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platinum resistance thermometer

Its operations are carried out in such a way as to fully exploit the fast response of the thermistor and the high accuracy of the platinum thermometer. The resistance of the platinum is measured by passing the alternating or direct current through it. British Standard 1904 recommends that to avoid significant heating of platinum wire being tested in air for use in commercial thermometers, the measuring current should not exceed 2 milliamperes per 0.001 inch of wire diameter. He was invited to become a member of the Electrical Standards Committee of the British Association, and in 1899 put forward his proposals in detail. In the range -200°C ≤ ϑ < 0°C electrical resistance at temperature tis calculated according to the polynomial: In the range of 0°C ≤ ϑ ≤ 850°C coefficient cis set to zero and the polynomial becomes: For conversion of electrical resistance to temperature the above equations can be used after solving for t: Polynomial coefficients for conversion of resistance to temperature, or vice versa, from platinum resistance thermometers according to IPTS-6… Thermometer continuously monitors bath temperature and displays… Related Products: High Temperature Water Bath Morphy-Richards’ electric blankets are tested at temperatures up to 90°C with one of a set of platinum resistance thermometers and multipoint recorders supplied by the Cambridge Instrument Co. Ltd. In the following year Callendar, working with Professor W. C. Roberts-Austen in the laboratory of the Royal Mint, made the first accurate determination of the melting points of the purest gold and silver then available. Great care has to be exercised to avoid contamination of the platinum element and to minimise stressing the wire in order not to reduce its temperature coefficient of resistance. In particular, he showed that the clay used for the former, or some constituent of it, had attacked the platinum, while the iron protection tube—or even traces of volatile metallic impurities in the iron—had also been responsible. This was followed by several other papers which he contributed on the same subject during the next few years. This may cause an undesirable change in resistance. A combination of traces of sulphur and silica or silicates will attack platinum in the presence of carbon, hydrogen or other reducing agent. PlatinumThermometryat11iffhTemperatures. That Professor Callendar and Mr. Glazebrook be requested to consider further the selection of wires for the construction of a number of platinum resistance thermometers for standard tests. The reading of voltage is converted into the temperature with the help of the calibration equation. In addition to the measurement of elevated temperatures, the platinum resistance thermometer is also finding a number of applications where the accurate determination or control of sub-zero temperatures is needed. A platinum-resistance thermometer has a resistance of 5Ω at 0°C and 9Ω at l00°C. The late Professor H. L. Callendar may fairly be regarded as the father of platinum resistance thermometry; the fundamentals of the thermometers in use today are unchanged from those he described in 1887, when as a young research worker of only 23 at the Cavendish Laboratory, Cambridge, he published a paper “On the Practical Measurement of Temperature” (1). Hall (11) and this will not be discussed further here. The platinum is an unreactive metal and can easily be drawn into fine wires. Because of the current, the voltage induces across the metal which measures through the voltmeter. The platinum resistance thermometer, the most accurate and sensitive means of temperature measurement, was introduced and developed by the late Professor H. L. Callendar, C.B.E., F.R.S. He was able, however, to reproduce the effects they had observed and to show that they were not inherent in the method but were merely incidental to the particular form of instrument on which they had experimented. For resistance thermometry, therefore, extreme precautions have to be taken not only in the preparation and melting of the platinum but in its subsequent drawing to fine wire in order to maintain an exceptionally high state of purity and complete freedom from contamination during later processing. It is used both for precision measurements of the highest accuracy and for routine industrial work. Only a relatively few such applications can be described and illustrated here. It is used both for precision measurements of the highest accuracy and for routine industrial work. It is used both for precision measurements of the highest accuracy and for routine industrial work. By using our site, you agree to our use of cookies.Find out more in our Privacy Policy. A. Harker and P. Chappuis Comparison of Platinum and Gas Thermometers. Platinum Resistance Thermometers (PRTs) rely on the fact that platinum, like many other metals, exhibits increased electrical resistance as temperature rises. Compensation for temperature variations in the leads may be provided by either a three-wire or a four-wire system. PRTs are available in several different forms. Save my name, email, and website in this browser for the next time I comment. In the three-wire system two leads are in adjacent arms of a bridge, thus cancelling their changes of resistance, while the third lead carries only the energising current. where α is the mean temperature coefficient of resistance from 0° to 100°C, i.e. He was elected a Fellow of Trinity College, Cambridge, for his research on this subject. R. J. Corruccini (10), of the National Bureau of Standards, suggests that rapid cooling after annealing is undesirable because it may decrease the value of the temperature coefficient of resistance. Platinum Resistance Thermometer How it works: The simplest resistance thermometer configuration uses two wires. Two of the illustrations give examples of the wide use of platinum resistance thermometers in the storage, processing and transport of food. The relation between A, B, α and δ is the same as those above mentioned and the other relations are: The range of industrial applications of the platinum resistance thermometer, as indicated earlier in this article, is extremely varied and involves the measurement or control of temperatures from the region of −200°C up to 1000°C. PT100 platinum resistance thermometers Platinum resistance thermometers (PRTs) offer excellent accuracy over a wide temperature range (from –200 to +850 °C). This article discusses the development and construction of resistance thermometers and their uses in a wide range of industries. A platinum resistance thermometer has also become a standard in resistance thermometers because of its utilization of platinum. The platinum sensing coil is enclosed inside a bulb which is either made of glass or Pyrex. Hall A Design for Precision Platinum Resistance Thermometers. T. S. Sligh Jr., Recent Modifications in the Construction of Platinum Resistance Thermometers, C. H. Meyers Coiled Filament Resistance Thermometers. resistance is dropping rapidly. In later years other manufactures of scientific instruments also came into the field, and today a wide range of types is available to meet the many varied conditions encountered in industry. A multi-point indicator working in conjunction with four platinum resistance thermometers by The Foster Instrument Co. Ltd. in one of the cold storage plants of Birds Eye Foods Ltd. As RTD elements are fragile, they are often housed in protective pr… Contents Page 1.Introduction 1 2.Backgroundandbasicconcepts. British Standard 1904:1952 states that the ratio R100/R0 for silk-covered wire should be not less than 1.385. A High-Quality Platinum Resistance Thermometer to 661°C (85.57 KB) An Investigation of Long-Term Stability of a Precision Platinum Resistance Thermometer up to 660°C (164.52 KB) Fixed Points for Secondary Level and Industrial Calibration (496.68 KB) Fixed … The platinum resistance thermometer, by Sangamo Weston Limited, is sheathed with nylon tube. Repeatability and stability: The platinum resistance thermometer is the primary interpolation instrument used by the National Institute of Standards and Technology from -260 to 962°C. Platinum Resistance Thermometer Definition: The platinum thermal resistance (PTR) uses platinum for determining the temperature. Your email address will not be published. The figure below shows the platinum resistance thermometer. Hall (7), of the National Physical Laboratory, described a construction in which the element is wound on a fused quartz frame in a hermetically sealed envelope, while his colleague, C. R. Barber (8), has described a thermometer of very small dimensions in which a formless coil is contained in a fine glass U-tube. The platinum resistance thermometer was developed into a successful and accurate instrument by Callendar. J. The current is proportional to the supply voltage of the bridge, and so either the voltage must be stabilised, or voltage compensation must be provided in the galvanometer movement. Home > Journal Archive > The Platinum Resistance Thermometer. Conforms to ASTM D 445 Built-in platinum resistance thermometer On-screen temperature monitoring RS 232 and RS 485 communication ports A keypad permits temperature selection to two decimal places. If we measure the resistance of wire of known length, diameter and composition, we can determine its temperature. The industrial type thermometer is shown in the figure below. T. S. Sligh (5), of the U.S. Bureau of Standards, developed this design so that strain is further reduced. A. Extensive Range of Platinum Resistance Thermometer (RTD's) A platinum RTD (Resistance Temperature Detector) with a resistance of 100 ohms at 0°C which changes with temperature. Resistance thermometers, also called resistance temperature detectors (RTDs), are sensorsused to measure temperature. As well as on the very high purity of the special Thermopure platinum wire provided for this purpose, the accuracy and stability of resistance thermometers depend upon the care given to their design and construction. The wire is formed into a coil of some 500 turns and … These applications, as will be seen later, include temperature recording or control in the production of liquid oxygen and nitrogen, of chemicals, and of rubber, in the storage of refrigerated meat and fruit and of timber and coal, and in space heating and ventilation. These are required to measure the temperatures of the oil, the fuel, the cabin air, the outside air—for air-speed correction—and the de-icing mats. They are suitable for applications in the temperature range of -200°C to 600°C but are more commonly used in the range … The Platinum Resistance Thermometer A REVIEW OF ITS CONSTRUCTION AND APPLICATIONS By liodney Price The platinum resistance thermometer is a versatile instrument for temperature measurement in the range from - 200" to 1000°C. Although platinum is resistant to a wide range of acids and other reagents, it is desirable to be familiar with the conditions in which the metal is attacked. Here the double wires are used for reducing the inductive effect. Siemens On the Increase of Electrical Resistance in Conductors with Rise of Temperature, Report of Committee of the British Association on the New Pyrometer of Mr. Siemens. The platinum increases its repeatability throughout the circuits the thermometer is used in. The sheathed sensitive element, made from silk-covered Thermopure platinum wire, may be seen formed in a spiral attached to a wheel-shaped frame. A platinum resistance thermometer (PRT) is a thermometer constructed from a high purity platinum element (wire-wound coil or thin film) placed in a tube of metal or glass and sealed with an inert atmosphere and/or mineral insulator. The first term in this expression is the “platinum temperature”, derived by considering that the temperature interval between 0° and 100°C can be divided into equal degrees C of temperature by equating temperature to the electrical resistance of a platinum thermometer in this range, and that the relationship can then be extrapolated according to a straight line law. The photograph was taken at the advance base “South Ice”, 4,400 feet above sea level and 300 miles south of Shackleton on the Weddell Sea. Assuming that resistance changes uniformly with temperature, calculate the resistance of the thermometer when the temperature is 45°C. A. The resistance thermometer uses a sensitive element made of extremely pure metals like platinum, copper or nickel. Such an arrangement is shown in the diagram below. © Johnson Matthey 2020 | Terms and Conditions | Careers at Johnson MattheyWe use cookies to help understand how people use our website. The resistance of the platinum wire of a platinum resistance thermometer at the ice point is 5 Ω and at steam point is 5.39 Ω. Dr. H. Lister, the glaciologist of the Trans-Antarctic Expedition led by Sir Vivian Fuchs, using a platinum resistance thermometer to measure temperatures from −15° to − 60°C at different depths in the ice. Values greater than 1.3910 for the ratio R100/R0 for Diamel-covered Thermopure platinum wire are obtainable. AM1880 Standard Platinum Resistance Thermometers (SPRT) interpolates temperature in the range from -200°C to 670°C on the International Temperature Scale of 1990 (ITS-90). The same author has also described a platinum-sheathed diameter thermometer for use at low temperatures (9). The following are the disadvantages of platinum thermal resistance. In another construction described by C. H. Meyers (6), also of the Bureau of Standards, the wire is first wound into a fine helix and then this helix is wound on to a former. The platinum resistance thermometer—in which the principle of measurement is the variation in the resistance of a platinum wire as a function of temperature—is generally accepted as the most accurate temperature measuring instrument available. In 1902 he was appointed to the Professorship of Physics at the Royal College of Science, London. Resistance thermometers, also called resistance temperature detectors or resistive thermal devices (RTDs), are temperature sensors that exploit the predictable change in electrical resistance of some materials with changing temperature.As they are almost invariably made of platinum, they are often called platinum resistance thermometers (PRTs). It works on the principle that the resistance of platinum changes with the change of temperature. The insulator deposit on the surface of the glass tube is also used for sensing the temperature. A platinum resistance thermometer consists of a platinum coil that is present inside a cross frame. The thermometer has a wide range from  200 to 1200° Celsius. In the four-wire system a lead equivalent to the element leads and subject to the same ambient temperature variations is put in an adjacent arm of the bridge. Each of these forms has its own benefits and drawbacks. C. R. Barber A Platinum Resistance Thermometer for Use at Low Temperatures. Circuit diagram of a three-wire platinum resistance thermometer and bridge. Ships carrying refrigerated meat or fruit may have nearly a hundred platinum resistance thermometers connected to multi-point indicators, while in the control of space-heating in large buildings such as cinemas a number of instruments will be similarly connected to one indicator. H. L. Callendar On the Practical Measurement of Temperature. According to the International Temperature Scale, temperature is related to the resistance of a platinum thermometer according to the following formulae: For the temperature range from 0° to 630.5°C. where Rt and R0 are the values for the resistance of the thermometer at the temperature of measurement and at 0°C respectively. The use of a synthetic epoxy-base enamel developed by Johnson Matthey and known as Diamel similarly limits the annealing temperature, but very little strain is caused by the enamelling process and Diamel-covered wire may be used up to 130°C. It is referred to as a temperature sensor. The platinum wire is protected by the stainless steel tube or by the glass coating. He showed that the gas thermometer had given results so discordant as greatly to retard the progress of research. The values of R0, A and B are determined by calibration at the ice, steam and sulphur (444.6°C) points, and that of C by calibration at the boiling point of oxygen (−182.97°C). Callendar occupied the new Chair of Physics at McGill University, Montreal, from 1893 to 1898, when he returned to England to become Professor of Physics at University College, London. On the other hand, platinum thermometers standardised at selected fixed points easily gave a consistency of one-tenth of a degree at 1000°C. Section of a typical platinum resistance thermometer element, comprising a former of ceramic, glass or metal wound with fine Thermopure platinum wire. A platinum resistance thermometer (PRT) is a piece of platinum wire which determines the temperature by measuring its electrical resistance. Other examples are in the storage of fruit in carbon-dioxide, in dock-side grain silos and in refrigerated cargo ships. Reports, 1874, 242. For typical 25.5ohm SPRT this may be 500mm of 0.1mm diameter wire whose purity is 99.9999%. In describing this work in a lecture to the Royal Institute Professor Roberts-Austen said “I am satisfied that at temperatures about 1000°C the comparative results afforded by this method are accurate to the tenth of a degree, a result which would certainly have been deemed impossible a year or two ago”. Checking temperature in the production of granular fertilizer, flowing at 25 tons per hour on a conveyor belt, in the Ipswich works of Fisons Limited. A physicist in the Johnson Matthey Process Control Laboratory determining the temperature coefficient of resistance between 0° and and 100°C of the Thermopure platinum produced specially for resistance thermometry. In this PTR, the double wire of the platinum is wound on the strip of the mica. When manufactured carefully, these devices offer an excellent combination of sensitivity, range and reproducibility. It is denoted by tpt. The ideal mounting for the element wire is one which minimises the strain caused in the wire by thermal expansion and contraction of the winding former. 12th Resistance thermometers come in a number of construction forms and … J. Base metal thermocouples could be used to measure such temperatures, but would require either control of, or adjustment for, the cold junction temperature, while their low output would necessitate a very sensitive measuring device or some form of amplification. The relationship between temperature and the resistance of a platinum resistance thermometer, and H. L. Callendar’s method of making the necessary calculations, are given in more detail, together with the tables compiled by G. S. Callendar and F. E. Hoare, in a booklet Platinum for Resistance Thermometry (12) which was last revised in September 1958. Firstly how is a thermometer made. The platinum resistance thermometer is a versatile instrument for temperature measurement in the range from — 200° to 1000°C. Temperatures from 0° to 60°C are measured with platinum resistance thermometers by Elliott Brothers (London) Ltd., who also supplied this part of the control panel. The meter gives the precise reading of temperature. Many RTD elements consist of a length of fine wire wrapped around a ceramic or glass core but other constructions are also used. Any impurity in platinum lowers its temperature coefficient of resistance, and this characteristic of the metal is in fact the most sensitive indication of its purity. The linearization equation for the Pt100 thermometer is. For some work, such as refrigerated cargo ships, when speed of response must be sacrificed to protection against corrosion, metal sheaths are completely covered with vulcanised rubber. The terminals of the copper wire are joined together with the help of the thick copper lead. To provide manufacturing method of platinum resistance thermometer for clarifying mechanism of quantitative resistance change in oxidation-reduction of platinum resistance wire to obtain a stable platinum resistance thermometer with few change of resistance in operating temperature range. The resistance thermometer had in fact been introduced by C. W. (later Sir William) Siemens. R. J. Corruccini Annealing of Platinum for Thermometry. This fully established the absolute reliability of the platinum resistance thermometer and confirmed Callendar’s original claims put forward in his paper in 1887. To prevent contamination of the platinum wire, therefore, all parts of the thermometer should be clean. Hall The Accurate Measurement of Temperature, Platinum for Resistance Thermometry, Johnson, Matthey & Co. Ltd., London, 1958, Enter your email address to receive our quarterly alerts. He was so quickly successful in solving the problem that he was able to present his first results to the Royal Society in June 1886 and publish a full dissertation on the matter in the Philosophical Transactions of the Royal Society in 1887. 例文帳に追加. The resistance of metals increases with increasing temperature. The special grade of metal prepared, known as JMC Thermopure platinum, consistently gives values greater than 1.3923 for the ratio R100/R0 and provides a sound basis for the design and construction of accurate and reliable thermometers. The Ebonite cap is placed at the open end of the tube. An excellent account of the laboratory procedure involved in this class of work has been given by J. Platinum Resistance Thermometers (PRTs) Fluke Calibration PRTs provide a wide operating range and high accuracy required for precision temperature measurement in the laboratory, factory, or field. For very accurate temperature measurement, say to 0.001°C, special precaution must naturally be taken to remove every source of possible error. Definition: The platinum thermal resistance (PTR) uses platinum for determining the temperature. Mostly, platinum is used in resistance thermometer. Glass or ceramic seal the sensing element. Callendar carried out a great deal of research to establish the constancy of the relation between the resistance of a platinum wire and its temperature, and this work, together with his four-lead method of compensation, established the accuracy and reliability of the instrument. Unit can be used on bench or mounted on a 1/2" diameter support rod. The results fully confirmed Callendar’s claims, and led to the establishment of the platinum resistance thermometer as a means of defining a major portion of the International Temperature Scale. The material has an accurate resistance/temperature relationship which is used to provide an indication of temperature. He died in 1930 at the age of 67. Thus Callendar gave to science a new tool for accurate temperature measurement. The selection of suitable protection for the winding depends on the range of temperatures to be measured, the accuracy and life required, and the corrosive nature of the surroundings. The advantages of this device were quickly appreciated, and a distinguished committee of the British Association was appointed to test the instruments and report upon them. A. But when platinum measures the temperature higher than 1200°C they start evaporating. In 1900 the Practical Temperature Standdards Sub-committee of the British Association agreed: That a particular sample of platinum wire be selected (Mr. Matthey of Johnson and Matthey had now supplied the Committee with two samples of very pure wire, which on test gave excellent results by the Callendar difference formula). 151 pt=ioou1 R—R B /N ' (1) *M00 " whereR=observedresistanceatthetemperature,t°, R=" " "o°C, ^,00="." A platinum resistance thermometer consists of a coil of platinum wire wound on a ceramic former. It rapidly becomes brittle if it is heated in contact with phosphorus, arsenic, antimony, selenium or tellurium. We place the whole arrangement in an evacuated tube which is made of stainless steel. For a normal commercial accuracy of approximately ±1°C throughout the range of the instrument there is a choice between deflection instruments, null-balance bridges and ratiometers. Before Callendar, others had tried without success to use metals to make accurate thermometers but he brought to the problem a finer skill and inventiveness as shown in many ways. Read about company. Required fields are marked *. A Platinum Resistance Thermometer, commonly referred to as RTD Sensors, PRT Sensors or Pt100 Sensors, is a type of resistance temperature sensor used for a … The coil arrangement generates very little strain when there is a rise in temperature. In a modern passenger aircraft there may be up to fourteen resistance thermometers. The temperature measurement through platinum resistance thermometer is easier as compared to the gas thermometer. In 1892 platinum thermometers were used in blast furnaces by Sir Lowthian Bell, while a little later some 65 thermometers and recorders were installed on the annealing furnaces at John Lysaght’s sheet steel works at Newport, Monmouthshire. ^uraZT.'] The spar also carries two ice detectors. The melting point of the thermometer is 1800° Celcius. Difference between Step-up and Step-down transformer, Two Wattmeter Method – Balanced Load Condition, Two Wattmeter Method of Power Measurement, Difference Between Conduction and Convection, Difference Between Circuit Switching and Packet Switching, Difference Between Static and Kinetic Friction, Difference Between Ductility and Malleability, Difference Between Physical and Chemical Change, Difference Between Alpha, Beta and Gamma Particles, Difference Between Electrolytes and Nonelectrolytes, Difference Between Electromagnetic Wave and Matter Wave. Under his supervision standard thermometers were made at the National Physical Laboratory and submitted to long and careful testing. John Ancsin suggests that the quartz support for the platinum winding forms a eutectic at 830°C. Silk-covered or synthetic-enamelled wire is used to make commercial thermometers to measure low temperatures, but silk covering produces strain in platinum wire, the effect of which upon its resistance characteristics cannot be entirely removed owing to the impossibility of heating the wire to a sufficiently high temperature. Because of these properties of platinum, it is used as a sensing element in thermometer. A BIOGRAPHICAL NOTE BY DR. L. H. CALLENDAR. He first had the idea of sealing the platinum wire he was testing inside the bulb of the gas thermometer he had made as a standard, thus getting a perfect comparison between the two; he overcame previous troubles, such as the shifting zero, by using very pure platinum and by ensuring that the wire was free from strain, and the uncertainty of the resistance of the leads by fitting duplicate leads. The requirements of the International Temperature Scale of 1948 for the purity and physical condition of platinum to be used in resistance thermometry are based upon the change in resistance between 0° and 100°C, this range being known as the fundamental interval: the ratio R100/R0 is required to be greater than 1.3910. In October 1885, Callendar, having taken a double First in Classics and Mathematics at Cambridge University, started as a research physicist under Professor J. J. Thompson to work on the variation of the electrical resistance of platinum as a means of measuring temperature. For JMC platinum the values of the coefficients in equation (2) are: It was first suggested by Callendar that the arithmetical computation could be greatly reduced by rewriting (1) for the range 0–100°C in the form. Its sensitivity and reliability are evident from the fact that it was first used in 1928 to define the International Temperature Scale from −190° to 660°C and has thus been the primary international standard for over thirty years. C. R. Barber Platinum Resistance Thermometer of Small Dimensions. It is only used when high accuracy is not required as the resistance of the connecting wires is always included with that of the sensor leading to errors in the signal. The platinum resistance thermometer is a versatile instrument for temperature measurement in the range from — 200° to 1000°C. The other end of the copper leads are joined to the terminal AB fitted in the Ebonite cap. It was shown that platinum in porcelain thermometers could be heated and cooled between 0° and 1000°C for three months without measurable alteration in the zero of the instruments. By automatic scanning and digital display, the black panels in the centre of the picture show temperature and weight. The earliest record of an important use in industry was in 1891, when Sir Robert Mond, working with Callendar, introduced the thermometers at one of his works. The selection of a suitable process depends on the materials used in construction, but a typical method is to wash all parts in benzene, boil in dilute nitric acid and wash several times in distilled water. Had given results so discordant as greatly to retard the progress of research and drawbacks fact been by... Out-Of-Balance current may be provided by either a three-wire or a PT1000 sensor platinum.... Properties of platinum thermal resistance ( PTR ) uses platinum for determining the temperature its electrical resistance in! The RTD wire is protected by mild-steel, brass, copper or nickel must naturally be to! Output than a thermocouple discusses the development and a platinum-resistance thermometer has a wide from. 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Sheaths and used in a spiral attached to a wheel-shaped frame appears on surface., after assembly and just before annealing, the gauge being adjusted… Tweet platinum thermometer and secondary.. Is required others are protected by mild-steel, brass, copper or nickel this will not be discussed further.! Silk-Covered wire should be not less than 1.385 thermometer consists of a length of fine wire wrapped around ceramic... Pt1000 sensors with resistance 1000 ohms at 0 °C offer an excellent account of the mica is used an. Very accurate temperature measurement in the Ebonite cap is placed at the same subject during the next years. Start evaporating, range and reproducibility P. Chappuis Comparison of platinum resistance thermometer elements calls a! Than 1.3910 for the ratio R100/R0 for Diamel-covered Thermopure platinum wire, may be by! This subject alternating or direct current through it the values for the resistance of the Laboratory procedure involved in class. Wire wrapped around a ceramic former current may be seen formed in a wide range measurement! Determine its temperature into glass sheaths ; others are protected by the stainless steel tube by!, to measure temperature grain silos and in refrigerated cargo ships used to provide an indication of.. C. W. ( later Sir William ) Siemens or mounted on a 1/2 '' diameter support rod just annealing... The galvanometer in the range from — 200° to 1000°C from silk-covered Thermopure platinum wire is 5.795.. Show temperature and weight uses platinum for determining the temperature range of measurement mean temperature coefficient of thermometers.

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