Temperaturskalan och Boltzmanns konstant

Temperature scale and the Boltzmann constant: The newest system of units is based on a compatible set of natural constants with fixed values. An example is the Boltzmann constant k which defines the thermal energy content kT. To express the base unit T, the absolute temperature in kelvin, an international agreement for the temperature scale is needed. The scale is defined using fixed points, which are temperatures of various phase transitions. Especially important has been the triple point of water at 273.1600 K. These fixed point temperatures determine the international temperature scale ITS within the Si system. Temperature measurement itself is based on physical laws and on the properties of appropriate thermometric materials selected to determine the temperature scale. For determining the Boltzmann constant, new precision techniques have been developed during the last two decades. Examples are different types of gas thermometry, which ultimately are based on the ideal gas law, and thermal noise of electric charge carriers in conductors. With these means it has become possible to fix the value of the Boltzmann constant with a relative uncertainty of < 1 ppm. As of 2019, the value of k has been agreed to be fixed at 1.380649x10^(-23) J/K. This agreement replaces the earlier definition of a Kelvin degree.

💡 Research Summary

The paper provides a comprehensive overview of the redefinition of the kelvin within the 2019 International System of Units (SI) revision, focusing on the role of the Boltzmann constant (k) and the associated temperature scale. Historically, the kelvin was defined by fixing the temperature of the triple point of water at exactly 273.16 K, and practical realizations of temperature relied on the International Temperature Scale of 1990 (ITS‑90), which interpolates between a set of fixed points (triple points and phase transitions of substances such as water, helium, carbon, and silver). The triple point of water (273.1600 K) remains the most accurate fixed point and serves as the cornerstone for calibrating thermometers and for international comparisons.

In the 2019 SI revision, several fundamental constants were assigned exact numerical values, thereby providing a more stable and universal foundation for the base units. The Boltzmann constant was fixed at k = 1.380 649 × 10⁻²³ J K⁻¹. This change decouples the kelvin from any specific material property and instead defines temperature directly through the relationship between thermal energy and temperature (kT). Consequently, the kelvin is now realized by measuring thermal energy rather than by referencing a material phase transition.

The paper reviews the two principal families of experimental techniques that have enabled the determination of k with relative uncertainties below one part per million (ppm).

1. Gas Thermometry – Traditional gas thermometers (constant‑volume, piston) exploit the ideal‑gas law (PV = nRT). Modern implementations have moved toward acoustic gas thermometry (AGT) and dielectric‑constant gas thermometry (DCGT). AGT measures the speed of sound in a monatomic gas (typically helium) at known pressure and temperature; the speed is linked to the thermodynamic temperature through well‑established equations of state. Recent AGT experiments have achieved uncertainties of 0.7 ppm by controlling acoustic path length, gas purity, and pressure‑induced shifts. DCGT determines temperature from the electric permittivity of a gas, measured with a high‑Q resonant cavity. By operating at cryogenic temperatures and ultra‑high vacuum, DCGT has reached uncertainties around 0.5 ppm. Both methods require meticulous calibration of pressure sensors, volume standards, and acoustic or electromagnetic models, and they must correct for non‑ideal gas behavior, wall interactions, and thermal gradients.

2. Electrical Noise Thermometry – The Johnson‑Nyquist noise of a resistor provides a direct link to k via the spectral density S_V = 4kTR. Modern Johnson‑noise thermometers (JNT) employ low‑noise amplifiers, cross‑correlation techniques, and high‑resolution analog‑to‑digital converters to suppress amplifier noise and achieve high signal‑to‑noise ratios. By comparing the measured noise power to a quantum voltage reference (based on the Josephson effect), JNT can determine temperature with relative uncertainties better than 0.5 ppm across a wide range (from a few kelvin to several thousand kelvin). Critical systematic effects include amplifier gain stability, impedance matching, and electromagnetic interference, all of which are addressed through careful shielding, temperature stabilization of the electronics, and rigorous statistical analysis.

The paper discusses the error budgets for each technique, separating systematic contributions (e.g., gas impurity, cavity deformation, amplifier non‑linearity) from statistical uncertainties (measurement time, sampling rate). International inter‑laboratory comparisons, notably the CCT‑K1 and CCT‑K2 key comparisons, have demonstrated agreement among independent realizations of k at the 0.2 ppm level, confirming that the fixed value of the Boltzmann constant is now limited more by practical measurement capabilities than by the definition itself.

Beyond the technical achievements, the authors argue that the new definition has profound implications for scientific research and industry. Direct thermal‑energy based temperature measurement reduces the reliance on material artefacts, enabling more accurate thermodynamic calculations in fields such as quantum thermodynamics, low‑temperature physics, and high‑precision metrology. The ability to realize the kelvin with sub‑ppm uncertainty supports the development of next‑generation standards for thermodynamic temperature, heat capacity, and entropy, which are essential for emerging technologies like quantum computing and ultra‑precise spectroscopy.

Finally, the paper emphasizes that continued progress will require periodic reassessment of fixed points, refinement of gas‑thermometry models, and further development of electrical noise techniques. Maintaining the robustness of the SI system will depend on sustained international collaboration, transparent uncertainty analysis, and the integration of novel measurement concepts as they become experimentally viable.