)(V~/Vd
(2)
(3)
Thus T (in the range near To)should be a (nearly) linear function of Vl/VZ. Our tests with this circuit have been made with a constant voltage power supply (set at 1.0 V) so that it was necessary to make only an occasional check measurement of V2. Thus VI was proportional to temperadeg/pV, ture, and sensitivity obtained was 1.0 X with only 0.06 milliampere through each thermistor. As shown by eqn. (3), sensitivity can be improved by increasing V2, but this improvement is largely illusory because of the increased self-heating of the thermistors that accompanies the increased current in the bridge.
Volume 49, Number 7, July 1972
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