Optical \(n(p,\ T_{90})\) Measurement Suite 2: H\(_2\)O and D\(_2\)O

Abstract

A suite of measurements of refractive index \(n(p,\ T_{90})\) is reported for gas phase ordinary water H\(_2\)O and heavy water D\(_2\)O. The methodology is optical refractive index gas metrology, operating at laser wavelength \(633\ \text {nm}\) and covering the range \((293< T_{90} < 433)\ \text {K}\) and \(p < 2\ \text {kPa}\). A key output of the work is the determination of molar polarizabilities \(A_{\text {R}} = 3.7466(18) \cdot [1 + 1.5(6) \times 10^{-6} (T/\text {K} - 303) ]\ \text{cm}^3 \cdot \text{mol}^{-1}\) for ordinary water, and \(A_{\text {R}} = 3.7135(18) \cdot [1 + 4.4(10) \times 10^{-6} (T/\text {K} - 303) ]\ \text{cm}^3 \cdot \text{mol}^{-1}\) for heavy water, with the numbers in parentheses expressing standard uncertainty. For heavy water, this work appears to be only the second gas phase measurement to date. For both ordinary and heavy water, this work agrees within \(0.15\ \%\) with recent ab initio theoretical results for \(A_{\text {R}}\), but the comparison is affected by imperfect knowledge of dispersion. For ordinary water, the close agreement between the present work and theory suggests problems at the \(2\ \%\) level in the low density limit of the reference formulation for refractivity.