The energy meaning of Boltzmann’s constant

The atomic scale is the only relevant thermodynamic scale in our universe, since quantum properties restrict classical considerations of subatomic physics and disappear for larger scales. Then the characteristic energy that dictates the value of the unit of temperature can be the classical thermal energy defined for simplest atoms. It is shown that vibrational frequency of a classical model hydrogen atom, of the radius of its Rydberg wavelength, is in far-infrared range and from its quantum of energy one can obtain the value of Boltzmann’s constant that serves as the measure of the absolute temperature in kelvins.

Hydrochemical and operational parameters driving carbonate scale kinetics at geothermal facilities in the Bavarian Molasse Basin

The majority of scales observed at geothermal facilities exploring the Malm Aquifer in the Bavarian Molasse Basin are carbonates. They form due to a disruption of the lime–carbonic acid equilibrium during production caused by a reduction of the partial pressure of carbon dioxide due to pressure change and degassing. These scales are found at the pumps, production pipes, filters, heat exchangers, and occasionally in the injection pipes. In this study, scales of all sections of geothermal facilities were taken. The database consists of scale samples from 13 geothermal pumps, 6,000 m production pipe (sample interval 10 - 12 m), 11 heat exchanger revisions, 2 injection pipes, and numerous filter elements. The samples were analyzed by SEM-EDX, XRD, Raman spectroscopy, and acid digestion to assess their chemical and mineralogical composition. From direct gauge measurements at six facilities during pump changes, scale rates were determined along the production pipes. From indirect measurements (multifinger caliper measurements) scale rates are derived for the region below the pump. Hydrochemical analyses from the wellhead were taken from 13 sites to feed the hydrogeochemical models. The calcite scale rates in the production pipes increase from the pump to the wellhead, where they reach 1.5 - 4.1 $$\mu$$ μ mol/($$\hbox {m}^2\,\cdot$$ m 2 · s). Scale rates below the pump reach up to 1.5 $$\mu$$ μ mol/($$\hbox {m}^2\,\cdot$$ m 2 · s). Given the slight change of hydrochemistry on the rise through the production pipe, where < 4 % of dissolved calcium ions precipitate as scale, scale rates cannot be derived from water samples at the wellhead, but require direct gauge measurements. The small amount of precipitation, together with fully turbulent conditions suggests that all measured rates are controlled by the surface-reaction of calcite crystallization following the nomenclature of Appelo and Postma (2004). Two approaches are used for the modeling of the scale rates. The first approach is based on hydrogeochemical modeling with PHREEQC. Scale rates calculated by this method are one order of magnitude higher than the measured ones. The second approach is based on correlations between the measured scale rates at the wellhead at six facilities and identified thermodynamic scale drivers ($$\Delta$$ Δ log (p$$\hbox {CO}_2$$ CO 2 ), $$\Delta$$ Δ total pressure, $$\Delta$$ Δ pH, and $$\hbox {SI}_{{calcite}}$$ SI calcite ). The correlations allow linear regressions which are used for the prediction of the scale rate at the wellhead, along the whole production pipe, and below. The modeling results show that scale prediction based on the new regressions that rely on thermodynamic scale drivers works better than existing hydrogeochemical models, already without implementation of kinetic parameters ($$\hbox {CO}_2$$ CO 2 -stripping and magnesium inhibition).

Internal pressure and state assessment of the inherent macroscopic force fields of liquids

A theoretical approach is proposed for describing the nature of the internal pressure of liquids (Pi), which allows us to overcome the uncertainty of its definition and propose a new thermodynamic scale for liquids.

The thermodynamic scale of inorganic crystalline metastability

The space of metastable materials offers promising new design opportunities for next-generation technological materials, such as complex oxides, semiconductors, pharmaceuticals, steels, and beyond. Although metastable phases are ubiquitous in both nature and technology, only a heuristic understanding of their underlying thermodynamics exists. We report a large-scale data-mining study of the Materials Project, a high-throughput database of density functional theory–calculated energetics of Inorganic Crystal Structure Database structures, to explicitly quantify the thermodynamic scale of metastability for 29,902 observed inorganic crystalline phases. We reveal the influence of chemistry and composition on the accessible thermodynamic range of crystalline metastability for polymorphic and phase-separating compounds, yielding new physical insights that can guide the design of novel metastable materials. We further assert that not all low-energy metastable compounds can necessarily be synthesized, and propose a principle of ‘remnant metastability’—that observable metastable crystalline phases are generally remnants of thermodynamic conditions where they were once the lowest free-energy phase.