(a) Basic Considerations. The resistance thermometer is based upon the inherent characteristic of metals to change electrical resistance* when they undergo a change in temperature. The electrical resistance of verj pure metals varies with temperature from about 0.3 to 0 6% resistance — change per degree at room temperature (or about 0.17 to

‘For many metals the change is completely reversible over fairly large temperature ranges.

0.3 3% per degree Eahrenheit). Industrial resistance — thermometer bulbs are usually made of platinum, copper, or nickel.

An impurity or alloying constituent in a metal decreases the temperature dependence markedly except for a few unusual alloys. Pure platinum in a fully annealed and strain-free state has a resistance—temperature relationship that is especially stable and reproducible. For this reason, pure platinum has been chosen as the international standard of temperature measurement in the temperature range from the liquid oxygen boiling point to the antimony melting point. For the resistance element, platinum is drawn into wire with utmost care to maintain high purity, and the wire is formed into a coil that is carefully supported so that it will not be subjected to mechanical strain caused by differential thermal expansion. Rugged designs are required in military and other applications so that vibration and mechanical shocks will not give momentary or permanent detrimental strain to the platinum coil.

Pure nickel has also been widely used for industrial and many military applications where moderate temperature ranges are involved Tungsten, copper, and some other metals are also used

The fractional change m electrical resistance of a material per unit change in temperature is the temperature coefficient of resistance for the material. The coefficient is expressed as the fractional change in resistance (ohms per ohm) per degree of temperature change at a specific temperature. For most metals, the temperature coefficient is positive.

For pure metals the change in resistance with tempera­ture is practically linear, at least over a substantial range of temperature The relationship can be expressed as

Rt = R0 (1 + at) (4.1)

where Rt equals the resistance in ohms at temperature t, R0 equals the resistance in ohms at 0°C (or some other reference temperature), and the coefficient a is the tem­perature coefficient of resistance. In differential form the relationship is

1 dR

Ro dt

When the resistance does not vary linearly with the temperature, it is customary to include quadratic and cubic terms

Rt = R0 (1 + at + bt2 + ct3) (4.3)

where the coefficients a, b, and c are determined from measurements of the resistance at three or more tempera­tures uniformly spaced over the working range of tempera­ture.

The resistance—temperature relation for platinum is given by the Callendar—VanDusen equation:

Rt

Rn (4.4)

where T is the temperature in degrees Centigrade and (3 is taken as zero for T above 0°C.

(b) Comparison of Resistance Materials. In Fig. 4.10 the resistance R and dR/dT vs. temperature T for a typical platinum resistance sensing element are normalized to 1.00 ohm at 0°C.

-400-200 0 200 400 600 800 10001200 1400 TEMPERATURE, °F

.003

.002 E .c

0

Fig. 4.10—Resistance and sensitivity versus temperature for various materials. Figure is for platinum with a resistance of 1.00 ohm at 32° F.

Tables 4.6 and 4.7 give the values of resistance vs. temperature for platinum, nickel, and copper.

Platinum. As noted earlier, platinum is the standard reference material for resistance thermometers. Recently, sensors made of very thin platinum films deposited on a substrate (usually a ceramic) have come into use. This method of constructing resistance thermometers leads to small sensing elements with high impedance (resistance) values.

Copper. Copper is inexpensive and has the most nearly linear relation of known metals over a rather wide temperature range. Copper has low resistance to oxidation above moderate temperatures and has much poorer stability
and reproducibility than platinum in most applications. The low resistance of copper is a disadvantage when a high — resistance element is desired.

Nickel. Nickel has been widely used as a temperature sensing element over the range from about —100 to +300°C (—150 to 570°F), principally because of its low cost and the high value of its temperature coefficient. Above 300°C (570 F), the resistance—temperature relation for nickel changes character. Nickel is very susceptible to contamina­tion by certain materials, and the relation of resistance to temperature is not as well known nor as reproducible as that of platinum.

Tungsten. The resistance vs. temperature relation of tungsten is not as well known as that of platinum. Full annealing of tungsten is impractical, and therefore tungsten sensors have been found to be less stable than well-made platinum sensors. Tungsten has been shown to have good resistance to very high nuclear-radiation levels and com­pares with platinum in this respect. Because of its mechani­cal strength, extremely fine tungsten wires are rugged, and sensors having high resistance values can be manufactured.

Table 4.6—Resistance vs. Temperature (°F) for Platinum, Nickel, and Copper Resistance Elements* Nickel Platinum 100 ohms 200 ohms Copper °F 10 ohms 100 ohms (type I)+ (type II)T 10 ohms at 25‘ 0 9.290 91.165 89.94 227.190 8.358 32 10.000 98.129 100.00 235.116 9.042 50 10.398 102.030 105.84 239.696 9.428 100 11.496 112.807 122.79 252.890 10.498 150 12.585 123.495 140.92 266.811 11.568 200 13.665 134.095 160.34 281.498 12.638 250 14.736 144.605 181.16 296.993 13.708 300 15.798 155.027 203.51 313.341 14.778 350 16.851 165.361 227.51 330.589 400 17.895 175.606 253.26 340.787 450 18.930 185.762 367.986 500 19.956 195.829 388.242 550 20.973 205.808 409.614 600 21.981 215.699 432.162 650 22.980 225.500 700 23.970 235.213 750 24.951 244.838 800 25.922 254.374 850 26.885 263.821 900 27.839 273.179 950 28.783 282.449 1000 29.719 291.630 1050 30.646 300.723 1100 31.563 309.727 •From Scientific Apparatus Makers Association Standard RC 21-4-1966. tType I nickel resistance thermometers include a series padding resistor to match a specific curve with nickel of varying purity. JType II nickel resistance thermometers include a series and shunt padding resistor to facilitate linear temperature readout.

°С	Platinum	N ickel 100 ohms 200 ohms (type 1)+ (type И) ф	Copper
10 ohms	100 ohms	10 ohms at 25°C
0	10.00	98.129	100.00	235 116	9 042
50	11.976	117 521	130.62	258.923	10.968
100	13.923	136.625	165.20	285.141	12 894
150	15.841	155.442	204.44	314.013	14.820
200	17.729	173.972	249.02	345 809
250	19.588	192.215		380 825
300	21.418	210.171		419.386
350	23 218	227.840
400	24.990	245.221
450	26.732	262.315
500	28 444	279.122
550	30.128	295.642
600	31.782	311.875

Table 4.7—Resistance vs. Temperature (°С) for Platinum, Nickel, and Copper Resistance Elements*

•From Scientific Apparatus Makers Association Standard RC 21-4-1966. tType I nickel resistance thermometers include a series padding resistor to match a specified curve with nickel of varying purity. JType II nickel resistance thermometers include a series and shunt padding resistor to facilitate linear temperature readout.

Table 4.8 lists some typical characteristics of the principal resistance thermometers.

(c) Resistance-Element Structure. The elements of re­sistance thermometers can be constructed in a variety of ways, varying from a cage-like open array of resistance wires within a guard screen to a coil wound on a mandrel and encased in a rugged well. The choice of structure depends on such factors as (1) compatibility of the resis­tance material with the environment, (2) requirements for speed of response, (3) extent of immersion permitted, and (4) expected mechanical stresses to be experienced.

Figure 4.11 shows six types of resistance elements, and Fig. 4.12 shows a typical resistance element assembly in a protecting well.

(d) Resistance-Thermometer Instrumentation. The in­strument measuring the changes in resistance usually employs some form of Wheatstone bridge circuit and may be either an indicator or a recorder. The bridge may be the balanced or unbalanced type. Potentiometnc methods of measuring the resistance are used occasionally.

Figure 4.13 is a diagram of a typical Wheatstone bridge used for resistance-thermometer measurement a and b are ratio arms of equal resistance, and r is a variable resistance, the value of which can be adjusted to balance the bridge so that, except for lead resistance, r = x, x being the resistance of the thermometer resistor.

Copper lead wires have a temperature coefficient of the same order of magnitude as that of a thermometer resistor, and, if their resistance is appreciable in comparison with that of the thermometer resistor, the lead wires may introduce large and uncertain errors into the measurement of temperature. Since the thermometer resistor usually must be placed at a considerable distance from the bridge, the resistance of the lead wires must be compensated. Figure 4.13 illustrates one method of accomplishing this result. Three wires (A, B, and C) connect the measuring instrument and the thermometer resistor (x). Of these, A and C should be identical in size, length, and material and should be placed side by side throughout their length so as to be at the same temperature. The В wire, which is one of the battery wires, need not be similar to the others, however, it is common practice to form the three wires into a cable and make them all alike. A and C are in the thermometer resistor arm (x) and the variable resistance arm (r), respectively. Their resistance remains equal al­though their temperature conditions may change, and, hence, with a one-to-one bridge ratio, such changes have no effect on the bridge reading.

No variable contact resistances should be included in the bridge arms, because the variations in bridge balance introduced at the contacts may be sufficient to affect the reliability of the measurements. The effect of these variations, as well as those resulting from unequal lead resistances, may be reduced by using a resistor of several hundred ohms resistance in the thermometer.

WELL-TYPE ELEMENT

PLATINUM WIRES

CERAMIC COATING PLATINUM TUBE

LEAD WIRE

MINIATURE CERAMIC-COATED ELEMENT

temperatures and are relatively easy to install However, at low temperatures, higher output and higher accuracy are much in favor of resistance sensors

Some of the principal advantages of resistance sensors over thermocouples are

1 A much higher output voltage can be obtained

2 Related recording, controlling, or signal conditioning equipment can be simpler, more accurate, and much less expensive because of the higher possible bridge output signal

3 The output voltage per degree for resistance sensors can be chosen to be exactly as desired over wide limits by adjusting the excitation current and/or the bridge design

4 A reference-junction temperature or compensating device is unnecessary

5 The shape of the curve of output vs temperature can be controlled, within limits, for certain resistance sensor bridge designs

6 The output of a resistance sensor bridge can be made to vary with temperature and another variable bj causing the excitation to vary with the second variable

7 Because of the higher output voltage, more electrical noise can be tolerated with resistance sensors, therefore, longer lead wires can be used

8 Sensitivity to small temperature changes can be much greater

9 In moderate temperature ranges, absolute accuracy and calibration and stability of calibration for resistance elements can be better by a factor of 10 to 100

Thermistors. Thermistors are relatively inexpensive and are very sensitive to temperature The change in resistance per unit change in temperature is large They are available in small sizes and are available with unusually high resistance values when desired Thermistors have a particu­larly nonlinear resistance—temperature relation Because of the nonlinear relation, relatively numerous calibration points are necessary, and the expense of calibration at many points is frequently a major part of the cost of a thermistor temperature sensor

Semiconductors The resistance—temperature relation for the semiconductors consisting of alloy combinations is very complex and therefore requires many more calibra­tion points than platinum sensors At very low tempera­tures semiconductor thermometer^ consisting of doped
germanium sensors have been looked upon with much favor, at least for applied thermometry, as compared to all other methods of measuring temperature When it is necessary to make continuous measurements over the range from approximately 1 to 40°K, they can be used to good advantage

Carbon Resistors At extremely low temperatures car­bon resistors are very sensitive to temperature They have been widely used, mainly for research purposes, for temperature measurements from about 0 1 to 15 or 20°K with good results Their stability is less than might be desired