Heat capacity ratio in liquids at high pressure

Abstract

The heat capacity ratio or Laplace coefficient γ=Cp/CV is determined at high pressure and high temperature by a numerical procedure from sound velocity measurements for a dozen liquids, including alkali metals and iron. The obtained data provide insight into this quantity that is difficult to measure experimentally. In addition, an analytical expression of the heat capacity ratio as a function of pressure is proposed, based on reasonable assumptions. This expression can be used for interpolation, extrapolation at high pressure, or to easily convert isothermal quantities into adiabatic ones or inversely.

Structure and Dynamics in Liquid Iron at High Pressure and Temperature. A First Principles Study

“…Comparison with the “experimental” γ exp ( q ) at ambient pressure, shows that our calculated γ th ( q ) follow a similar qualitative behavior, which suggests that the generalized hydrodynamic model might be more appropriate for describing the microscopic dynamics of l‐Fe in the whole pressure range. Note, moreover, that the decrease with pressure of the γ ( q ) functions is in qualitative agreement with the semiempirical results for the pressure dependence of γ 0 in l‐Fe, which indicate that γ 0 decreases with increasing pressure approaching a value of unity for very high pressure (Ayrinhac, 2021). For comparison, the semiempirical expression of Ayrinhac (2021) gives for l‐Fe at 28 GPa and 2560 K an estimate γ 0 ≈ 1.15.…”

“…The data for γ exp (q) are somewhat noisy in the low q region, but it can be observed that γ exp (q) decreases in this q range and approaches unity beyond q/ q p ≈ 0.5. The interpolating line suggested by Hosokawa et al (2008), points to γ exp (q → 0) ≡ γ 0 ≈ 1.60 − 1.80, which compares well with other semiempirical values derived from other thermophysical magnitudes, that is, γ 0 = 1.80 (Iida et al, 2006), 1.57 (Blairs, 2007), and 1.62 (Ayrinhac, 2021). Regarding our calculated results we remark three aspects: (a) γ v (q) is always larger than γ th (q), (b) the values of γ(q) for both models decrease with increasing pressure, and (c) the γ v (q) are monotonically increasing functions of q, whereas γ th (q) initially decrease, coming close to unity when q/q p ≈ 0.5.…”

The Phonon Theory of Liquids and Biological Fluids: Developments and Applications

“…The phonon theory of liquids has also been widely utilized as a theoretical framework in applied and fundamental research, such as nanofluidics, supercritical fluids technologies, confined liquids, heat transfer and thermal conductivity, solid/liquid interfaces, and planetary science, − to name a few. For instance, it was demonstrated that in gas giants such as Jupiter and Saturn, supercritical hydrogen has a crossover in all its major thermodynamic properties at approximately 10 GPa and 3000 K. As a result, determination of the Frenkel line in supercritical H 2 enabled a demarcation of the boundary between interior and atmosphere in gas giants .…”

Determination of indium melting curve at high pressure by picosecond acoustics

“…Previous authors provided a data review and an accurate evaluation of thermodynamic quantities at ambient pressure: v(T ) [33], ρ(T ) [27] and C p (T ) [71] (fitted by a third order polynomial in Ref. [49]).…”

“…Sound velocities in solids and liquids are markedly different and changes in sound velocities are a very sensitive probe to detect a solid-liquid phase transition [18,46,47] or subtle transformations in the liquid phase [19,20]. Furthermore, accurate velocity measurements allow to derive useful thermodynamical quantities and to obtain the equation of state of the liquid [48,49]. We have thus reexamined the properties of liquid indium in the temperature range 420-680 K and from ambient pressure to 6 GPa by PA technique combined with an externally heated diamond anvil cell (hDAC).…”