Callendar-van Dusen Equation

Note that IPTS-68 and many simpler interpolation schemes still in use, such as the Callendar-van Dusen equation described below, use the ratio R(7)/R(273.15 K) based on the ice point as the reference temperature. 

Callendar-van Dusen Equation. The complexity of the ITS-90 equations, especially for temperatures below 273.16 K, creates an awkward situation. For practical use, the Callendar-van Dusen equation, which was the basis for IPTS-48, is still a very convenient form. This is especially true if one wishes to determine the resistance R of a Pt thermometer digitally under computer control and convert it into a temperature with a reasonably simple algorithm. The general form of the Callendar-van Dusen equation is... 

Commercial platinum RTDs are almost always described by the following R f) relationship, known as the Callendar-Van Dusen equation ... 

It is often necessary to invert the Callendar-Van Dusen equation to express f as a function of R. For the high temperature range (f > 0 °C), the quadratic Eq. 2b is readily solved for t R) in closed form ... 

This is the same form as the high-temperature Callendar-Van Dusen equation given in Eq. 2b, but in general, the constants Ci and C2 will be different from A and B. A parabohc fit with the form of Eq. 6 should be adequate for microfabricated metallic RTDs over temperature ranges spanning several hundred degrees (recall that semiconducting resistance elements are known as thermistors, which are beyond the scope of this entry and would be better described by an Arrhenius-type R(X) behavior). 

Resistance Temperature Detectors (RTD) use a different linearisation function. The Callendar-van Dusen Equation relates resistance R) to temperature T) according to... 

Adoption of the IPTS-68 scale eliminated the need for the Callendar-Van Dusen equation above 90 K. The IPTS-68 provides analytical relationships which allow thermometers to be calibrated between 13.81 and 90.188 K. However, since fixed points are required, the process is tedious at best. Nonetheless, Eqs. (8.32) and (8.33) are often used for engineering purposes to represent the resistance-temperature relation of platinum resistance thermometers. 

Platinum Resistance Thermometers (PRTs) PRTs (sometimes seen as Resistance Temperature Detectors, or RTDs) are the thermometers of choice in high-quality blackbodies. They are reliable and accurate, although they require recalibration every 2 or 3 years. They are generally used with dedicated blackbody controllers that measure the PRT resistance, convert it to temperature, and adjust heaters to maintain the desired temperature. These controllers are programmable to accept calibration constants they convert the measured PRT resistance to temperature using the Callendar-Van Dusen equation ... 

Compared to the Z function, the Callendar-Van Dusen type analytical relations require measurements at many fixed points. For the 13.81 to 90.188 K region as defined by IPTS-68, there are six fixed points the reference function involves 20 coefficients and four polynomial equations for the deviations. It is interesting to note that maximum differences between the IPTS-68 and, for example, the NBS-55 scale, are only about 0.015 K. 

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