Thermal Diffusivity of CO_{2} in the Critical Region
Abstract
We have measured the Rayleigh linewidth in CO_{2} in the critical region using a selfbeat spectrometer. The linewidth was measured as a function of both temperature and cell height. The thermal diffusivity χ calculated using the LandauPlaczek equation is in excellent agreement with the values that have been obtained by thermodynamic measurements at three temperatures within the temperature range we investigated (TT_{c}=1.04, +1.06, and +3.8C°). Thus the LandauPlaczek equation is directly verified in the critical region, at least for temperatures not too close to T_{c}. However, we find that very near T_{c} [for ∊≡(TT_{c})T_{c}<~10^{4}], the correlation length in CO_{2} is of sufficiently long range (~250 Å at ∊=10^{4}) to require that the Fixmanmodified linewidth equation be used in order to correctly describe the linewidth behavior. The thermal diffusivity was obtained along the critical isochore for the temperature range 0.02<=(TT_{c})<=5.3C^{∘} and along both the gas and liquid sides of the coexistence line for 0.02<=(T_{c}T)<=2.3 C°. The results are (in units of cm^{2}/sec): along the critical isochore, χ=(18.1+/0.5)×10^{6}(T T_{c})^{0.73+/0.02} along the gas coexistence line, χ=(36.0+/3.0)×10^{6}(T_{c} T)^{0.66+/0.05} and along the liquid coexistence line, χ=(34.8+/2.5)×10^{6}(T_{c} T)^{0.72+/0.05}. These exponents are in reasonable quantitative agreement with the prediction of Kadanoff and Swift that χ~∊^{ν}(ν~23). Our exponents are also in accord with the thermalconductivity divergence λ~∊^{12} predicted by Fixman and by Mountain and Zwanzig, if the isothermal compressibility diverges as ∊^{54}, as predicted by the Ising model. Thus both theory and experiment indicate a stronger divergence in the thermal conductivity than has heretofore been assumed. Our subcritical exponents are also in agreement with the linewidth measurements by Saxman and Benedek in SF_{6}; however, above the critical temperature they obtained an exponent of 1.27, in definite disagreement with our result.
 Publication:

Physical Review
 Pub Date:
 July 1968
 DOI:
 10.1103/PhysRev.171.152
 Bibcode:
 1968PhRv..171..152S