Application of rational functions in primary and secondary thermometry

Method has been developed for determination of acoustic and microwave resonance frequences in acoustic gas thermometry by fitting of frequency dependencies of acoustic signal and complex transmission coefficient of the resonator by microwave radiation. The method does not require setting of initial parameters. The method is based on the representation of fitting function used for approximation of frequency dependence in acoustic gas thermometry by rational function. Then approximation of experimental frequency dependence by rational function is performed by quickly converged series of linear approximations. This series can be easily implemented on PC. Method eliminates setting of initial parameters. This simplifies and accelerates approximation of frequency dependences and determination of resonant frequences. Approximation of temperature dependencies of resistivity of standard rhodium-iron resistance thermometers was performed by rational function in the temperature range from 0.5 to 273 K as an alternative for traditional approximation by two different polynomial functions in temperature subranges from 0.5 to 26 K and from 26 to 273 K. It has been shown that the approximation of the temperature dependence of resistivity of rhodium-iron thermometer by single rational function provides deviation of fitting function from experimental points less than 0.5 mK in the range from 0.5 to 273 K. Amount of parameters of such rational function is less than amount of parameters of two polynomial functions providing comparable deviation at experimental points. Obtained result significantly simplifiers resistance to temperature transfer for rhodium-iron standard thermometers.