A theoretical equation of state for methane

Kerley, Gerald I.

doi:10.1063/1.327452

Cited by 13 publications

(8 citation statements)

References 18 publications

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“…where the rotational but not vibrational states of the methane molecule are excited at the relevant temperatures (Kerley 1980). The parameter x in equation (A7) is less than unity since the estimated Debye temperature for methane is in excess of 100 K; we estimate x-0.8-0.9.…”

Section: Appendixmentioning

confidence: 93%

Thermodynamics of clathrate hydrate at low and high pressures with application to the outer solar system

Lunine¹,

Stevenson²

1985

ApJS

350

285

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The thermodynamic stability of clathrate hydrate is calculated under a wide range of temperature and pressure conditions applicable to solar system problems, using a statistical mechanical theory developed by van der Waals and Platteeuw (1959) and existing experimental data on properties of clathrate hydrates and their components. At low pressure, dissociation pressures and partition functions (Langmuir constants) for CO clathrate (hydrate) have been predicted, using the properties of clathrate containing, as guests, molecules similar to CO. The comparable or higher propensity of CO to incorporate in clathrate relative to N 2 is used to argue for high CO-toN 2 ratios in primordial Titan if N 2 was accreted as clathrate. The relative incorporation of noble gases in clathrate ~rom a solar composition gas at low temperatures is calculated and applied to the case of giant-planet atmospheres and icy satellites. It is argued that nonsolar but well-constrained noble gas abundances will be measured by Galileo in the Jovian atmosphere if the observed carbon enhancement is due to bombardment of the atmosphere by clathrate-bearing planetesimals sometime after planetary formation. The noble gas abundances in Titan's atmosphere are also predicted under the hypothesis that much of the satellite's methane accreted as clathrate. Double occupancy of clathrate cages by H 2 and CH 4 in contact with a solar composition gas is exaniined, and it is concluded that potentially important amounts of H 2 may have incorporated in satellites as clathrate. The kinetics of clathrate formation is also exaniined, and it is suggested that, under thermodynamically appropriate conditions, essentially complete clathration of water ice could have occurred in high-pressure nebulae around giant planets but probably not in the outer solar nebula; comets probably did not aggregate as clathrate. At moderate pressures, the phase diagram for methane clathrate hydrate in the presence of 15% ammonia (relative to water) is constructed, and application to the early Titan atmospheric composition is described. The high-pressure stability of CH 4 , N 2 , and mixed CHc N 2 clathrate hydrate is calculated; conversion back to water and CH 4 and/ or N 2 fluids or solids is predicted for pressures ~ 12 kilobars (independent of temperature) and temperatures ~ 320 K (independent of pressure). The effect of animonia is to shrink the T-P stability field of clathrate with increasing animonia concentration. These results imply that (1) clathrate is stable throughout the interior of Oberon-and Rhea-sized icy satellites, and (2) clathrate incorporated in the innermost icy regions of Titan would have decomposed, perhaps allowing buoyant methane to rise. Brief speculation on the implications of this conclusion for the origin of surficial methane on Titan is given. A list of suggested experiments and observations to test the theory and its predictions is presented.

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Section: Appendixmentioning

confidence: 93%

Thermodynamics of clathrate hydrate at low and high pressures with application to the outer solar system

Lunine¹,

Stevenson²

1985

ApJS

350

285

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“…Although there exist various EOS of methane (e.g., Kerley 1980;Setzmann & Wagner 1991;Sherman et al 2012), none of them covers the entire pressuretemperature region required for Uranus and Neptune interior models. We have therefore computed a new methane EOS using DFT-MD simulations.…”

Section: Methanementioning

confidence: 99%

Planetary Ices and the Linear Mixing Approximation

Bethkenhagen

Meyer

Hamel

et al. 2017

ApJ

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The validity of the widely used linear mixing approximation for the equations of state (EOS) of planetary ices is investigated at pressure-temperature conditions typical for the interior of Uranus and Neptune. The basis of this study are ab initio data ranging up to 1000 GPa and 20 000 K calculated via density functional theory molecular dynamics simulations. In particular, we calculate a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the self-diffusion coefficients in the ternary mixture are calculated along three different Uranus interior profiles and compared to the values of the pure compounds. We find that deviations of the linear mixing approximation from the results of the real mixture are generally small; for the thermal EOS they amount to 4% or less. The diffusion coefficients in the mixture agree with those of the pure compounds within 20% or better. Finally, a new adiabatic model of Uranus with an inner layer of almost pure ices is developed. The model is consistent with the gravity field data and results in a rather cold interior (T core ∼ 4000 K).

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“…The mass-radius relation and central pressure were in reasonable agreement with predictions using SESAME EOS 5520 up to a mass ∼0.1 M E above which the isentrope from the tabular EOS became unusable. For CH 4 , three SESAME EOS were available: 5500 and 5501 (Kerley 1980), both tabulated to 2.5 g cm −3 and respectively with a Maxwell construction and van der Waals loops in the liquid-vapor region; and -25 -5502 (Johnson 1984), tabulated to 0.47 g cm −3 and based on NBS gas phase data. The mass-radius relation was calculated for 5500, which is the most relevant for planetary structures, for an isentrope passing through 70 K at zero pressure.…”

Section: Icesmentioning

confidence: 99%

Mass-Radius Relationships for Exoplanets

Swift

Eggert

Hicks

et al. 2011

ApJ

151

100

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For planets other than Earth, particularly exoplanets, interpretation of the composition and structure depends largely on comparing the mass and radius with the composition expected given their distance from the parent star. The composition implies a mass-radius relation which relies heavily on equations of state calculated from electronic structure theory and measured experimentally on Earth. We lay out a method for deriving and testing equations of state, and deduce mass-radius and mass-pressure relations for key, relevant materials whose equation of state is reasonably well established, and for differentiated Fe/rock.We find that variations in the equation of state, such as may arise when extrapolating from low pressure data, can have significant effects on predicted massradius relations, and on planetary pressure profiles. The relations are compared with the observed masses and radii of planets and exoplanets, broadly supporting recent inferences about exoplanet structures. Kepler-10b is apparently 'Earthlike,' likely with a proportionately larger core than Earth's, nominally 2/3 of the mass of the planet. CoRoT-7b is consistent with a rocky mantle over an Fe-based core which is likely to be proportionately smaller than Earth's. GJ 1214b lies between the mass-radius curves for H 2 O and CH 4 , suggesting an 'icy' composition with a relatively large core or a relatively large proportion of H 2 O. CoRoT-2b is less dense than the hydrogen relation, which could be explained by an anomalously high degree of heating or by higher than assumed atmospheric opacity.HAT-P-2b is slightly denser than the mass-radius relation for hydrogen, suggesting the presence of a significant amount of matter of higher atomic number.CoRoT-3b lies close to the hydrogen relation. The pressure at the center of Kepler-10b is 1.5 +1.2 −1.0 TPa. The central pressure in CoRoT-7b is probably close to 0.8 TPa, though may be up to 2 TPa. These pressures are accessible by pla--3nar shock and ramp loading experiments at large laser facilities. The center of HAT-P-2b is probably around 210 TPa, in the range of planned National Ignition Facility experiments, and that of CoRoT-3b around 1900 TPa.

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A theoretical equation of state for methane

Cited by 13 publications

References 18 publications

Thermodynamics of clathrate hydrate at low and high pressures with application to the outer solar system

Thermodynamics of clathrate hydrate at low and high pressures with application to the outer solar system

Planetary Ices and the Linear Mixing Approximation

Mass-Radius Relationships for Exoplanets

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