The reference thermometer's contribution to uncertainty

• Calibration uncertainty: from the certificate, at the relevant point, divided by its coverage factor.
• Drift: estimated from calibration history; treated as rectangular with half-width equal to the expected change over the interval, or as a correction with uncertainty if predictable.
• Interpolation: if the reference was calibrated at 0, 20, 50 °C and used at 35 °C, the fit residuals or a stated interpolation uncertainty apply.
• Self-heating: for resistance thermometers, the difference between the measurement current used at calibration and in use.
• Readout: the indicator or bridge used to read the reference has its own calibration and resolution.
• Immersion: if immersion differs from the calibration condition.

A reference PRT with a 0.01 °C certificate, 0.01 °C annual drift, and a 0.005 °C readout contributes roughly u ≈ 0.009 °C — around 0.02 °C at k = 2 before any bath or UUT effects.

Where the floor comes from

The reference sets the floor on what can be claimed, and the floor is not the number on the certificate — it is that number combined with everything that has happened since. For the reference PRT in the summary above, laid out properly:

So a reference advertised as a 0.02 °C thermometer is really a 0.026 °C reference in service, before the bath, the unit under test or anything else in the budget. That is not a criticism of the instrument; it is what the certificate always meant, and the gap between the two numbers is where most optimistic budgets go wrong.

Interpolation between calibration points

A certificate gives corrections at discrete points. Using the reference at a temperature between them means interpolating, and the interpolation has its own uncertainty. For a PRT with a smooth, well-understood characteristic and points every 50 °C, the term is small — a millikelvin or two. For a thermocouple, whose deviation curve is neither smooth nor predictable, interpolating across a wide gap can contribute more than the certificate does. Calibrate at points close to where you work rather than relying on the curve between them.

Keeping the floor low

• Shorten the interval, or make the drift term time-proportional by recording the date of use. Drift is usually the second-largest term and the easiest to attack.
• Calibrate the reference and readout as a system where they stay together. A system calibration removes the separate readout term, and is usually smaller than the two evaluated apart.
• Measure self-heating rather than bounding it: read at the normal current and at half, and multiply the difference by 4/3 to get the correction.
• Add interim checks — an ice point trended monthly. They shrink the drift term by evidence and they are what locates the onset of a change if the instrument is ever found out of tolerance.
• Handle it as the reference standard it is. A single thermal shock or a knock can move a PRT by more than a year of drift, and the certificate will not know.