Abstract
The Boltzmann constant can be optically determined by measuring the Doppler width of an absorption line of molecules at gas phase. We propose to apply a near infrared cavity ring-down (CRD) spectrometer for this purpose. The superior sensitivity of CRD spectroscopy and the good performance of the near-ir lasers can provide ppm (part-per-million) accuracy which will be competitive to present most accurate result obtained from the speed of sound in argon measurement. The possible influence to the uncertainty of the determined Doppler width from different causes are investigated, which includes the signal-to-noise level, laser frequency stability, detecting nonlinearity, and pressure broadening effect. The analysis shows that the CRD spectroscopy has some remarkable advantages over the direct absorption method proposed before. The design of the experimental setup is presented and the measurement of C2H2 line near 0.8 μm at room temperature has been carried out as a test of the instrument.
Highlights
The Boltzmann constant kB is a fundamental constant that relates the thermodynamic temperature to thermal energy
Using an optimized cw-cavity ring down spectroscopy (CRDS) setup [12], we has shown that the minimal detectable absorption coefficient αmin can be as low as 7 × 10−11/cm
We have explored the possibility to apply a near infrared cavity ring-down spectrometer to the determination of the Boltzmann constant by measuring the Doppler width of a molecular absorption line
Summary
The Boltzmann constant kB is a fundamental constant that relates the thermodynamic temperature to thermal energy. In order to determine the Doppler width of a molecular absorption line with ppm accuracy, it is necessary to achieve sufficient frequency precision in the spectral scanning. This can be accomplished by using CRDS based on a frequency-locked laser. Ing the sub-Doppler hyperfine structure measurements of O2 molecule [17] Very recently, they locked the laser frequency to the stabilized ring-down cavity to increase the ring-down event acquisition rates and a minimal detectable absorption coefficient αmin of 2 × 10−10/cm has been achieved [18]. Measurements of the C2H2 788 nm line at room temperature will be given as a demonstration of the present CRD spectrometer
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