THE difficulty of reconciling line spectra with the kinetic theory of gases, has been referred to by Prof. Fitzgerald (NATURE, January 3, p. 221). The following considerations show that it is possible under certain suppositions to have a number of spectral rays with a very restricted number of degrees of freedom. Most of us, I believe, now accept a definite atomic charge of electricity, and if each charge is imagined to be capable of moving along the surface of an atom, it would represent two degrees of freedom. If a molecule is capable of sending out a homogeneous vibration, it means that there must be a definite position of equilibrium of the “electron.” If there are several such positions, the vibrations may take place in several periods. Any one molecule may perform for a certain time a simple periodic oscillation about one position of equilibrium, and owing to some impact the electron may be knocked over into a new position. The vibrations under these circumstances would not be quite homogeneous, but if the electron oscillates about any one position sufficiently long to perform a few thousand oscillations, we should hardly notice the want of homogeneity. Each electron at a given time would only send out vibrations which in our instruments would appear as homogeneous. Each molecule could thus successively give rise to a number of spectral rays, and at any one time the electron in the different molecules would, by the laws of probability, be distributed over all possible positions of equilibrium, so that we should always see all the vibrations which any one molecule of the gas is capable of sending out. The probability of an electron oscillating about one of its positions of equilibrium need not be the same in all cases. Hence a line may be weak not because the vibration has a smaller amplitude, but because fewer molecules give rise to it. The fact that the vibrations of a gas are not quite homogeneous, is borne out by experiment. If impacts become more frequent by increased pressure, we should expect from the above views that the time during which an electron performs a certain oscillation is shortened; hence the line should widen, which is the case. I have spoken, for the sake of simplicity, as if an electron vibrating about one position of equilibrium could only do so in one period. If the forces called into play, by a displacement, depend on the direction of the displacement, there would be two possible frequencies. If the surface is nearly symmetrical, we should have double lines.

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The Kinetic Theory of Gases

Introduction.- The First Vertebrates, Jawless Fishes, the Agnathans.- The Earliest Jawed Vertebrates, the Gnathostomes.- Evolution of Modern Fishes: Critical Biological Innovations.- Tetrapods and the Invasion of Land.- Crucial Vertebrate Innovations.- The Dinosaur Integument.- Mammal-like Reptiles.- Reptiles Return to the Sea.

Origin and evolution

Gas hydrates have received considerable attention due to their important role in flow assurance for the oil and gas industry, their extensive natural occurrence on Earth and extraterrestrial planets, and their significant applications in sustainable technologies including but not limited to gas and energy storage, gas separation, and water desalination Given not only their inherent structural flexibility depending on the type of guest gas molecules and formation conditions, but also the synthetic effects of a wide range of chemical additives on their properties, these variabilities could be exploited to optimise the role of gas hydrates This includes increasing their industrial applications, understanding and utilising their role in Nature, identifying potential methods for safely extracting natural gases stored in naturally occurring hydrates within the Earth, and for developing green technologies This review summarizes the different properties of gas hydrates as well as their formation and dissociation kinetics and then reviews the fast-growing literature reporting their role and applications in the aforementioned fields, mainly concentrating on advances during the last decade Challenges, limitations, and future perspectives of each field are briefly discussed The overall objective of this review is to provide readers with an extensive overview of gas hydrates that we hope will stimulate further work on this riveting field

Gas hydrates in sustainable chemistry

The radii and orbital periods of 4,000+ confirmed/candidate exoplanets have been precisely measured by the Kepler mission. The radii show a bimodal distribution, with two peaks corresponding to smaller planets (likely rocky) and larger intermediate-size planets, respectively. While only the masses of the planets orbiting the brightest stars can be determined by ground-based spectroscopic observations, these observations allow calculation of their average densities placing constraints on the bulk compositions and internal structures. However, an important question about the composition of planets ranging from 2 to 4 Earth radii (R⊕) still remains. They may either have a rocky core enveloped in a H2-He gaseous envelope (gas dwarfs) or contain a significant amount of multicomponent, H2O-dominated ices/fluids (water worlds). Planets in the mass range of 10-15 M⊕, if half-ice and half-rock by mass, have radii of 2.5 R⊕, which exactly match the second peak of the exoplanet radius bimodal distribution. Any planet in the 2- to 4-R⊕ range requires a gas envelope of at most a few mass percentage points, regardless of the core composition. To resolve the ambiguity of internal compositions, we use a growth model and conduct Monte Carlo simulations to demonstrate that many intermediate-size planets are "water worlds."

https://www.pnas.org/content/pnas/116/20/9723.full.pdf

Growth model interpretation of planet size distribution

Habitability is a widely used word in the geoscience, planetary science, and astrobiology literature, but what does it mean? In this review on habitability, we define it as the ability of an environment to support the activity of at least one known organism. We adopt a binary definition of “habitability” and a “habitable environment.” An environment either can or cannot sustain a given organism. However, environments such as entire planets might be capable of supporting more or less species diversity or biomass compared with that of Earth. A clarity in understanding habitability can be obtained by defining instantaneous habitability as the conditions at any given time in a given environment required to sustain the activity of at least one known organism, and continuous planetary habitability as the capacity of a planetary body to sustain habitable conditions on some areas of its surface or within its interior over geological timescales. We also distinguish between surface liquid water worlds (suc...

Habitability: a review

In this work, we study the transport of methane in the external water envelopes surrounding water-rich super-Earths. We investigate the influence of methane on the thermodynamics and mechanics of the water mantle. We find that including methane in the water matrix introduces a new phase (filled ice), resulting in hotter planetary interiors. This effect renders the super-ionic and reticulating phases accessible to the lower ice mantle of relatively low-mass planets (∼5 M{sub E} ) lacking a H/He atmosphere. We model the thermal and structural profile of the planetary crust and discuss five possible crustal regimes which depend on the surface temperature and heat flux. We demonstrate that the planetary crust can be conductive throughout or partly confined to the dissociation curve of methane clathrate hydrate. The formation of methane clathrate in the subsurface is shown to inhibit the formation of a subterranean ocean. This effect results in increased stresses on the lithosphere, making modes of ice plate tectonics possible. The dynamic character of the tectonic plates is analyzed and the ability of this tectonic mode to cool the planet is estimated. The icy tectonic plates are found to be faster than those on a silicate super-Earth. A mid-layer of lowmore » viscosity is found to exist between the lithosphere and the lower mantle. Its existence results in a large difference between ice mantle overturn timescales and resurfacing timescales. Resurfacing timescales are found to be 1 Ma for fast plates and 100 Ma for sluggish plates, depending on the viscosity profile and ice mass fraction. Melting beneath spreading centers is required in order to account for the planetary radiogenic heating. The melt fraction is quantified for the various tectonic solutions explored, ranging from a few percent for the fast and thin plates to total melting of the upwelled material for the thick and sluggish plates. Ice mantle dynamics is found to be important for assessing the composition of the atmosphere. We propose a mechanism for methane release into the atmosphere, where freshly exposed reservoirs of methane clathrate hydrate at the ridge dissociate under surface conditions. We formulate the relation between the outgassing flux and the tectonic mode dynamical characteristics. We give numerical estimates for the global outgassing rate of methane into the atmosphere. We find, for example, that for a 2 M{sub E} planet outgassing can release 10{sup 27}-10{sup 29} molecules s{sup –1} of methane to the atmosphere. We suggest a qualitative explanation for how the same outgassing mechanism may result in either a stable or a runaway volatile release, depending on the specifics of a given planet. Finally, we integrate the global outgassing rate for a few cases and quantify how the surface atmospheric pressure of methane evolves over time. We find that methane is likely an important constituent of water planets' atmospheres.« less

https://iopscience.iop.org/article/10.1088/0004-637X/792/2/125/pdf

Structure and dynamics of cold water super-earths: the case of occluded ch4 and its outgassing

Traditional definitions of the habitable zone assume that habitable planets contain a carbonate-silicate cycle that regulates CO2 between the atmosphere, surface, and the interior. Such theories have been used to cast doubt on the habitability of ocean worlds. However, Levi et al (2017) have recently proposed a mechanism by which CO2 is mobilized between the atmosphere and the interior of an ocean world. At high enough CO2 pressures, sea ice can become enriched in CO2 clathrates and sink after a threshold density is achieved. The presence of subpolar sea ice is of great importance for habitability in ocean worlds. It may moderate the climate and is fundamental in current theories of life formation in diluted environments. Here, we model the Levi et al. mechanism and use latitudinally-dependent non-grey energy balance and single-column radiative-convective climate models and find that this mechanism may be sustained on ocean worlds that rotate at least 3 times faster than the Earth. We calculate the circumstellar region in which this cycle may operate for G-M-stars (Teff = 2,600 to 5,800 K), extending from about 1.23 to 1.65, 0.69 to 0.954, 0.38 to 0.528 AU, 0.219 to 0.308 AU, 0.146 to 0.206 AU, and 0.0428 to 0.0617 AU for G2, K2, M0, M3, M5, and M8 stars, respectively. However, unless planets are very young and not tidally locked, our mechanism would be unlikely to apply to stars cooler than a ~M3. We predict C/O ratios for our atmospheres (about 0.5) that can be verified by the JWST mission.

The ice cap zone: a unique habitable zone for ocean worlds

Whether volatiles can be entrapped in a background matrix composing planetary envelopes and be dragged via convection to the surface is a key question in understanding atmospheric fluxes, cycles, and composition. In this paper, we consider super-Earths with an extensive water mantle (i.e., water planets), and the possibility of entrapment of methane in their extensive water-ice envelopes. We adopt the theory developed by van der Waals & Platteeuw for modeling solid solutions, often used for modeling clathrate hydrates, and modify it in order to estimate the thermodynamic stability field of a new phase called methane filled ice Ih. We find that in comparison to water ice VII the filled ice Ih structure may be stable not only at the high pressures but also at the high temperatures expected at the core-water mantle transition boundary of water planets.

http://iopscience.iop.org/article/10.1088/0004-637X/769/1/29/pdf

Volatile transport inside super-earths by entrapment in the water-ice matrix

We consider super-Earth sized planets which have a water mass fraction that is large enough to form an external mantle composed of high pressure water ice polymorphs and that lack a substantial H/He atmosphere. We consider such planets in their habitable zone so that their outermost condensed mantle is a global deep liquid ocean. For these ocean planets we investigate potential internal reservoirs of CO2; the amount of CO2 dissolved in the ocean for the various saturation conditions encountered, and the ocean-atmosphere exchange flux of CO2. We find that in steady state the abundance of CO2 in the atmosphere has two possible states. When the wind-driven circulation is the dominant CO2 exchange mechanism, an atmosphere of tens of bars of CO2 results, where the exact value depends on the subtropical ocean surface temperature and the deep ocean temperature. When sea-ice formation, acting on these planets as a CO2 deposition mechanism, is the dominant exchange mechanism, an atmosphere of a few bars of CO2 is established. The exact value depends on the subpolar surface temperature. Our results suggest the possibility of a negative feedback mechanism, unique to water planets, where a reduction in the subpolar temperature drives more CO2 into the atmosphere to increase the greenhouse effect.

Amit Levi

Papers

Growth model interpretation of planet size distribution

Structure and dynamics of cold water super-earths: the case of occluded ch4 and its outgassing

The ice cap zone: a unique habitable zone for ocean worlds

Volatile transport inside super-earths by entrapment in the water-ice matrix

The Abundance of Atmospheric CO2 in Ocean Exoplanets: a Novel CO2 Deposition Mechanism