Calibration fixed-point

For a long time fixed-point calibrations were much used in high-pressure measurements, especially with piston-cylinder, belt, and multianvil apparatus, where optical or X-ray access was difficult but electrical wires could be introduced easily. The useful fixed points were related to sharp changes in the electrical resistance at first-order phase transitions. Sharp transitions with minor hysteresis (for instance, in resistance measurements) were considered to be the most useful. For this almost historical reason, some recommended fixed points are given in Table 2.3. 

Basic Concepts and Definitions. The task of relating thermometer output (i.e., magnitude of the variable dependent on temperature) to its temperature is achieved through calibration. Two general means of calibration are available (1) fixed-point calibration, and (2) compari-... 

Fixed-point calibration has the highest accuracy, but to achieve such accuracy requires great precautions and is very time-consuming. Most freezing- and triple-point cells are difficult to maintain and usually cannot accommodate more than one sensor at a time. Thus, fixed-point calibrations are usually carried out only for high-precision thermometers and usually only at national laboratories. However, easily maintained water triple-point (or ice-point) systems are used in many laboratories to correct thermometer drift, particularly for SPRTs. 

The calibration curve of each rosetta strain gauge was so obtained and ftg.5 shows the sum of the principal stresses at the measuring points versus pressure inside the vessel. Further tests were carried out to obtain the calibration factor and to check that it remained constant on the whole scan area of the test surface. This was achieved through additional measurements using the SPATE system on fixed points on the surface located very close to the applied rosetta strain gauges. This procedure gave the following results ... 

The fixed points in the lTS-90 are given in Tabie 11.39. Platinum resistance thermometers are recommended for use between 14 K and 1235 K (the freezing point of silver), calibrated against the fixed points. Below 14 K either the vapor pressure of helium or a constant-volume gas thermometer is to be used. Above 1235 K radiometry is to be used in conjunction with the Planck radiation law,... 

From the ventilation point of view, the fixed points -38.83 °C (triple-point of mercury), 0.010 °C (triple-point of water), 29.76 °C (melting point of gallium), and 156.60 °C (freezing point of indium) are of relevance. The triple-point of water is relatively simple to achieve and maintain with a triple-point apparatus. Some freezing point cells are covered in standards. In practical temperature calibration of measuring instruments, the lTS-90 fixed points are not used directly. 

The so-called standard instrument is used for interpolation between the fixed points and for the calibration of other thermometers lower in the metrological hierarchy. The standard instrument in the moderate temperature range is a special platinum resistance probe, as it has to fulfill set requirements. It is important in all calibration that traceability to a primary normal, here the fixed-point ITS-90 scale, exists. 

These fixed points are used to calibrate a different kind of thermometer that is easier to use than a gas thermometer. Over the temperature range from 13.8033 to 1234.93 °A (or K), which is the temperature interval most commonly encountered, the thermometer used for ITS-90 is a platinum resistance thermometer. In this thermometer, the resistance of a specially wound coil of platinum wire is measured and related to temperature. More specifically, temperatures are expressed in terms of W(T9o), the ratio of the resistance R(Ttriple point of water R (273.16 K), as given in equation (1.11)... 

The form of the difference function and the fixed points used for calibration depend upon the temperature region. For example, in the temperature range from 24.5561 to 273.16 K,... 

The deviation function AW Too) is obtained as a function of r90 for various temperature intervals by calibration of the platinum resistance thermometer, using specified fixed points from Table A2.1. The form of the AW(Too) function is dependent on the temperature range in which the thermometer is being calibrated. For example, in the temperature subrange from 234.3156 to 302.9146 K, the form of the deviation function is... 

Calibration (Fixed) points used to determine coefficients in the deviation function... 

In addition to the fixed points listed, calibration al the triple point (ip) of HA) is required. 

In summary, to obtain 7% from a platinum resistance thermometer, one selects the range of interest, calibrates the thermometer at the fixed points specified for those ranges, and uses the appropriate function to calculate AW(Tw) to be used in equation (A2.5). Companies are available that perform these calibrations and provide tables of W T<)0) versus 790 that can be interpolated to give 7% for a measured W T90). 

Figure 4.36. Cross validation between two HPLCs A stock solution containing two compounds in a fixed ratio was diluted to three different concentrations (1 10 20) and injected using both the 10 and the 20 /xl loop on both instruments. The steps observed at Amount = 100 (gray ellipses) can be explained with effective loop volumes of 9.3 and 20 pi (model 1) and 14.3 and 20 pi (model 2) instead of nominally 10 and 20 pi. This is irrelevant as both a sample and the calibration solution will be run using the same equipment configuration. The curved portion of the model 2 calibration function was fitted using Y = A /x this demonstrates the nonlinearity of the response at these high concentrations. The angle between the full and the dotted line indicates the bias that would obtain if a one-point calibration scheme were used.

The idea that certain physical states could reproduce always the same temperature rises in the second half of seventeenth century (Hooke, 1664 Renaldini, 1694, see e.g. ref. [8]). Intuitions of this idea can be also found in Aristotele and Galeno. Nowadays, the importance of the control of the thermometric calibration is underestimated and the use of reference fixed points is usually limited to metrological laboratories. 

It is worth remarking that, in fact, such devices do not supply true reference fixed points as explained in Section 8.2, since these devices were calibrated one by one against primary thermometers. Their accuracy is 0.1-0.2 mK. 

Secondary thermometers must be calibrated by means of a primary thermometer or at fixed points as discussed in Chapter 8. Secondary thermometers are often quite easy to use and more sensitive than primary thermometers. A typical example of secondary thermometer is the electrical resistance thermometer (see Section 9.6). 

The most interesting liquids for low-temperature thermometry are 3He and 4He, especially for the calibration of resistance thermometers in the range from 0.5 to 4.2 K. Vapour pressure of H2 is also interesting to realize vapour pressure-fixed points included in ITS-90. The measure of He vapour pressure has been carried out with great accuracy [42,43] to establish the ITS-90 (see Section 8.3). There are several experimental precautions to be observed in order to obtain reliable measurements [2],... 

Even if nowadays, the MCT may be considered a primary thermometer only on a narrow temperature range, it is considered the best dissemination standard in the millikelvin range [56-59], In fact, the 3He melting pressure is a good thermometric property because of its sensitivity over three decades of temperature with a resolution A T/T up to 10 5 [56], The good repeatability, the insensitivity to magnetic fields up to 0.5 T [60] and the presence of temperature-fixed points allow for the control of possible shifts in the calibration curve of the pressure transducer. The usefulness of these fixed points is evident, considering that the ITS-90 is based just on the definition of fixed points. 

Last, we wish to remind that thermal cycling may spoil the thermometer calibration. The frequent check of the calibration by means of reference fixed points (see Section 8.5) is advisable. 

Between the triple point of equilibrium hydrogen (13.8033 K) and the freezing point of silver (1234.93 K), Tgo is defined by means of platinum resistance thermometers calibrated at specific sets of defining fixed points. The temperatures are given in terms of the ratio of the resistance of the thermometer at temperature Tgo to the resistance at the triple point of water ... 

Fixed-point realization, procedures for achieving, 24 444 Fixed points, secondary, 24 442t Fixed-point thermometer calibration,... 

Temperature measurement(s), 24 433-467, 75 469, 77 783-784 of critical current density, 23 847-848 fixed-point thermometer calibration,... 

Industrial resistance thermometers are also the subject of a number of national and international standards, which describe both calibration constants and classes of accuracy and interchangeability. IEC publication 751 was revised in 1976 to conform to ITS-90, and national standards will be revised to conform to this document. IEC 751 uses the fixed-point values of ITS-90 with the simpler algorithm of IPTS-48 ... 

Schooley, J. F., Ed., 1982, Temperature—Its Measurement and Control in Science und Industry, Vol. 5, American Institute of Physics, New York. An excellent source of state-of-the-art thermometry comprised of papers from the Sixth International Temperature Symposium. Topics which are covered include temperature scales and fixed points, radiation, resistance, thermocouple, and electronic thermometry, temperature control, and calibration techniques. Preceding volumes in the series date back to 1939. 

For a leak-detection system that features fixed-point detectors to be reliable, it must be monitored and calibrated frequently. As discussed in Section... 

Manufacturers of fixed-point leak detection sensors can furnish all the equipment and gases required to perform calibration checks. 

Although there is no record that he ever calibrated the tube, he used it in temperature study. Galileo s thermometer was impossible to calibrate even if he had decided on fixed points with which to establish specific temperatures because it was exposed to the atmosphere and subject to variations in atmospheric pressure. By 1640, it was realized that the air thermometer was subject to variations of barometric pressure and the sealed thermometer was created. However, the need to establish fixed points of reference had still not been addressed. 

The need to establish fixed points to provide uniformity between thermometers is no different than the need for uniformity with any measurement system. Many thermometers were built in the following years, but either there was no calibration, or the calibration was not based on any repeatable fixed point. One of the first attempts of establishing calibration points was made in 1693 by Carlo Renal-dini of Padua, who set the low temperature point with ice. For the next point, he took 11 ounces of boiling water and mixed it with one ounce of cold water. Next he mixed 10 ounces of boiling water with two ounces of ice water. The process continued until 12 divisions were established on the thermometer. Although Renaldini had an interesting approach to establishing fixed points on the thermometer, it was neither practical nor accurate. 

Six different points were adopted because no one thermometer can read a full range of temperatures, and no one thermometer can read a wide range of temperatures accurately. Thus, different fixed points allowed for thermometers measuring different ranges to be accurately calibrated. 

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