Uncertainty of the calibration of paired temperature sensors for heat meters

In heat meters, the temperatures of the incoming and the outgoing water are measured with calibrated platinum resistance thermometers. They are subject to legal metrology and the requirements for the uncertainty associated with the temperature difference are specified in national and regional standards. It is difficult to calculate this uncertainty, since it depends on the characteristics of both sensors and correlation needs to be considered. Causes of that correlation include calibration in the same facility, losses due to heat conduction, and common electrical measurements. Therefore, an analytical calculation of the temperature difference and the associated uncertainty is quite complicated, requiring several steps, corrections, and approximations. Monte Carlo techniques avoid these difficulties by simulating the calibration of both sensors simultaneously. As expected, the correlation reduces the uncertainty associated with the temperature difference indicated by the sensor pair considerably. Monte Carlo simulation and analytical calculations are briefly described and their results are compared.