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Limitations in the accuracy of industrial thermometers

When we calibrate a thermometer for a client, we make an estimate of the uncertainty in temperatures measured using that thermometer.

The uncertainty is based in part on measurements made during the calibration and in part on our understanding of the causes of errors. As industry requires ever increasing accuracies, we must improve our understanding of the various effects that lead to errors or uncertainty in the temperature measurements. Recently, we have decided to explore in detail three effects that occur in industrial thermometers:

Immersion effects 

When a thermometer is immersed into a calibration bath, heat migrates along the thermometer to the cooler end of the thermometer sticking out of the bath. This leads to a temperature gradient along the thermometer and a small error in the temperature measurement due to the tip of the thermometer not being at the bath temperature. Very simple models show that the temperature error decreases exponentially as the thermometer is immersed to greater depths, with the 1/e length associated with the exponential behaviour (the effective diameter) approximately equal to the diameter of the thermometer. This model leads us to simple rules of thumb for ensuring the error is sufficiently small: 

  • For industrial thermometry or 1% accuracy, the thermometer should be immersed to 5 diameters,
  • For laboratory thermometry or 0.01% accuracy, the thermometer should be immersed to 10 diameters
  • For high-accuracy metrology or 0.0001% accuracy, the thermometer should be immersed to 15 diameters. 

The model and the rules of thumb turn out to be quite useful. However, we recently noticed that in oil baths, the 1/e lengths determined from immersion profiles were much larger than the diameter of the thermometers. We have concluded that for most thermometers the effective diameter is made much larger by the boundary layer of oil attached to the thermometer, which may be as much as 10 mm thick. We are currently carrying out experiments to better explain the immersion characteristics of thermometers and develop more reliable rules of thumb. 

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All sensors suffer from hysteresis, and industrial platinum resistance thermometers (IPRTs) are no exception. Hysteresis is a type of memory effect whereby the sensor response depends on previous measurements. For example, a temperature indication may be different on rising temperature compared to a falling temperature. In IPRTs, a major cause of hysteresis is caused by a combination of the differential thermal expansion of the platinum wire and the ceramic substrate, and friction between the wire and substrate. This causes the wire to be under compression when the temperature changes in one direction and under tension when the temperature changes in the other direction.

IPRT manufacturers are well aware of these effects and various compromises are made between the hysteresis, which decreases if the wire is unsupported, and sensitivity to vibration and shock which decreases with increased support. The hysteresis in IPRTs varies from about 0.05% to 0.0001% depending on the construction of the sensor.

The problem we have as a calibration lab is that if we calibrate in both directions the calibration takes twice as long. If we calibrate in one direction, there may be large errors in subsequent measurements that depend on how the thermometer is used.  In the second case we must have a good understanding of the hysteresis effects in order to offer the lowest practical uncertainty to our clients. MSL is working to better understand the hysteresis effect, with the aim of developing efficient calibration schemes and improved estimates of uncertainty due to hysteresis. 

Ageing effects in thermocouples

Thermocouples have been in use as temperature sensors for over a century now and are the most common temperature sensor. They are probably the most misunderstood, but that’s another story (see MSL Technical Guide 11). Despite the long use of thermocouples the knowledge of the behaviour of thermocouples with time and temperature is quite patchy. Some thermocouples, like Type K and Type N, are relatively well understood because of the research involved in developing Type N as replacement for rather poorly behaved Type K thermocouple.

After more than 20 years, MSL is re-establishing a calibration facility for thermocouples. In order to provide an accurate estimate of the uncertainty in a thermocouple calibration we need to have measured the Seebeck coefficient of the wire in the region of the wire that will be exposed to temperature gradients. Having built a simple machine for measuring the Seebeck coefficients, we realised that it would then be a simple matter to age a set of thermocouples in a furnace over a period of a year to determine the effect on the Seebeck coefficient. We hope to have started collecting data for the study by early 2010. 

For further information contact  Rod White

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