Specific heat of CO2near the critical point

Abstract

We describe an experiment to measure the specific heat of C${\mathrm{O}}_2$ to an accuracy of 1% along the critical isochore for $4\times {10}^{-5\mathrm{}}<\left|t\right|<3\mathrm{}\times {10}^{-2\mathrm{}}$, where $t=1-\frac{T}{T_c}$, giving details of the method and the analysis. After applying a correction term for the effect of gravity on the specific heat of the 1-mm-high sample, we fitted the data with functions of the form $C_v=A{\mathrm{}\left|t\right|\mathrm{}}^{-\alpha }+B$. With the constraint $\alpha ={\alpha }^{\prime }$ the optimum value of the exponent was $\alpha =0.124\mathrm{}\pm 0.005$. When this constraint was relaxed, we obtained $\alpha =0.124\mathrm{}\pm 0.014$ and ${\alpha }^{\prime }=0.124\mathrm{}\pm 0.012$. These results are in good agreement with predictions based on renormalization-group analysis and numerical estimates for the three-dimensional Ising lattice. For the ratio $\frac{A^{+}}{A^{-}}$ of the coefficients of the divergent term on each side of $T_c$, we obtained the value 0.54, which is within the range of predictions from scaling and the renormalization-group method, but disagrees with the estimate for the Ising model. We also present the results of measurements of the thermal relaxation time of the sample.