Resistance Temperature Correlation
Mathematical models describe the relationship between the electrical resistance of platinum and its temperature over a specific range. Scientists use the callendar van dusen equation to linearize output from resistance temperature detectors across cryogenic and high heat environments. It defines the curve using constant coefficients derived from ice and steam point measurements.
Coefficient Derivation
Platinum purity influences the alpha constant which describes the average slope between freezing and boiling points of water. Calibration labs determine the beta and delta coefficients by measuring resistance at the boiling point of oxygen and the melting point of zinc. These values remain stable provided the sensing element undergoes no mechanical strain or chemical contamination.
Reliability depends on the precise determination of the resistance at the ice point which acts as the reference for all other temperature points in the span.
Range Limit
Cryogenic measurements require the inclusion of the beta term to account for non linear behavior below zero degrees celsius. If the application stays above the freezing point, the calculation simplifies to a second order polynomial. Errors emerge when practitioners apply the formula beyond the calibrated range of the platinum sensor.
Uncertainty Contribution
High precision thermometers rely on these coefficients to achieve accuracies within fractions of a kelvin. Because resistance changes are small, slight errors in the coefficients lead to large temperature offsets in industrial control systems. Proper implementation ensures interchangeability between different sensor batches.
This mathematical framework remains the standard for industrial platinum resistance thermometry.
