Thermodynamic anomalies near the critical point of CO2

Existing experimental data on the compressibility, chemical potential, specific heat, and critical opalescence of C${\mathrm{O}}_2$ are analyzed to determine a parametric, scaling-law representation for the critical region. A representation of the form of the linear model of Schofield is found to be consistent with these data for scaling-law amplitudes $a=22\mathrm{}$, $b^2=g=1.30\mathrm{}$, exponents $\beta =0.347\mathrm{}$, $\gamma =1.22\mathrm{}$, $\alpha =0.09\mathrm{}$, and for a slowly varying (nondivergent) background. This representation corresponds approximately to the use of the mean range of local density correlations and of the macroscopic order as fundamental (parametric) variables to locate positions in thermodynamic space. The representation thus obtained is used to predict effects of gravity and the shape of contours of equal wave scattering close to the critical point. The predictions are investigated experimentally by studying the dependence of the scattering of laser light on chemical potential (height) and temperature. Satisfactory agreement is found to within the precision of the measurements. In addition, it is verified experimentally that contours of equal opalescence have the same shape as contours of equal mean relaxation time of local density fluctuations. This demonstrates that the relaxation time and the correlation length obey equivalent scaling-law homogeneity relationships close to the critical point. Some discrepancies among existing experiments and between experiment and theory are noted and discussed briefly. In particular, there remain unexplained discrepancies between the values of the critical-point exponents found here and those predicted by the Ising model.