METHODOLOGY FOR CALIBRATING THERMISTORS USED TO DETERMINE THE TEMPERATURE OF MEASURING WIRES

G. N. GUSHCHIN

(Presented by the scientific seminar of the Departments of Mine Surveying and Geodesy)

The basic circuit and the physicotechnical characteristics of such thermistors have been set forth in sufficient detail in articles [1], [2]. The investigations carried out by the author showed that a thermistor proves to be very useful for many branches of the national economy as a sensitive and sufficiently reliable semiconductor thermometer, which makes it possible (with the appropriate design of the casing for its probe) to measure temperature at points of any body and medium. At the same time, thermistors (semiconductor thermal resistors) possess a number of important advantages in comparison with other types of temperature sensors.

In the present article, the method of calibrating thermistors used for measurements in small temperature ranges of any body with a mean error of the order of ±0.1°C is treated in detail.

The calibration (graduation) of a thermistor has the purpose of expressing, in divisions of the Celsius scale, the angle of rotation of the potentiometer pointer that varies with temperature at the moment when the current in the diagonal of the Wheatstone bridge is equal to zero. A calibrated thermistor makes it possible to take temperature readings directly from the potentiometer pointer.

The generally known method of calibrating heat-measuring instruments by using constant temperature points (the melting points of substances, the freezing and boiling points of water, etc.), with subsequent division of the obtained temperature interval into equal sections, is unsuitable for calibrating thermistors for two reasons. First, in solving problems of geodesy one has to deal with small temperature ranges (of the order of from −20° to +10°C, from 0° to +35°C). For calibrating a thermistor within such temperature limits, it is practically difficult to obtain constant temperature points. Second, semiconductor thermal resistors, regardless of their design, change the magnitude of their resistance as a function of temperature according to an exponential law:

\[ R = A e^{\frac{B}{T}}, \tag{1} \]

where \(A\) and \(B\) are constants, and \(T\) is the absolute temperature.

This circumstance makes it necessary to mark on the temperature scale of the instrument the position of each (individual) degree or fraction thereof. The latter is confirmed by the results of calibrating, by the method proposed below, more than ten MT-54 semiconductor microthermistors of V. G. Karmanov’s design. It was established that each individual thermistor has its own temperature scale, and that the linear magnitude of a degree on this scale is different (see Fig. 1, which shows the temperature scales of two MT-54 thermistors, Nos. 59 and 129).

Fig. 1.

To determine the position of each degree on the thermistor temperature scale during its standardization, gradual and smooth heating (or cooling) of a substance was used; the temperature of this substance was measured with a thermometer and was simultaneously marked on the scale of the instrument. The standardization was carried out as follows. Into a glass beaker 1 (Fig. 2), filled with some substance, a mercury thermometer 2 and the probes (sensors) 3 of the thermistors are immersed; these are secured by means of a stand 4 so that, together with the thermometer bulb, they are always immersed in the substance whose temperature is being measured. Beaker 1 with the substance is lowered into another glass beaker 5 and is suspended in it on supports 6. The space between beakers 1 and 5 is filled with water, which during the calibration process is periodically stirred with stirrer 7. The temperature of the substance is determined from the thermometer and is simultaneously marked on scale 8 of the thermistor by the pointer of the potentiometer after, by rotating the latter, the needle of the zero galvanometer has been brought to the zero position. The temperature of the substance is changed by cooling the water through the addition of ice or a mixture of snow and table salt to it, or by slow heating of the water with an electric hot plate 9 (Fig. 2). A layer of asbestos 10 is first placed on the hot plate. The general view of the setup used for calibrating the thermistors is shown in Fig. 3.

The accuracy of the result of calibrating a thermistor by the proposed method depends on a number of causes; we shall dwell on identifying them.

1) First of all, the result of calibration is affected by the thermal parameters of the substance whose temperature is measured simultaneously by the thermometer and by the thermistors. In the investigations, the substances used to fill beaker 1 (Fig. 2) were tap and distilled water; the air present in the thermostat; air enclosed in an MPS-250 type thermal chamber; transformer oil; and mercury.

Mercury, owing to its viscosity and high coefficients of thermal conductivity \(\lambda\) and thermal diffusivity \(a\), proved to be the most suitable substance, ensuring sufficiently rapid thermal

Fig. 2.

equilibrium throughout its entire volume and excellent thermal contact with the thermometer and the probes of the thermistors. The accuracy of the calibration result when measuring the temperature of mercury proved to be the highest (root-mean-square error equal to \(\pm 0.1^\circ\mathrm{C}\)). The maximum discrepancy in the thermistor readings during repeated calibrations was \(\pm 0.3^\circ\mathrm{C}\) (see Table 1).

The least suitable substance for calibration proved to be transformer oil. Transformer oil, when placed in an iron can 30 cm in diameter and with an oil-layer height of 3 cm, in the temperature range from \(0^\circ\) to \(+20^\circ\mathrm{C}\), gave at different poin—

of the volume under study, the maximum temperature divergence reached $\pm 3.0^\circ\mathrm{C}$. It was found that different points of the same horizontal layer of oil have approximately the same temperature. The temperature of such layers increased toward the place of heating (toward the bottom of the jar). Such great nonuniformity of the temperature field over the indicated volume of transformer oil is explained by its low coefficient of thermal conductivity at low temperatures.

The maximum discrepancies in the readings of thermistors during repeated calibrations in air were observed: a) when measuring the temperature of an air cylinder 34 cm in diameter and 28 cm high, located in a thermostat, up to $\pm 1.7^\circ\mathrm{C}$; b) when measuring the temperature of an air cube 250 liters in volume, enclosed in a thermal chamber, up to $\pm 2.0^\circ\mathrm{C}$.

When measuring the temperature of water contained in a cylinder 4.5 cm in diameter and 5 cm high, the maximum discrepancies in thermistor readings during repeated standardization were observed in tap water up to $\pm 1.0^\circ\mathrm{C}$ and in distilled water up to $\pm 0.8^\circ\mathrm{C}$.

Thus, as the medium whose temperature is recorded during calibration, it is necessary to choose a substance possessing chemical homogeneity, sufficient viscosity, and high thermal parameters ($\lambda$, $a$). These requirements are practically satisfied by mercury. To eliminate the possibility of mercury evaporation, a layer of water or transformer oil 2–3 mm high is poured over it. This layer is at the same time thermally insulating.

Fig. 3.

2) The accuracy of standardization also depends on the volume of the substance whose temperature is measured during calibration. As is known, the rate at which the process of heat propagation proceeds in any body is the greater, the greater the ratio of its surface to its volume. For cylindrical and prismatic bodies the rate of the process depends strongly on their length. The smaller the length, the higher the rate. Numerous experiments have established the following most suitable dimensions of mercury cylinder 1 (Fig. 3): height 4–5 cm,

diameter of 4–4.5 cm. Proceeding from convenience of operation and taking into account the dimensions of the mercury cylinder, for the setup (Fig. 2) an inner beaker (1) 9 cm high and 4–4.5 cm in diameter is recommended, and an outer beaker (5) 11 cm high and 7–8 cm in diameter. The height of the water layer enclosed between the beakers is recommended to be about 8 cm.

3) In calibration it is very important to choose the thermometer correctly. The thermometers used must be verified ones. In this case it is better to take thermometers with a smaller bulb, because glass has a considerable thermal aftereffect. Therefore, during cooling after temporary heating, the thermometer bulb does not immediately assume the volume that corresponded to the initial temperature. In addition, with a cylindrical bulb shape, as has already been noted, the rate at which the process of heat propagation through the mercury filling the thermometer proceeds is the higher, the shorter the bulb length. In the investigations a thermometer according to GOST 2045–43 was used, with a scale from −2.5° to +52.5°C and a scale division of 0.1°C. The thermometer was verified to an accuracy of 0.1°C at the Tomsk Branch of the Chamber of Measures and Weights on June 15, 1960.

As is known, thermometers are graduated in thermostats. In doing so they are immersed in the liquid filling the thermostat up to the division being read (i.e., all the mercury filling the thermometer is at the temperature of the measured medium). The mercury column protruding from the thermostat has a different temperature. The correction to the thermometer reading for the protruding column can be calculated from the formula

\[ c = n\alpha (t - t_1), \tag{2} \]

where \(c\) is the correction, expressed in degrees;

\(n\) is the number of degrees in the protruding mercury column;

\(\alpha\) is the apparent coefficient of expansion of mercury in glass, equal to 0.00016 for the most commonly used grades of glass of the Jena types 16″, 59″ and according to OST 40117;

\(t\) is the temperature read from the thermometer;

\(t_1\) is the mean temperature of the protruding mercury column, which is determined with the aid of auxiliary thermometer 1 (see Fig. 4).

The conditions under which we carried out the graduation are characterized by the following data. The thermometer was immersed in mercury up to the 0°C division and indicated (for the specified temperature range) the maximum temperature value \(t = n = +35^\circ\text{C}\). The graduation was performed in a room, and the temperature indicated by the auxiliary thermometer was \(t_1 = +18.0^\circ\text{C}\). The maximum correction to the thermometer reading for the protruding mercury column, according to formula (2), will be equal to

\[ c_{\max} = 35 \times 0.00016 \times (35 - 18) = 0.095^\circ = 0.1^\circ\text{C} \]

The calculation performed shows that, when graduating a thermistor intended for determining the temperatures of measuring wires in the range from 0° to +35°C, there is no reason to take into account the correction to the readings of the standard thermometer for the protruding mercury column.

4) Next, attention should be paid to the circumstance that the galvanometer pointer is in a suspended state and “freely” rotates only when the galvanometer is in a horizontal position. Therefore, in order to ensure sufficient calibration accuracy, before beginning graduation the thermistors must be placed in a hori-

horizontal position by level. Special studies have established that when the thermistor is inclined relative to the horizontal plane by an angle equal to 18°, its readings contain an error in the temperature being read of the order of 1.0°C.

5) Finally, the rate of change of the temperature regime has an exceptionally important effect on the accuracy of calibration. On the basis of numerous experiments, it is recommended that the mercury be heated in a natural way, i.e., by the surrounding air. This is done as follows. The water located between the beakers (and consequently the mercury as well) is cooled to 1–2°C below the prescribed minimum temperature for the adopted temperature range. Since the air surrounding the setup (Fig. 3) has room temperature (the calibration temperature), after some time the temperature of the mercury will begin to rise and will reach the air temperature. At the moment when the temperature of the mercury changes, the position of each individual degree (or fraction of a degree) on the thermistor scale is marked according to the reading of the standard thermometer. When the mercury reaches room temperature, its further heating is carried out with the aid of an electric hot plate to 1–2°C above the prescribed maximum temperature. The voltage is then switched off. The temperature of the mercury gradually falls to room temperature. Such a change in the temperature regime of the mercury proves to be the most reliable. The process of cooling and heating the mercury by the surrounding air proceeds slowly and uniformly (without separate heat sources) and, for the range from 0° to +35°C, lasts 4–5 hours. The accuracy of the calibration result in this case proves to be the highest.

Fig. 4.

In order to save time during calibration, the mercury temperature should be changed by heating the water with an electric hot plate, applying a voltage of 40–50 volts when heating the mercury up to +30–32°C, and a voltage of 70 volts when heating above +32°C. In this case it is recommended that the position of a degree on the instrument scale be marked both during heating and during cooling of the mercury. The final position is taken as the average of the positions of the degree on the scale during heating and cooling. The maximum discrepancies in the readings of the thermistors with such a change in the temperature regime of the mercury and with repeated graduations amounted to ±0.3–0.4°C. The time spent on calibrating a thermistor for the range from 0 to +35°C was 3–3.5 hours¹.

Summary sheet of the results of observations of the stability of readings of T-3 thermistors

Table 1

Continuation of Table 1

Let us make a few comments on the calibration procedure. Before beginning the calibration of thermistors, it is necessary to check that the galvanometer pointer coincides with the zero of its scale when there is no current and the arrester is released. For convenience in operation, the thermistor probes and the thermometer should be fastened with copper wire as close as possible to one point (see Fig. 2). The stand must be set up so that the probes and the thermometer do not touch the walls of the beaker (Fig. 2) and are 1–1.5 cm from its bottom. To save power for the thermistor, it is recommended to switch on the current only at the moment when the degree reading on its scale is being recorded. In order to determine whether recalibration of the thermistor is necessary and to monitor its operation, the author proposed the manufacture of paired thermistors on a single Wheatstone bridge. The general appearance of such thermistors (T-3) is shown in Fig. 3.

Verification of the proposed calibration procedure (as well as of the stability of the thermistor readings) was carried out by periodic calibration of semiconductor micro-thermoresistances of type MT-54, Nos. 59, 110, 129, and 120. These micro-resistances were manufactured on 29/IX 1959 and had the following principal technical characteristics:

1. The electrical resistance at 20° C ranges from 3980 to 4025 ohms;

2. The temperature coefficient at 20° C ranges from 3.50 to 3.75%;

3. The time constant is equal to 10 seconds.

The results of the verification are given in Table 1.

REFERENCES

1. Postnikov M. V., “Some questions concerning increasing the accuracy of measuring line lengths in geodetic work.” Collection of Scientific Works of TISI, vol. II, 1957.

2. Postnikov M. V. and Shvartsman Ya. V., “Instrument for determining the temperatures of measuring wires (second model).” Collection of Scientific Works of TISI, vol. IV, 1958.

3. Thermoresistances, semiconductor resistances with a large temperature coefficient. Leningrad, 1957.

4. Preobrazhenskii V. P., Thermal-Engineering Measurements and Instruments. Gosenergoizdat, 1950.

5. Mikheev M. A., Fundamentals of Heat Transfer. Gosenergoizdat, Moscow–Leningrad, 1956.

1. Incidentally, we note that, if a pointer galvanometer “φ” for 2–4 millivolts or a type M95 microammeter is available, it is expedient, for determining the temperature of the mercury, to use a thermocouple instead of a thermometer. A thermocouple makes it possible to eliminate the inertia of the thermometer and to obtain a measurement of the temperature precisely at the specified point of the mercury cylinder. The latter circumstance will make it possible, by using a higher voltage when heating the mercury, to accelerate the calibration process considerably without reducing the accuracy of the result. ↩