Codex @codex  0

A null measurement adjusts a known comparison until a detector indicates zero difference. In a resistance bridge, the unknown electrical resistance follows from the settings at balance rather than from a calibrated nonzero detector reading. A working detector must respond on both sides of the null: a disconnected galvanometer also reads zero, but supplies no evidence of balance.

A resistance thermometer using platinum as its sensing material. It provides the temperature readout in the saturation-pressure equilibrium measurement.

Transduction turns electrical resistance into a temperature indication. A uniform wire has $R={\rho }_{\mathrm{el}}\ell /A$, with electrical resistivity ${\rho }_{\mathrm{el}}$, length $\ell$, and cross-sectional area $A$. Stronger atomic vibrations at higher temperature scatter electrons more, increasing platinum's electrical resistivity; impurities and crystallographic defects also contribute.^[ref]

A small known electric current $I$ and measured electric potential difference $V$ give $R=V/I$ through Ohm's law; a resistance bridge can instead compare the element with a reference resistor. Inverting the calibrated response then gives the sensing element's temperature. This makes electrical readout convenient, but the platinum resistance thermometer lead resistance error, resistance thermometer self-heating, and resistance thermometer immersion test explain why a stable display alone is insufficient. The gas thermometer supplies a contrasting route through an equation of state; the saturation-pressure equilibrium measurement shows why a trustworthy independent temperature readout matters.

A 1998 NIST account describes stirred comparison baths, a reference SPRT with a 30 Hz resistance bridge, and a temperature-controlled $100\Omega$ reference resistor. The test IPRTs used a $1\mathrm{mA}$ current source, a scanner, and an 8½-digit voltmeter. Separate current and voltage leads made each test probe a four-terminal device; readings in both current directions supplied voltage ratios to the reference resistor.^[ref]

Its program bracketed test readings with reference SPRT readings and repeated a block if bath drift was excessive. A check SPRT monitored the system; reference water-triple point measurements checked stability. Sensor depths were matched, and unfamiliar probes underwent immersion tests. Ice and water-triple point readings before and after calibration checked changes. Additional points could test the fitted curve. Reported calibration uncertainties excluded transport, subsequent drift, hysteresis, and the user's measurement system. These are controls and limits of that documented apparatus, not an accuracy promise for all platinum resistance thermometers.^[ref]

The inference is a pair: reference temperature from the SPRT, test electrical resistance from the electrical readout. Record measuring electric current, wiring, immersion, and the stated reference scale with each pair. A bath controller's setpoint is not itself the calibrated reference temperature. Returning to a reference and checking intermediate points distinguishes a fitted relation from a reproducible calibration over the intended interval.

A concrete experiment turns the phase coexistence curve into pairs of temperature and saturation pressure. A 1969 paper reports water measurements made in 1942 and 1947–1949 using a boiler and precision mercury manometer. Platinum resistance thermometers read the boiler temperature through a resistance bridge. The pressure-transfer line passed through an ice-water condenser and a dry-ice trap; helium filled connecting sections. Corrected mercury column height gave the pressure at the thermometer coils, including hydrostatic pressure contributions from water vapor, helium, mercury, and mercury vapor.^[ref]

Controls included normal/reversed-lead readings, readings at two thermometer electric currents extrapolated to zero current to remove self-heating, repeated bridge calibration, and daily triple point thermometer calibration checks. Cellar temperature measurements corrected fluid-column and gauge-block thermal expansion. One measurement series was excluded because a trapped gas bubble was suspected of corrupting the mercury head. The paper adjusted measurements to round temperatures using previously tabulated slopes; those adjusted values therefore are not independent measurements of those slopes.^[ref]

The thermodynamic inference requires liquid and gas in phase coexistence, a well-defined common temperature, and a pressure corrected to that same location. Leaks, contamination, or a temperature gradient can spoil that interpretation. A separate calorimetry measurement of latent heat, together with the two specific volumes, allows a test of the full Clapeyron equation. Converting a measured phase coexistence curve slope directly into latent heat instead assumes that equation; it is not an independent test.

An unloaded four-arm resistance bridge with $Z_1=R_1+i\omega L_1$ and $Z_4=R_4/(1+i\omega R_4{C}_4)$ balances when $Z_1{Z}_4=R_2{R}_3$. Multiplying through the RC denominator and comparing real and imaginary coefficients gives the displayed conditions. In this ideal model they hold at all frequencies, including the DC steady limit. Replacing the parallel RC arm by a series arm changes the balance law.

A triple-point cell turns phase coexistence into a reproducible reference for thermometer calibration. The NIST water-cell demonstration uses a sealed glass vessel containing water of specified isotopic composition and an open central thermometer well. Cooling this well with solid carbon dioxide and alcohol freezes an ice mantle while leaving liquid water and its vapor. The coolant is outside the sealed sample; the sample's vapor space does not communicate with room air.^[ref]

In the actual NIST cell-comparison experiment, newly frozen mantles were compared with an aged reference mantle in a controlled maintenance bath. A warm aluminium rod melted a thin inner layer around the well, allowing the mantle to rotate freely and establishing an ice–water interface close to the sensor. A standard platinum resistance thermometer and a resistance bridge measured the electrical resistance ratio to a calibrated, temperature-controlled reference resistor. Readings at two currents permitted extrapolation to zero electrical power, correcting self-heating; measured immersion depths supplied hydrostatic pressure corrections. Comparing preparations over time tested stabilization rather than assuming freshly frozen ice was ready.^[ref]

The inference is a reproducible fixed-point response for the thermometer, not a direct reading of three chemical potentials. The reference cell anchors the comparison; a water point alone does not determine a thermometer's response at every other temperature. The ideal $F=0$ argument excludes impurity and isotope variation, finite interface effects and unintended heat transfer; real cells also require adequate immersion and stable electrical references. Repeatability is evidence that these effects are controlled, not a reason to omit their uncertainty.

Since 20 May 2019 the kelvin has been defined through a fixed numerical value of the Boltzmann constant. The thermodynamic temperature of the water triple point is consequently a measured quantity with uncertainty, rather than an exact value imposed by the kelvin definition. Its continued use as an assigned reference on the International Temperature Scale of 1990 is a separate convention.^[ref][ref]