Equation of state ofN2and Ne near their critical points. Scaling, corrections to scaling, and amplitude ratios

Five stacked parallel plates forming four capacitors were used to measure the density at four different heights for nitrogen and neon near their critical points. Measurements were made on fluid samples with an average density very close to the critical value in a temperature range $-5\mathrm{}\times {10}^{-2\mathrm{}}<t<\mathrm{}1\mathrm{}\times {10}^{-3\mathrm{}}$ where $t$ is the reduced temperature $\frac{(T-T_c)}{T_c}$. These measurements allow simultaneous determinations of (1) the coexistence curve, (2) isothermal compressibility both in one-phase ($T>\mathrm{}{T}_c$) and the two-phase region ($T<\mathrm{}{T}_c$), and (3) the density as a function of chemical potential of these fluids. For data outside the gravitationally rounded region, power-law analyses including correction to scaling terms were used. Data in the gravitationally rounded region were analyzed with the use of the restricted cubic model. Consistent results in $T_c$ (on the order of 0.2 mK) and the leading amplitudes were found between data in these two regions. In addition to the leading exponent $\beta$ and $\gamma$ we also determined from our data the correction to scaling exponent $\Delta$ and three universal amplitude ratios. Our values for these quantities are in good agreement with theoretical predictions.