The Callendar–Van Dusen equation is an equation that describes the relationship between resistance (R) and temperature (T) of

platinum Platinum is a chemical element; it has Symbol (chemistry), symbol Pt and atomic number 78. It is a density, dense, malleable, ductility, ductile, highly unreactive, precious metal, precious, silverish-white transition metal. Its name origina ...

resistance thermometers (RTD). As commonly used for commercial applications of RTD thermometers, the relationship between resistance and temperature is given by the following equations. The relationship above 0 °C (up to the melting point of aluminum ~ 660 °C) is a simplification of the equation that holds over a broader range down to -200 °C. The longer form was published in 1925 (see below) by M.S. Van Dusen and is given as:"Callendar-Van Dusen equations for the calibration of platinum resistance thermometers", WIKA data sheet IN 00.29 ∙ 08/2014, https://www.wikapolska.pl/upload/DS_IN0029_en_co_59667.pdf :

R(T) = R(0) 1 + A*T + B*T^2 + (T - 100)C*T^3

While the simpler form was published earlier by Callendar, it is generally valid only over the range between 0 °C to 661 °C and is given as: :

R(T) = R(0) ( 1 + A*T + B*T^2).

Where constants A, B, and C are derived from experimentally determined parameters α, β, and δ using resistance measurements made at 0 °C, 100 °C and 260 °C. Together,

R(T) = \left\{
	\begin{array}{lr}
		R(0) + A\cdot T + B\cdot T^2 & \text{if }0^\circ \text{C} \le T < 661^\circ\text{C}\\
	   	R(0) + A\cdot T + B\cdot T^2 + C\cdot (T-100)T^3 & \text{if }-200^\circ\text{C} It is important to note that these equations are listed as the basis for the temperature/resistance tables for idealized platinum resistance thermometers and are not intended to be used for the calibration of an individual thermometer, which would require the experimentally determined parameters to be found.

These equations are cited in International Standards for platinum RTD's resistance versus temperature function

DIN/IEC 60751 (also called IEC 751)
also adopted a
BS-1904
and with some modification, JIS C1604. The equation was found by British physicist Hugh Longbourne Callendar, and refined for measurements at lower temperatures by M. S. Van Dusen, a chemist at the U.S. National Bureau of Standards (now known as the

National Institute of Standards and Technology The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into Outline of p ...

) in work published in 1925 in th
Journal of the American Chemical Society
Starting in 1968, the Callendar-Van Dusen Equation was replaced by an interpolating formula given by a 20th order polynomial first published i
The International Practical Temperature Scale of 1968
by the Comité International des Poids et Mesures. Starting in 1990, the interpolating formula was further refined with the publication o
The International Temperature Scale of 1990
The

ITS-90 The International Temperature Scale of 1990 (ITS-90) is an equipment calibration standard specified by the International Committee of Weights and Measures (CIPM) for making measurements on the Kelvin and Celsius temperature scales. It is an appro ...

is published by the Comité Consultatif de Thermométrie and the Comité International des Poids et Mesures. This work provides a 12th order polynomial that is valid over an even broader temperature range that spans from 13.8033 K to 273.16 K and a second 9th order polynomial that is valid over the temperature range of 0 °C to 961.78 °C.

References

External links

Caldus. Callendar-Van Dusen conversion between resistance and temperature in python.
{{DEFAULTSORT:Callendar-Van Dusen equation Thermometers Equations