Uncertainty from the calibration bath or dry block

In a comparison calibration the reference and unit under test are assumed to be at the same temperature. They are not. The source fluctuates in time and varies in space; the budget must include both.

Components

• Temporal stability: standard deviation of the source temperature over the acquisition window, evaluated from the reference readings.
• Radial (well-to-well) gradient: the difference between the reference well and the UUT well, from a characterisation with two references.
• Axial gradient: temperature variation along the immersion depth, relevant when sensors have different sensing lengths.
• Loading: in dry blocks, several probes or a large probe alter the gradient.
• Stem conduction: heat flow along the probe stem in dry blocks affects the sensing element.

EURAMET guidance on dry-block calibrators describes how to characterise these effects; the results should be recorded per source and per temperature range.

Separating the three effects

The source contributes through three distinct routes, and they are measured differently. Lumping them into one bath term hides which one is worth fixing.

The swap technique for radial difference is worth knowing because it removes the instruments' own errors from the measurement: whatever remains after averaging the two orientations is the difference between the wells, not between the thermometers.

Loading changes all three

A dry block characterised with one probe in it behaves differently with four. Each additional probe is a conduction path to the room, and a block with every well occupied runs cooler at the top and has a steeper axial gradient than the empty characterisation showed. The same is true of a bath, less severely. So the characterisation should be done under the loading the block is actually used with — or a loading component added, which is the honest but larger option.

EURAMET cg-13 describes these measurements for block calibrators and cg-20 the equivalent for chambers. The results belong in a record per source, per temperature range, with the loading stated — not a single number carried forward from whenever the instrument was new.

Reducing the terms rather than reporting them

• Match the well to the probe. The air gap in an oversized well is the largest single contributor to both the radial and axial terms in a dry block.
• Insulate the block mouth and the exposed stem. This attacks the axial gradient and the stem conduction at the same time, and costs nothing.
• Take reference and UUT readings simultaneously rather than sequentially. Sequential readings convert the temporal stability term into a drift over the gap between them, which is much larger.
• Place reference and UUT in adjacent wells at the same depth, and record which wells were used. The radial term is well-pair specific.
• For the lowest uncertainties, accept that a block cannot get there. A stirred bath reduces all three terms by roughly an order of magnitude, and no amount of characterisation closes that gap.