453:
be round or flat, but must be an electrical insulator. The coefficient of thermal expansion of the winding core material is matched to the sensing wire to minimize any mechanical strain. This strain on the element wire will result in a thermal measurement error. The sensing wire is connected to a larger wire, usually referred to as the element lead or wire. This wire is selected to be compatible with the sensing wire, so that the combination does not generate an emf that would distort the thermal measurement. These elements work with temperatures to 660 °C.
71:
430:). This layer is usually just 10 to 100 ångströms (1 to 10 nanometers) thick. This film is then coated with an epoxy or glass that helps protect the deposited film and also acts as a strain relief for the external lead wires. Disadvantages of this type are that they are not as stable as their wire-wound or coiled counterparts. They also can only be used over a limited temperature range due to the different expansion rates of the substrate and resistive deposited giving a "
704:
758:(Standard SPRTs). They are constructed like the UPRT, but the materials are more cost-effective. SPRTs commonly use reference-grade, high-purity smaller-diameter platinum wire, metal sheaths and ceramic type insulators. Internal lead wires are usually a nickel-based alloy. Standard PRTs are more limited in temperature range (−200 °C to 500 °C) and are approximately accurate to ±0.03 °C over the temperature range.
458:
725:
439:
413:
434:" effect that can be seen in the resistive temperature coefficient. These elements work with temperatures to 300 °C (572 °F) without further packaging, but can operate up to 600 °C (1,112 °F) when suitably encapsulated in glass or ceramic. Special high-temperature RTD elements can be used up to 900 °C (1,652 °F) with the right encapsulation.
751:, depending on temperature range. Larger-diameter platinum wire is used, which drives up the cost and results in a lower resistance for the probe (typically 25.5 Ω). UPRTs have a wide temperature range (−200 °C to 1000 °C) and are approximately accurate to ±0.001 °C over the temperature range. UPRTs are only appropriate for laboratory use.
844:– was caused by multiple failures of RTDs which had become brittle and unreliable due to multiple heat-and-cool cycles. (The failures of the sensors falsely suggested that a fuel pump was critically overheating, and the engine was automatically shut down.) Following the engine failure incident, the RTDs were replaced with
747:(UPRTs). This accuracy is achieved at the expense of durability and cost. The UPRT elements are wound from reference-grade platinum wire. Internal lead wires are usually made from platinum, while internal supports are made from quartz or fused silica. The sheaths are usually made from quartz or sometimes
734:
eliminates voltage drop in the measuring leads as a contribution to error. To increase accuracy further, any residual thermoelectric voltages generated by different wire types or screwed connections are eliminated by reversal of the direction of the 1 mA current and the leads to the DVM (digital
452:
can have greater accuracy, especially for wide temperature ranges. The coil diameter provides a compromise between mechanical stability and allowing expansion of the wire to minimize strain and consequential drift. The sensing wire is wrapped around an insulating mandrel or core. The winding core can
764:
are designed to withstand industrial environments. They can be almost as durable as a thermocouple. Depending on the application, industrial PRTs can use thin-film or coil-wound elements. The internal lead wires can range from PTFE-insulated stranded nickel-plated copper to silver wire, depending on
714:
circuit shown, the voltage drop on the lower left hand side is V_rtd + V_lead, and on the lower righthand side is V_R3 + V_lead, therefore the bridge voltage (V_b) is the difference, V_rtd − V_R3. The voltage drop due to the lead resistance has been cancelled out. This always applies if R1=R2,
534:
of resistance 0.00385/°C (0.385%/°C) (European
Fundamental Interval). The sensor is usually made to have a resistance of 100 Ω at 0 °C. This is defined in BS EN 60751:1996 (taken from IEC 60751:1995). The American Fundamental Interval is 0.00392/°C, based on using a purer grade of platinum
529:
The platinum detecting wire needs to be kept free of contamination to remain stable. A platinum wire or film is supported on a former in such a way that it gets minimal differential expansion or other strains from its former, yet is reasonably resistant to vibration. RTD assemblies made from iron or
481:
The current international standard that specifies tolerance and the temperature-to-electrical resistance relationship for platinum resistance thermometers (PRTs) is IEC 60751:2008; ASTM E1137 is also used in the United States. By far the most common devices used in industry have a nominal resistance
476:
is based, while providing the durability necessary for industrial use. The basis of the sensing element is a small coil of platinum sensing wire. This coil resembles a filament in an incandescent light bulb. The housing or mandrel is a hard fired ceramic oxide tube with equally spaced bores that run
353:
is used for the highest-accuracy calibrations by national metrology laboratories. It uses the triple point, freezing point or melting point of pure substances such as water, zinc, tin, and argon to generate a known and repeatable temperature. These cells allow the user to reproduce actual conditions
345:
relationship of any RTD over a temperature range that represents the planned range of use, calibration must be performed at temperatures other than 0 °C and 100 °C. This is necessary to meet calibration requirements. Although RTDs are considered to be linear in operation, it must be proven
486:
at 0 °C and are called Pt100 sensors ("Pt" is the symbol for platinum, "100" for the resistance in ohms at 0 °C). It is also possible to get Pt1000 sensors, where 1000 is for the resistance in ohms at 0 °C. The sensitivity of a standard 100 Ω sensor is a nominal 0.385 Ω/°C. RTDs
572:
RTDs in industrial applications are rarely used above 660 °C. At temperatures above 660 °C it becomes increasingly difficult to prevent the platinum from becoming contaminated by impurities from the metal sheath of the thermometer. This is why laboratory standard thermometers replace the
407:
use a wire coil minimally supported within a sealed housing filled with an inert gas. These sensors work up to 961.78 °C (1,763.20 °F) and are used in the SPRTs that define ITS-90. They consist of platinum wire loosely coiled over a support structure, so the element is free to expand and
358:
temperature scale. Fixed-point calibrations provide extremely accurate calibrations (within ±0.001 °C). A common fixed-point calibration method for industrial-grade probes is the ice bath. The equipment is inexpensive, easy to use, and can accommodate several sensors at once. The ice point is
313:
has α = 0.003925 Ω/(Ω·°C) in the 0 to 100 °C range and is used in the construction of laboratory-grade RTDs. Conversely, two widely recognized standards for industrial RTDs IEC 60751 and ASTM E-1137 specify α = 0.00385 Ω/(Ω·°C). Before these standards were widely adopted, several different α
693:
For a balanced bridge usual setting is with R2 = R1, and R3 around the middle of the range of the RTD. So for example, if we are going to measure between 0 and 100 °C (32 and 212 °F), RTD resistance will range from 100 Ω to 138.5 Ω. We would choose R3 = 120 Ω. In that way we get a small
689:
The simplest resistance-thermometer configuration uses two wires. It is only used when high accuracy is not required, as the resistance of the connecting wires is added to that of the sensor, leading to errors of measurement. This configuration allows use of 100 meters of cable. This applies
668:
The RTD construction design may be enhanced to handle shock and vibration by including compacted magnesium oxide (MgO) powder inside the sheath. MgO is used to isolate the conductors from the external sheath and from each other. MgO is used due to its dielectric constant, rounded grain structure,
471:
have largely replaced wire-wound elements in industry. This design has a wire coil that can expand freely over temperature, held in place by some mechanical support, which lets the coil keep its shape. This “strain free” design allows the sensing wire to expand and contract free of influence from
664:
insulators are used at temperatures below about 250 °C. Above this, glass fibre or ceramic are used. The measuring point, and usually most of the leads, require a housing or protective sleeve, often made of a metal alloy that is chemically inert to the process being monitored. Selecting and
828:
A 1971 paper by
Eriksson, Keuther, and Glatzel identified six noble metal alloys (63Pt37Rh, 37Pd63Rh, 26Pt74Ir, 10Pd90Ir, 34Pt66Au, 14Pd86Au) with approximately linear resistance temperature characteristics. The alloy 63Pt37Rh is similar to the readily available 70Pt30Rh alloy wire used in
615:
If process temperatures are between −200 and 500 °C (−328.0 and 932.0 °F), an industrial RTD is the preferred option. Thermocouples have a range of −180 to 2,320 °C (−292.0 to 4,208.0 °F), so for temperatures above 500 °C (932 °F) it is the contact temperature
365:
is commonly used with secondary standard platinum resistance thermometers and industrial RTDs. The thermometers being calibrated are compared to calibrated thermometers by means of a bath whose temperature is uniformly stable. Unlike fixed-point calibrations, comparisons can be made at any
477:
transverse to the axes. The coil is inserted in the bores of the mandrel and then packed with a very finely ground ceramic powder. = This permits the sensing wire to move, while still remaining in good thermal contact with the process. These elements work with temperatures to 850 °C.
824:
invented the
Platinum Resistance Temperature Detector and presented a three-term interpolation formula. Siemens’ RTD rapidly fell out of favour due to the instability of the temperature reading. Hugh Longbourne Callendar developed the first commercially successful platinum RTD in 1885.
622:
If the process requires a very fast response to temperature changes (fractions of a second as opposed to seconds), then a thermocouple is the best choice. Time response is measured by immersing the sensor in water moving at 1 m/s (3.3 ft/s) with a 63.2% step
147:
The significant characteristic of metals used as resistive elements is the linear approximation of the resistance versus temperature relationship between 0 and 100 °C. This temperature coefficient of resistance is denoted by α and is usually given in units of
635:
If a tolerance of 2 °C is acceptable and the highest level of repeatability is not required, a thermocouple will serve. RTDs are capable of higher accuracy and can maintain stability for many years, while thermocouples can drift within the first few hours of
366:
temperature between −100 °C and 500 °C (−148 °F to 932 °F). This method might be more cost-effective, since several sensors can be calibrated simultaneously with automated equipment. These electrically heated and well-stirred baths use
715:
and R1, R2 >> RTD, R3. R1 and R2 can serve the use of limiting the current through the RTD, for example for a Pt100, limiting to 1 mA, and 5 V, would suggest a limiting resistance of approximately R1 = R2 = 5/0.001 = 5,000 Ohms.
1201:
1067:
535:
than the
European standard. The American standard is from the Scientific Apparatus Manufacturers Association (SAMA), who are no longer in this standards field. As a result, the "American standard" is hardly the standard even in the US.
1612:
709:
In order to minimize the effects of the lead resistances, a three-wire configuration can be used. The suggested setting for the configuration shown, is with R1 = R2, and R3 around the middle of the range of the RTD. Looking at the
241:
346:
that they are accurate with regard to the temperatures with which they will actually be used (see details in
Comparison calibration option). Two common calibration methods are the fixed-point method and the comparison method.
34:
used to measure temperature. Many RTD elements consist of a length of fine wire wrapped around a heat-resistant ceramic or glass core but other constructions are also used. The RTD wire is a pure material, typically
2910:"On the Increase of Electrical Resistance in Conductors with Rise of Temperature, and Its Application to the Measure of Ordinary and Furnace Temperatures; Also on a Simple Method of Measuring Electrical Resistances"
684:
1739:
1483:
1409:
1335:
393:
are cheap and widely used. They have very reproducible results at low temperatures. They are the most reliable over extremely wide range of temperatures. They generally do not suffer from significant
47:(Cu). The material has an accurate resistance/temperature relationship which is used to provide an indication of temperature. As RTD elements are fragile, they are often housed in protective probes.
379:
The three main categories of RTD sensors are thin-film, wire-wound, and coiled elements. While these types are the ones most widely used in industry, other more exotic shapes are used; for example,
765:
the sensor size and application. Sheath material is typically stainless steel; higher-temperature applications may demand
Inconel. Other materials are used for specialized applications.
647:
538:
Lead-wire resistance can also be a factor; adopting three- and four-wire, instead of two-wire, connections can eliminate connection-lead resistance effects from measurements (see
665:
designing protection sheaths can require more care than the actual sensor, as the sheath must withstand chemical or physical attack and provide convenient attachment points.
735:
voltmeter). The thermoelectric voltages will be produced in one direction only. By averaging the reversed measurements, the thermoelectric error voltages are cancelled out.
3099:
L. J. Eriksson, F. W. Keuther, and J.J. Glatzel (1971). “A Linear
Resistance Thermometer,” Proceedings of the Fifth Temperature Symposium, Washington, DC, 1971, pp. 989–995
1073:
905:
542:); three-wire connection is sufficient for most purposes and is an almost universal industrial practice. Four-wire connections are used for the most precise applications.
629:
A standard RTD sheath is 3.175 to 6.35 mm (0.1250 to 0.2500 in) in diameter; sheath diameters for thermocouples can be less than 1.6 mm (0.063 in).
596:, platinum RTDs are less sensitive to small temperature changes and have a slower response time. However, thermistors have a smaller temperature range and stability.
303:
1642:
1262:
1231:
274:
359:
designated as a secondary standard because its accuracy is ±0.005 °C (±0.009 °F), compared to ±0.001 °C (±0.0018 °F) for primary fixed points.
1505:
582:
144:
has a very linear resistance–temperature relationship; however, copper oxidizes at moderate temperatures and cannot be used over 150 °C (302 °F).
158:
140:
elements have a limited temperature range because the temperature coefficient of resistance changes at temperatures over 300 °C (572 °F).
408:
contract with temperature. They are very susceptible to shock and vibration, as the loops of platinum can sway back and forth, causing deformation.
895:
Resistance-thermometer elements functioning up to 1000 °C can be supplied. The relation between temperature and resistance is given by the
3019:
314:
values were used. It is still possible to find older probes that are made with platinum that have α = 0.003916 Ω/(Ω·°C) and 0.003902 Ω/(Ω·°C).
114:
relationship is defined as the amount of resistance change of the sensor per degree of temperature change. The relative change in resistance (
856:
Temperature sensors are usually supplied with thin-film elements. The resistance elements are rated in accordance with BS EN 60751:2008 as:
1650:
426:
have a sensing element that is formed by depositing a very thin layer of resistive material, normally platinum, on a ceramic substrate (
1415:
1341:
1270:
604:
The two most common ways of measuring temperatures for industrial applications are with resistance temperature detectors (RTDs) and
1499:
For positive temperature, solution of the quadratic equation yields the following relationship between temperature and resistance:
1617:
Then for a four-wire configuration with a 1 mA precision current source the relationship between temperature and measured voltage
573:
metal sheath with a glass construction. At very low temperatures, say below −270 °C (3 K), because there are very few
321:– carefully introducing impurities, which become embedded in the lattice structure of the platinum and result in a different
3079:. Research Triangle Park, North Carlolina: The Instrumentation, Systems and Automation Society (ISA). pp. 173–175.
3084:
2886:
1786:
1779:
896:
523:
2851:
Meaning that the same measurement remains unchanged for the same temperature under influence of the surroundings.
3169:
2956:
2939:
3056:"Omega Engineering | Shop for Sensing, Monitoring and Control Solutions with Technical Expertise"
2842:
Consistency of repeatitive measurement under influence of the surroundings over a long period of time
1196:{\displaystyle R_{T}=R_{0}\left\;(0\;{}^{\circ }\mathrm {C} \leq T<850\;{}^{\circ }\mathrm {C} ).}
1062:{\displaystyle R_{T}=R_{0}\left\;(-200\;{}^{\circ }\mathrm {C} <T<0\;{}^{\circ }\mathrm {C} ),}
837:
814:
703:
586:
487:
with a sensitivity of 0.375 and 0.392 Ω/°C, as well as a variety of others, are also available.
3027:
2945:. Gaithersburg, MD: National Institute of Standards and Technology. NIST Special Publication 250-81.
3041:
724:
683:
2909:
661:
531:
115:
1744:
1496:
coefficients are relatively small, the resistance changes almost linearly with the temperature.
136:
and has the most stable resistance–temperature relationship over the largest temperature range.
2981:
3174:
790:
731:
515:
281:
103:
3077:
Measurement and
Control Basics, resources for measurement and control series. (3:e upplagan)
730:
The four-wire resistance configuration increases the accuracy of measurement of resistance.
472:
other materials; in this respect it is similar to the SPRT, the primary standard upon which
1620:
1607:{\displaystyle T={\frac {-A+{\sqrt {A^{2}-4B\left(1-{\frac {R_{T}}{R_{0}}}\right)}}}{2B}}.}
1240:
1209:
821:
794:
786:
252:
502:
Resistance thermometers are constructed in a number of forms and offer greater stability,
8:
1264:
is the resistance at 0 °C, and the constants (for an α = 0.00385 platinum RTD) are:
836:
made extensive use of platinum resistance thermometers. The only in-flight shutdown of a
125:
3055:
3080:
2882:
711:
236:{\displaystyle \alpha ={\frac {R_{100}-R_{0}}{100~^{\circ }{\text{C}}\cdot R_{0}}},}
3164:
2940:"Standard Platinum Resistance Thermometer Calibrations from the Ar TP to the Ag FP"
798:
129:
813:
as a suitable element. The necessary methods of construction were established by
3145:
Standard
Platinum Resistance Thermometer Calibrations from the Ar TP to the Ag FP
2876:
657:
530:
copper are also used in some applications. Commercial platinum grades exhibit a
774:
511:
3121:
3158:
2917:
1745:
Temperature-dependent resistances for various popular resistance thermometers
845:
833:
806:
802:
507:
91:
51:
518:
and require a power source to operate. The resistance ideally varies nearly
2823:
782:
605:
491:
431:
367:
70:
55:
778:
133:
118:
of resistance) varies only slightly over the useful range of the sensor.
3109:
Wings in Orbit: Scientific and
Engineering Legacies of the Space Shuttle
490:"Pt200" redirects here. For the isotope of platinum (Pt-200 or Pt), see
370:
and molten salts as the medium for the various calibration temperatures.
2818:
2813:
2808:
1758:
781:
in metals is dependent on the temperature was announced in 1821 by Sir
593:
578:
483:
394:
78:
Common RTD sensing elements for biomedical application constructed of
3147:. Gaithersburg, MD: National Institute of Standards and Technology.
608:. The choice between them is typically determined by four factors.
503:
457:
386:
are used at ultra-low temperatures (−273 °C to −173 °C).
383:
310:
121:
79:
36:
1734:{\displaystyle T={\frac {-A+{\sqrt {A^{2}-40B(0.1-V_{T})}}}{2B}}.}
646:
1478:{\displaystyle C=-4.183\times 10^{-12}~^{\circ }{\text{C}}^{-4}.}
841:
810:
748:
438:
427:
59:
1404:{\displaystyle B=-5.775\times 10^{-7}~^{\circ }{\text{C}}^{-2},}
1330:{\displaystyle A=3.9083\times 10^{-3}~^{\circ }{\text{C}}^{-1},}
585:
and thus basically independent of temperature. As a result, the
412:
65:
652:
These elements nearly always require insulated leads attached.
574:
519:
473:
380:
355:
318:
141:
137:
87:
83:
44:
40:
31:
510:
in some cases than thermocouples. While thermocouples use the
550:
The advantages of platinum resistance thermometers include:
128:
as an element for a resistance temperature detector at the
616:
measurement device commonly found in physics laboratories.
589:
of the RTD is essentially zero and therefore not useful.
669:
high-temperature capability, and its chemical inertness.
653:
149:
851:
3136:
317:
These different α values for platinum are achieved by
1653:
1623:
1508:
1418:
1344:
1273:
1243:
1212:
1076:
908:
817:, Griffiths, Holborn and Wein between 1885 and 1900.
284:
255:
161:
690:
equally to balanced bridge and fixed bridge system.
793:with rising temperature was first described by Sir
577:, the resistance of an RTD is mainly determined by
514:to generate a voltage, resistance thermometers use
1733:
1636:
1606:
1477:
1403:
1329:
1256:
1225:
1195:
1061:
297:
268:
235:
3156:
3020:"Hand Held Thermometers | Charnwood Instruments"
2799:Copied from German version, please do not remove
785:. The practical application of the tendency of
745:Ultra Precise Platinum Resistance Thermometers
94:, resistance versus temperature relationship (
754:Another classification of laboratory PRTs is
545:
66:Resistance/temperature relationship of metals
2878:Sensor Technology Series: Biomedical Sensors
2870:
2868:
697:
58:in industrial applications below 600 °
1172:
1145:
1138:
1038:
1011:
1001:
738:
718:
539:
305:is the resistance of the sensor at 100 °C.
2865:
756:Standard Platinum Resistance Thermometers
743:The highest-accuracy of all PRTs are the
677:
672:
599:
456:
437:
411:
276:is the resistance of the sensor at 0 °C,
69:
16:Type of temperature sensor (thermometer)
3142:
3042:"Temperature Coefficient of Resistance"
2957:"RESISTANCE TEMPERATURE DETECTOR – RTD"
2937:
2907:
563:Suitability for precision applications.
3157:
3074:
3070:
3068:
2874:
50:RTDs, which have higher accuracy and
852:Standard resistance thermometer data
632:Accuracy and stability requirements
13:
3065:
1183:
1156:
1049:
1022:
14:
3186:
1233:is the resistance at temperature
723:
702:
694:measured voltage in the bridge.
682:
645:
374:
24:resistance temperature detectors
3114:
3102:
3093:
3048:
3034:
3024:www.instrumentationservices.net
640:
3012:
2999:
2974:
2949:
2931:
2901:
2845:
2836:
1712:
1693:
1187:
1139:
1053:
1002:
993:
981:
332:
1:
2858:
3123:Precision Low Current Source
897:Callendar–Van Dusen equation
524:Callendar–Van Dusen equation
7:
2802:
497:
10:
3193:
3075:Hughes, Thomas A. (2002).
768:
546:Advantages and limitations
489:
2908:Siemens, William (1871).
1756:
1751:
838:Space Shuttle Main Engine
522:with temperature per the
329:curve and hence α value.
2875:Jones, Deric P. (2010),
2829:
698:Three-wire configuration
397:or strain gauge effects.
390:Carbon resistor elements
74:SPRT glass capsule – RTD
3143:Strouse, G. F. (2008).
2938:Strouse, G. F. (2008).
739:Classifications of RTDs
719:Four-wire configuration
532:temperature coefficient
362:Comparison calibrations
350:Fixed-point calibration
298:{\displaystyle R_{100}}
116:temperature coefficient
54:, are slowly replacing
20:Resistance thermometers
1735:
1638:
1608:
1479:
1405:
1331:
1258:
1227:
1197:
1063:
678:Two-wire configuration
462:
443:
417:
299:
270:
237:
75:
1736:
1639:
1637:{\displaystyle V_{T}}
1609:
1480:
1406:
1332:
1259:
1257:{\displaystyle R_{0}}
1228:
1226:{\displaystyle R_{T}}
1198:
1064:
791:electrical resistance
787:electrical conductors
777:, the discovery that
732:Four-terminal sensing
673:Wiring configurations
600:RTDs vs thermocouples
516:electrical resistance
460:
441:
415:
300:
271:
269:{\displaystyle R_{0}}
238:
104:operating temperature
73:
3170:Resistive components
2961:www.punetechtrol.com
2914:The Bakerian Lecture
1651:
1621:
1506:
1416:
1342:
1271:
1241:
1210:
1074:
906:
881:−30 to +300 °C
873:−50 to +500 °C
822:Carl Wilhelm Siemens
773:Contemporary to the
560:Wide operating range
404:Strain-free elements
337:To characterize the
282:
253:
159:
801:of 1871 before the
583:boundary scattering
449:Wire-wound elements
126:Sir William Siemens
2881:, Momentum Press,
1731:
1634:
1604:
1475:
1401:
1327:
1254:
1223:
1193:
1059:
889:0 to +150 °C
789:to increase their
463:
444:
423:Thin-film elements
418:
295:
266:
233:
76:
3030:on March 5, 2009.
3007:RTD Element Types
2797:
2796:
1726:
1715:
1599:
1588:
1581:
1461:
1450:
1387:
1376:
1313:
1302:
893:
892:
712:Wheatstone bridge
228:
212:
202:
132:in 1871: it is a
3182:
3149:
3148:
3140:
3134:
3133:
3132:
3130:
3118:
3112:
3106:
3100:
3097:
3091:
3090:
3072:
3063:
3062:
3060:
3052:
3046:
3045:
3038:
3032:
3031:
3026:. Archived from
3016:
3010:
3009:
3003:
2997:
2996:
2995:
2993:
2988:
2983:Carbon Resistors
2978:
2972:
2971:
2969:
2967:
2953:
2947:
2946:
2944:
2935:
2929:
2928:
2926:
2924:
2905:
2899:
2898:
2897:
2895:
2872:
2852:
2849:
2843:
2840:
1749:
1748:
1740:
1738:
1737:
1732:
1727:
1725:
1717:
1716:
1711:
1710:
1683:
1682:
1673:
1661:
1643:
1641:
1640:
1635:
1633:
1632:
1613:
1611:
1610:
1605:
1600:
1598:
1590:
1589:
1587:
1583:
1582:
1580:
1579:
1570:
1569:
1560:
1538:
1537:
1528:
1516:
1484:
1482:
1481:
1476:
1471:
1470:
1462:
1459:
1456:
1455:
1448:
1446:
1445:
1410:
1408:
1407:
1402:
1397:
1396:
1388:
1385:
1382:
1381:
1374:
1372:
1371:
1336:
1334:
1333:
1328:
1323:
1322:
1314:
1311:
1308:
1307:
1300:
1298:
1297:
1263:
1261:
1260:
1255:
1253:
1252:
1232:
1230:
1229:
1224:
1222:
1221:
1202:
1200:
1199:
1194:
1186:
1181:
1180:
1175:
1159:
1154:
1153:
1148:
1137:
1133:
1132:
1131:
1099:
1098:
1086:
1085:
1068:
1066:
1065:
1060:
1052:
1047:
1046:
1041:
1025:
1020:
1019:
1014:
1000:
996:
980:
979:
964:
963:
931:
930:
918:
917:
862:Tolerance class
859:
858:
840:– mission
799:Bakerian Lecture
727:
706:
686:
649:
461:Coil-element PRT
304:
302:
301:
296:
294:
293:
275:
273:
272:
267:
265:
264:
242:
240:
239:
234:
229:
227:
226:
225:
213:
210:
208:
207:
200:
194:
193:
192:
180:
179:
169:
130:Bakerian lecture
124:was proposed by
3192:
3191:
3185:
3184:
3183:
3181:
3180:
3179:
3155:
3154:
3153:
3152:
3141:
3137:
3128:
3126:
3120:
3119:
3115:
3107:
3103:
3098:
3094:
3087:
3073:
3066:
3058:
3054:
3053:
3049:
3040:
3039:
3035:
3018:
3017:
3013:
3005:
3004:
3000:
2991:
2989:
2986:
2980:
2979:
2975:
2965:
2963:
2955:
2954:
2950:
2942:
2936:
2932:
2922:
2920:
2906:
2902:
2893:
2891:
2889:
2873:
2866:
2861:
2856:
2855:
2850:
2846:
2841:
2837:
2832:
2805:
2800:
1809:
1804:
1799:
1794:
1789:
1782:
1775:
1770:
1766:
1753:
1747:
1718:
1706:
1702:
1678:
1674:
1672:
1662:
1660:
1652:
1649:
1648:
1628:
1624:
1622:
1619:
1618:
1591:
1575:
1571:
1565:
1561:
1559:
1552:
1548:
1533:
1529:
1527:
1517:
1515:
1507:
1504:
1503:
1463:
1458:
1457:
1451:
1447:
1438:
1434:
1417:
1414:
1413:
1389:
1384:
1383:
1377:
1373:
1364:
1360:
1343:
1340:
1339:
1315:
1310:
1309:
1303:
1299:
1290:
1286:
1272:
1269:
1268:
1248:
1244:
1242:
1239:
1238:
1217:
1213:
1211:
1208:
1207:
1182:
1176:
1174:
1173:
1155:
1149:
1147:
1146:
1127:
1123:
1104:
1100:
1094:
1090:
1081:
1077:
1075:
1072:
1071:
1048:
1042:
1040:
1039:
1021:
1015:
1013:
1012:
975:
971:
959:
955:
936:
932:
926:
922:
913:
909:
907:
904:
903:
854:
829:thermocouples.
795:William Siemens
771:
762:Industrial PRTs
741:
721:
700:
680:
675:
658:silicone rubber
643:
602:
548:
500:
495:
468:Coiled elements
377:
335:
289:
285:
283:
280:
279:
260:
256:
254:
251:
250:
221:
217:
209:
203:
199:
195:
188:
184:
175:
171:
170:
168:
160:
157:
156:
68:
17:
12:
11:
5:
3190:
3189:
3178:
3177:
3172:
3167:
3151:
3150:
3135:
3113:
3101:
3092:
3086:978-1556177644
3085:
3064:
3047:
3033:
3011:
2998:
2973:
2948:
2930:
2900:
2887:
2863:
2862:
2860:
2857:
2854:
2853:
2844:
2834:
2833:
2831:
2828:
2827:
2826:
2821:
2816:
2811:
2804:
2801:
2798:
2795:
2794:
2792:
2790:
2788:
2786:
2784:
2782:
2779:
2776:
2773:
2769:
2768:
2766:
2764:
2762:
2760:
2758:
2756:
2753:
2750:
2747:
2743:
2742:
2740:
2738:
2736:
2734:
2732:
2730:
2727:
2724:
2721:
2717:
2716:
2714:
2712:
2710:
2708:
2706:
2704:
2701:
2698:
2695:
2691:
2690:
2688:
2686:
2684:
2682:
2680:
2677:
2674:
2671:
2668:
2664:
2663:
2660:
2658:
2656:
2654:
2652:
2649:
2646:
2643:
2640:
2636:
2635:
2632:
2630:
2628:
2626:
2624:
2621:
2618:
2615:
2612:
2608:
2607:
2604:
2602:
2600:
2598:
2596:
2593:
2590:
2587:
2584:
2580:
2579:
2576:
2574:
2572:
2570:
2568:
2565:
2562:
2559:
2556:
2552:
2551:
2548:
2546:
2544:
2542:
2540:
2537:
2534:
2531:
2528:
2524:
2523:
2520:
2518:
2516:
2514:
2512:
2509:
2506:
2503:
2500:
2496:
2495:
2492:
2490:
2488:
2486:
2484:
2481:
2478:
2475:
2472:
2468:
2467:
2464:
2461:
2459:
2457:
2455:
2452:
2449:
2446:
2443:
2439:
2438:
2435:
2432:
2430:
2428:
2426:
2423:
2420:
2417:
2414:
2410:
2409:
2407:
2404:
2402:
2400:
2398:
2395:
2392:
2389:
2386:
2382:
2381:
2379:
2376:
2374:
2372:
2370:
2367:
2364:
2361:
2358:
2354:
2353:
2351:
2348:
2346:
2344:
2341:
2338:
2335:
2332:
2329:
2325:
2324:
2322:
2319:
2317:
2315:
2312:
2309:
2306:
2303:
2300:
2296:
2295:
2293:
2290:
2288:
2286:
2283:
2280:
2277:
2274:
2271:
2267:
2266:
2264:
2261:
2259:
2257:
2254:
2251:
2248:
2245:
2242:
2238:
2237:
2235:
2233:
2231:
2229:
2226:
2223:
2220:
2217:
2214:
2210:
2209:
2207:
2205:
2203:
2201:
2198:
2195:
2192:
2189:
2186:
2182:
2181:
2179:
2177:
2175:
2172:
2169:
2166:
2163:
2160:
2157:
2153:
2152:
2150:
2148:
2146:
2143:
2140:
2137:
2134:
2131:
2128:
2124:
2123:
2121:
2119:
2117:
2114:
2111:
2108:
2105:
2102:
2099:
2095:
2094:
2092:
2090:
2088:
2085:
2082:
2079:
2076:
2073:
2070:
2066:
2065:
2063:
2061:
2058:
2055:
2053:
2050:
2047:
2044:
2041:
2037:
2036:
2034:
2032:
2029:
2026:
2024:
2021:
2018:
2015:
2012:
2008:
2007:
2005:
2003:
2000:
1997:
1995:
1992:
1989:
1986:
1983:
1979:
1978:
1976:
1974:
1971:
1968:
1966:
1963:
1960:
1957:
1954:
1950:
1949:
1947:
1945:
1942:
1940:
1938:
1935:
1932:
1929:
1926:
1922:
1921:
1919:
1917:
1914:
1912:
1910:
1907:
1904:
1901:
1898:
1894:
1893:
1891:
1889:
1886:
1884:
1882:
1879:
1876:
1873:
1870:
1866:
1865:
1863:
1861:
1859:
1857:
1855:
1852:
1849:
1846:
1843:
1839:
1838:
1836:
1834:
1832:
1830:
1828:
1825:
1822:
1819:
1816:
1812:
1811:
1806:
1801:
1796:
1791:
1784:
1777:
1772:
1767:
1762:
1761:
1757:Resistance in
1755:
1746:
1743:
1742:
1741:
1730:
1724:
1721:
1714:
1709:
1705:
1701:
1698:
1695:
1692:
1689:
1686:
1681:
1677:
1671:
1668:
1665:
1659:
1656:
1631:
1627:
1615:
1614:
1603:
1597:
1594:
1586:
1578:
1574:
1568:
1564:
1558:
1555:
1551:
1547:
1544:
1541:
1536:
1532:
1526:
1523:
1520:
1514:
1511:
1486:
1485:
1474:
1469:
1466:
1454:
1444:
1441:
1437:
1433:
1430:
1427:
1424:
1421:
1411:
1400:
1395:
1392:
1380:
1370:
1367:
1363:
1359:
1356:
1353:
1350:
1347:
1337:
1326:
1321:
1318:
1306:
1296:
1293:
1289:
1285:
1282:
1279:
1276:
1251:
1247:
1220:
1216:
1204:
1203:
1192:
1189:
1185:
1179:
1171:
1168:
1165:
1162:
1158:
1152:
1144:
1141:
1136:
1130:
1126:
1122:
1119:
1116:
1113:
1110:
1107:
1103:
1097:
1093:
1089:
1084:
1080:
1069:
1058:
1055:
1051:
1045:
1037:
1034:
1031:
1028:
1024:
1018:
1010:
1007:
1004:
999:
995:
992:
989:
986:
983:
978:
974:
970:
967:
962:
958:
954:
951:
948:
945:
942:
939:
935:
929:
925:
921:
916:
912:
891:
890:
887:
883:
882:
879:
875:
874:
871:
867:
866:
863:
853:
850:
775:Seebeck effect
770:
767:
740:
737:
720:
717:
699:
696:
679:
676:
674:
671:
642:
639:
638:
637:
633:
630:
627:
624:
620:
617:
613:
601:
598:
565:
564:
561:
558:
555:
547:
544:
512:Seebeck effect
499:
496:
479:
478:
469:
455:
454:
450:
442:Wire-wound PRT
436:
435:
424:
410:
409:
405:
399:
398:
391:
376:
373:
372:
371:
363:
360:
351:
334:
331:
307:
306:
292:
288:
277:
263:
259:
244:
243:
232:
224:
220:
216:
206:
198:
191:
187:
183:
178:
174:
167:
164:
67:
64:
22:, also called
15:
9:
6:
4:
3:
2:
3188:
3187:
3176:
3173:
3171:
3168:
3166:
3163:
3162:
3160:
3146:
3139:
3125:
3124:
3117:
3110:
3105:
3096:
3088:
3082:
3078:
3071:
3069:
3057:
3051:
3043:
3037:
3029:
3025:
3021:
3015:
3008:
3002:
2985:
2984:
2977:
2962:
2958:
2952:
2941:
2934:
2919:
2918:Royal Society
2915:
2911:
2904:
2894:September 18,
2890:
2888:9781606500569
2884:
2880:
2879:
2871:
2869:
2864:
2848:
2839:
2835:
2825:
2822:
2820:
2817:
2815:
2812:
2810:
2807:
2806:
2793:
2791:
2789:
2787:
2785:
2783:
2780:
2777:
2774:
2771:
2770:
2767:
2765:
2763:
2761:
2759:
2757:
2754:
2751:
2748:
2745:
2744:
2741:
2739:
2737:
2735:
2733:
2731:
2728:
2725:
2722:
2719:
2718:
2715:
2713:
2711:
2709:
2707:
2705:
2702:
2699:
2696:
2693:
2692:
2689:
2687:
2685:
2683:
2681:
2678:
2675:
2672:
2669:
2666:
2665:
2661:
2659:
2657:
2655:
2653:
2650:
2647:
2644:
2641:
2638:
2637:
2633:
2631:
2629:
2627:
2625:
2622:
2619:
2616:
2613:
2610:
2609:
2605:
2603:
2601:
2599:
2597:
2594:
2591:
2588:
2585:
2582:
2581:
2577:
2575:
2573:
2571:
2569:
2566:
2563:
2560:
2557:
2554:
2553:
2549:
2547:
2545:
2543:
2541:
2538:
2535:
2532:
2529:
2526:
2525:
2521:
2519:
2517:
2515:
2513:
2510:
2507:
2504:
2501:
2498:
2497:
2493:
2491:
2489:
2487:
2485:
2482:
2479:
2476:
2473:
2470:
2469:
2465:
2462:
2460:
2458:
2456:
2453:
2450:
2447:
2444:
2441:
2440:
2436:
2433:
2431:
2429:
2427:
2424:
2421:
2418:
2415:
2412:
2411:
2408:
2405:
2403:
2401:
2399:
2396:
2393:
2390:
2387:
2384:
2383:
2380:
2377:
2375:
2373:
2371:
2368:
2365:
2362:
2359:
2356:
2355:
2352:
2349:
2347:
2345:
2342:
2339:
2336:
2333:
2330:
2327:
2326:
2323:
2320:
2318:
2316:
2313:
2310:
2307:
2304:
2301:
2298:
2297:
2294:
2291:
2289:
2287:
2284:
2281:
2278:
2275:
2272:
2269:
2268:
2265:
2262:
2260:
2258:
2255:
2252:
2249:
2246:
2243:
2240:
2239:
2236:
2234:
2232:
2230:
2227:
2224:
2221:
2218:
2215:
2212:
2211:
2208:
2206:
2204:
2202:
2199:
2196:
2193:
2190:
2187:
2184:
2183:
2180:
2178:
2176:
2173:
2170:
2167:
2164:
2161:
2158:
2155:
2154:
2151:
2149:
2147:
2144:
2141:
2138:
2135:
2132:
2129:
2126:
2125:
2122:
2120:
2118:
2115:
2112:
2109:
2106:
2103:
2100:
2097:
2096:
2093:
2091:
2089:
2086:
2083:
2080:
2077:
2074:
2071:
2068:
2067:
2064:
2062:
2059:
2056:
2054:
2051:
2048:
2045:
2042:
2039:
2038:
2035:
2033:
2030:
2027:
2025:
2022:
2019:
2016:
2013:
2010:
2009:
2006:
2004:
2001:
1998:
1996:
1993:
1990:
1987:
1984:
1981:
1980:
1977:
1975:
1972:
1969:
1967:
1964:
1961:
1958:
1955:
1952:
1951:
1948:
1946:
1943:
1941:
1939:
1936:
1933:
1930:
1927:
1924:
1923:
1920:
1918:
1915:
1913:
1911:
1908:
1905:
1902:
1899:
1896:
1895:
1892:
1890:
1887:
1885:
1883:
1880:
1877:
1874:
1871:
1868:
1867:
1864:
1862:
1860:
1858:
1856:
1853:
1850:
1847:
1844:
1841:
1840:
1837:
1835:
1833:
1831:
1829:
1826:
1823:
1820:
1817:
1814:
1813:
1807:
1802:
1797:
1792:
1788:
1785:
1781:
1778:
1773:
1768:
1764:
1763:
1760:
1750:
1728:
1722:
1719:
1707:
1703:
1699:
1696:
1690:
1687:
1684:
1679:
1675:
1669:
1666:
1663:
1657:
1654:
1647:
1646:
1645:
1629:
1625:
1601:
1595:
1592:
1584:
1576:
1572:
1566:
1562:
1556:
1553:
1549:
1545:
1542:
1539:
1534:
1530:
1524:
1521:
1518:
1512:
1509:
1502:
1501:
1500:
1497:
1495:
1491:
1472:
1467:
1464:
1452:
1442:
1439:
1435:
1431:
1428:
1425:
1422:
1419:
1412:
1398:
1393:
1390:
1378:
1368:
1365:
1361:
1357:
1354:
1351:
1348:
1345:
1338:
1324:
1319:
1316:
1304:
1294:
1291:
1287:
1283:
1280:
1277:
1274:
1267:
1266:
1265:
1249:
1245:
1236:
1218:
1214:
1190:
1177:
1169:
1166:
1163:
1160:
1150:
1142:
1134:
1128:
1124:
1120:
1117:
1114:
1111:
1108:
1105:
1101:
1095:
1091:
1087:
1082:
1078:
1070:
1056:
1043:
1035:
1032:
1029:
1026:
1016:
1008:
1005:
997:
990:
987:
984:
976:
972:
968:
965:
960:
956:
952:
949:
946:
943:
940:
937:
933:
927:
923:
919:
914:
910:
902:
901:
900:
898:
888:
885:
884:
880:
877:
876:
872:
869:
868:
864:
861:
860:
857:
849:
847:
846:thermocouples
843:
839:
835:
834:Space Shuttle
830:
826:
823:
818:
816:
812:
809:, suggesting
808:
807:Great Britain
804:
803:Royal Society
800:
796:
792:
788:
784:
780:
776:
766:
763:
759:
757:
752:
750:
746:
736:
733:
728:
726:
716:
713:
707:
705:
695:
691:
687:
685:
670:
666:
663:
659:
655:
650:
648:
634:
631:
628:
625:
621:
619:Response time
618:
614:
611:
610:
609:
607:
606:thermocouples
597:
595:
590:
588:
584:
580:
576:
570:
569:
562:
559:
556:
554:High accuracy
553:
552:
551:
543:
541:
536:
533:
527:
525:
521:
517:
513:
509:
508:repeatability
505:
493:
488:
485:
475:
470:
467:
466:
465:
459:
451:
448:
447:
446:
440:
433:
429:
425:
422:
421:
420:
416:Thin-film PRT
414:
406:
403:
402:
401:
396:
392:
389:
388:
387:
385:
382:
375:Element types
369:
368:silicone oils
364:
361:
357:
352:
349:
348:
347:
344:
340:
330:
328:
324:
320:
315:
312:
290:
286:
278:
261:
257:
249:
248:
247:
230:
222:
218:
214:
204:
196:
189:
185:
181:
176:
172:
165:
162:
155:
154:
153:
151:
145:
143:
139:
135:
131:
127:
123:
119:
117:
113:
109:
105:
101:
97:
93:
89:
85:
81:
72:
63:
61:
57:
56:thermocouples
53:
52:repeatability
48:
46:
42:
38:
33:
29:
25:
21:
3175:Thermometers
3144:
3138:
3127:, retrieved
3122:
3116:
3108:
3104:
3095:
3076:
3050:
3036:
3028:the original
3023:
3014:
3006:
3001:
2992:November 16,
2990:, retrieved
2982:
2976:
2964:. Retrieved
2960:
2951:
2933:
2921:. Retrieved
2913:
2903:
2892:, retrieved
2877:
2847:
2838:
2824:Thermocouple
1765:ITS-90 Pt100
1616:
1498:
1493:
1489:
1487:
1234:
1205:
894:
865:Valid range
855:
831:
827:
819:
783:Humphry Davy
772:
761:
760:
755:
753:
744:
742:
729:
722:
708:
701:
692:
688:
681:
667:
651:
644:
641:Construction
603:
592:Compared to
591:
571:
568:Limitations:
567:
566:
549:
537:
528:
501:
492:platinum-200
480:
464:
445:
432:strain gauge
419:
400:
378:
342:
338:
336:
326:
322:
316:
308:
245:
146:
120:
111:
107:
99:
95:
90:(Cu) have a
77:
49:
27:
23:
19:
18:
2966:November 4,
2775:177.353177
2749:158.459633
2723:143.132242
2697:141.202958
2670:139.270697
2642:137.335456
2614:135.397232
2586:133.456024
2558:131.511828
2530:129.564642
2502:127.614463
2474:125.661289
2445:123.705116
2416:121.745943
2388:119.783766
2360:117.818581
2331:115.850387
2302:113.879179
2273:111.904954
2244:109.927708
2216:107.947437
2188:105.964137
2159:103.977803
2130:101.988430
1752:Temperature
779:resistivity
612:Temperature
594:thermistors
587:sensitivity
333:Calibration
134:noble metal
106:range. The
3159:Categories
3111:, page 251
2859:References
2819:Thermostat
2814:Thermistor
2809:Thermowell
2101:99.996012
2072:98.000470
2043:96.001893
2014:94.000276
1985:91.995602
1956:89.987844
1928:87.976963
1900:85.962913
1872:83.945642
1845:81.925089
1818:79.901192
1488:Since the
579:impurities
395:hysteresis
92:repeatable
1810:Typ: 105
1805:Typ: 104
1800:Typ: 103
1795:Typ: 102
1790:Typ: 101
1783:Typ: 201
1776:Typ: 501
1771:Typ: 404
1700:−
1685:−
1664:−
1557:−
1540:−
1519:−
1465:−
1453:∘
1440:−
1432:×
1426:−
1391:−
1379:∘
1366:−
1358:×
1352:−
1317:−
1305:∘
1292:−
1284:×
1178:∘
1161:≤
1151:∘
1044:∘
1017:∘
1006:−
988:−
815:Callendar
557:Low drift
384:resistors
215:⋅
205:∘
182:−
163:α
152:/(Ω·°C):
86:(Ni), or
43:(Ni), or
2803:See also
820:In 1871
520:linearly
504:accuracy
498:Function
311:platinum
122:Platinum
80:platinum
37:platinum
3165:Sensors
3129:May 20,
2923:May 14,
2781:1758.4
2778:175.84
2755:1573.1
2752:157.31
2729:1422.9
2726:142.29
2703:1403.9
2700:140.39
2676:1385.0
2673:138.50
2648:1366.0
2645:136.60
2620:1347.0
2617:134.70
2592:1328.0
2589:132.80
2564:1308.9
2561:130.89
2536:1289.8
2533:128.98
2508:1270.7
2505:127.07
2480:1251.6
2477:125.16
2451:1232.4
2448:123.24
2422:1213.2
2419:121.32
2394:1194.0
2391:119.40
2366:1174.7
2363:117.47
2337:1155.4
2334:115.54
2308:1136.1
2305:113.61
2279:1116.7
2276:111.67
2250:1097.3
2247:109.73
2222:1077.9
2219:107.79
2194:1058.5
2191:105.85
2165:1039.0
2162:103.90
2136:1019.5
2133:101.95
2107:1000.0
2104:100.00
878:F 0.15
842:STS-51F
811:platina
797:at the
769:History
749:Inconel
623:change.
575:phonons
482:of 100
428:plating
354:of the
32:sensors
30:), are
3083:
2885:
2578:10837
2550:12932
2522:15052
2494:18668
2466:22590
2437:27475
2292:11933
2263:15000
2200:10998
2171:14130
2142:18299
2113:23868
2084:31389
2078:980.4
2075:98.04
2057:11066
2049:960.9
2046:96.09
2031:10943
2028:14596
2020:941.2
2017:94.12
2002:14560
1999:19414
1991:921.6
1988:92.16
1973:19560
1970:26083
1962:901.9
1959:90.19
1944:26550
1934:882.2
1931:88.22
1916:36405
1906:862.5
1903:86.25
1888:50475
1878:842.7
1875:84.27
1851:822.9
1848:82.29
1824:803.1
1821:80.31
1774:Pt1000
1754:in °C
1449:
1375:
1301:
1281:3.9083
886:F 0.1
870:F 0.3
474:ITS-90
381:carbon
356:ITS-90
319:doping
246:where
201:
142:Copper
138:Nickel
102:) and
88:copper
84:nickel
82:(Pt),
45:copper
41:nickel
39:(Pt),
3059:(PDF)
2987:(PDF)
2943:(PDF)
2830:Notes
2679:3390
2662:6539
2651:3285
2634:7708
2623:3180
2606:9121
2595:3079
2567:2977
2539:2880
2511:2782
2483:2689
2463:3756
2454:2595
2434:4299
2425:2505
2406:5039
2397:2415
2378:6194
2369:2330
2350:7657
2343:3471
2340:2244
2321:9522
2314:4317
2311:2162
2285:5401
2282:2080
2256:6800
2253:2000
2228:8618
2225:1922
2197:1847
2174:3986
2168:1771
2145:5078
2139:1700
2116:6536
2110:1628
2087:8466
2081:1561
2060:8299
2052:1493
2023:1430
1994:1366
1965:1306
1937:1246
1909:1191
1881:1135
1854:1084
1827:1032
1769:Pt100
1429:4.183
1355:5.775
1206:Here
540:below
309:Pure
3131:2015
3081:ISBN
2994:2011
2968:2023
2925:2014
2896:2009
2883:ISBN
2772:200
2746:150
2720:110
2694:105
2667:100
2040:−10
2011:−15
1982:−20
1953:−25
1925:−30
1897:−35
1869:−40
1842:−45
1815:−50
1492:and
1167:<
1033:<
1027:<
832:The
662:PTFE
636:use.
626:Size
581:and
506:and
484:ohms
325:vs.
28:RTDs
2639:95
2611:90
2583:85
2555:80
2527:75
2499:70
2471:65
2442:60
2413:55
2385:50
2357:45
2328:40
2299:35
2270:30
2241:25
2213:20
2185:15
2156:10
2069:−5
1808:NTC
1803:NTC
1798:NTC
1793:NTC
1787:NTC
1780:PTC
1697:0.1
1644:is
1170:850
1009:200
991:100
805:of
660:or
654:PVC
341:vs
291:100
197:100
177:100
110:vs
98:vs
3161::
3067:^
3022:.
2959:.
2916:.
2912:.
2867:^
2127:5
2098:0
1688:40
1443:12
1436:10
1362:10
1288:10
1237:,
899::
848:.
656:,
526:.
62:.
3089:.
3061:.
3044:.
2970:.
2927:.
1759:Ω
1729:.
1723:B
1720:2
1713:)
1708:T
1704:V
1694:(
1691:B
1680:2
1676:A
1670:+
1667:A
1658:=
1655:T
1630:T
1626:V
1602:.
1596:B
1593:2
1585:)
1577:0
1573:R
1567:T
1563:R
1554:1
1550:(
1546:B
1543:4
1535:2
1531:A
1525:+
1522:A
1513:=
1510:T
1494:C
1490:B
1473:.
1468:4
1460:C
1423:=
1420:C
1399:,
1394:2
1386:C
1369:7
1349:=
1346:B
1325:,
1320:1
1312:C
1295:3
1278:=
1275:A
1250:0
1246:R
1235:T
1219:T
1215:R
1191:.
1188:)
1184:C
1164:T
1157:C
1143:0
1140:(
1135:]
1129:2
1125:T
1121:B
1118:+
1115:T
1112:A
1109:+
1106:1
1102:[
1096:0
1092:R
1088:=
1083:T
1079:R
1057:,
1054:)
1050:C
1036:0
1030:T
1023:C
1003:(
998:]
994:)
985:T
982:(
977:3
973:T
969:C
966:+
961:2
957:T
953:B
950:+
947:T
944:A
941:+
938:1
934:[
928:0
924:R
920:=
915:T
911:R
494:.
343:T
339:R
327:T
323:R
287:R
262:0
258:R
231:,
223:0
219:R
211:C
190:0
186:R
173:R
166:=
150:Ω
112:T
108:R
100:T
96:R
60:C
26:(
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