# A Radiometric Determination of the Stefan-Boltzmann Constant and Thermodynamic Temperatures between -40 degrees C and +100 degrees C

T.J. Quinn, J.E. Martin

## Abstract

The total radiant exitance of a black body at the temperature of the triple point of water, T$_{\text{tp}}$ (273.16 K), and at a series of other temperatures in the range from about 233 K (-40 degrees C) to 373 K (100 degrees C), has been measured by using a cryogenic radiometer. From the measurements at T$_{\text{tp}}$ a value for the Stefan-Boltzmann constant $\sigma$ has been calculated: $\sigma$ = (5.669 67 $\pm$ 0.000 76) $\times$ 10$^{-8}$ W m$^{-2}$ K$^{-4}$. This is the first radiometric determination of $\sigma$ having an uncertainty comparable with that calculated directly from fundamental physical constants. This measured value differs from the calculated one by 13 parts in 10$^{5}$, which is less than the combined standard deviations of the measured and calculated values. From the measurements of exitance at the other temperatures, values of the corresponding thermodynamic temperature T have been calculated by using Stefan's fourth-power law. Since the temperature of the radiating black body was also measured by platinum resistance thermometers calibrated on IPTS-68, values of (T-T$_{68}$) were obtained. These range from about -(5 $\pm$ 1.6) mK at 20 degrees C to -(28 $\pm$ 2.5) mK at 100 degrees C and +(5 $\pm$ 1.5) mK at -40 degrees C. The results confirm to within a few millikelvins the departure of T$_{68}$ from T above 0 degrees C already discovered by gas thermometry and show that similar departures, but of opposite sign, exist down to the lowest temperature measured, -40 degrees C. The uncertainties associated with these new values of T and (T-T$_{68}$) are similar to those of the best gas thermometry.