We propose that, at equilibrium, statistically equal temperatures as mechanical torques are exerted on each kind of gas phase molecules as rates of translational action [@t=ʃmvds/dt=ʃmr2ωdϕ/dt=mv2, J]. These torques result from the impulsive density of resonant quantum fields with molecules, configuring the trajectories of gas molecules while balancing molecular pressure (p=NkT) against the density of field energy (J/m3). Gibbs energy fields contain no resonant quanta at zero Kelvin, with this measure of chemical potential diminishing in magnitude as translational action of the vapor molecules and quantum field energy increases with temperature. In illustration, we show how impulsive torques from quantum fields drive the reversible thermodynamics of Carnot’s heat-work engine cycle, sustain the decreasing atmospheric temperature gradient of increasing molecular entropy with altitude, support the translational action and field energy of vortical wind flow in anticyclones, frictionally warming the Earth’s surface while recycling greenhouse infrared absorption of surface radiation, generating electrical power from air flow in wind farms and destructive power in tropical cyclones. These cases all distinguish symmetrically between a causal field of impulsive quanta (Σhν) that energizes the action of matter and the resultant vis viva of molecular mechanics (mv2). The quanta of these different fields display mean wavelengths from 10-4 m to 1012 m, with mechanical advantages many orders of magnitude greater than the corresponding translational actions, though with mean quantum frequencies (v) similar to those of radial Brownian movement for independent particles (ω). These energy fields are also thermodynamically reversible reservoirs for heat, optimizing work processes on Earth and delaying the achievement of maximum entropy production from short wave solar radiation in conversion to outgoing long wave radiation to space.

Clausius’ virial theorem set a basis for relating kinetic energy in a body of independent material particles to its potential energy, pointing to their complementary role with respect to the second law of maximum entropy. In action mechanics, expressing the entropy of ideal gases as a capacity factor for sensible heat or enthalpy plus the configurational work to sustain the relative translational, rotational and vibrational action yields algorithms for estimating chemical reaction rates and positions of equilibrium. All properties of state including entropy, work potential as Helmholtz and Gibbs energies and activated transition state reaction rates can be estimated, using easily accessible molecular properties, such as atomic weights, bond lengths, moments of inertia and vibrational frequencies. Understanding how Clausius’ virial theorem balances the internal kinetic energy with field potential energy justifies partitioning between thermal and statistical properties of entropy, yielding a more complete view of the evolutionary nature of the second law of thermodynamics. The ease of performing these operations is illustrated by three important chemical gas phase reactions, the reversible dissociation of the hydrogen molecules, lysis of water to hydrogen and oxygen and the reversible formation of ammonia from nitrogen and hydrogen. Employing the ergal also introduced by Clausius to define the reversible internal work to overcome molecular interactions plus the configurational internal work of negative Gibbs energy as a function of volume or pressure may provide a practical guide for managing risk in industrial processes and climate change at the global scale.

Seasonal oscillations in the partial pressure of carbon dioxide (pCO2) in the Earth’s atmosphere stronger in northern latitudes are assumed to show that terrestrial photosynthesis exceeds respiration in summer reducing the pCO2, but increasing in winter when respiration exceeds photosynthesis. We disagree, proposing that variations in the temperature of the surface mixing zone of seawater also regulate the atmospheric pCO2, thermodynamically. We show that carbonate (CO32-) concentrations will therefore increase in summer with CaCO3 (calcite or aragonite) becoming less soluble, so calcium and carbonate ions are predicted to aggregate more while CO2 concentration falls in warmer seawater, thermodynamically favoring lower atmospheric pCO2. In winter, these physical processes are reversed, redissolving suspended calcite thus increasing carbonate alkalinity; carbonate concentration lessens as bicarbonate and soluble CO2 increase, raising the pCO2 in air. Our numerical computation shows that thermal fluctuations in equilibria favor absorption from air of more than one mole of CO2 per square meter in summer, coinciding with calcite formation maximizing in warmer water, potentially augmenting limestone reefs if there is a trend for increasing temperature . Another assumption we challenge is that upwelling from deeper water is the sole cause of increases in dissolved inorganic carbon (DIC) and alkalinity in surface waters, particularly in the southern hemisphere. Instead, calcite dissolution is favored as water temperature falls near the surface. It is well established that the seasonal summer decline in atmospheric CO2 coincides in fertile seawater with higher rates of biotic calcification and acidity, allowing increased CO2 capture by photosynthesis. However, its reversal in winter is proposed to be also a result of the cyclic dissolution of calcite as temperature falls, facilitated by biogenic respiration now exceeding photosynthesis; this can mutually provide the CO2 needed to convert carbonate ion alkalinity from calcite dissolution with bicarbonate increasing. Physical reasons why this oscillation is more obvious in the northern hemisphere include greater seasonal variations in water temperature (ca. 7.1 oC) being almost twice that in the cooler southern hemisphere (ca. 4.7 oC) and the greater depth of the surface mixing zone of seawater in the southern oceans. Evidence from 13CO2 fluxes between surface seawater and air is also assessed to test this hypothesis but questions remain regarding the regional rates of inorganic precipitation and dissolution of CaCO3 in the mixing zone. In summary, rapid biogenic calcification is favored by summer photosynthesis, but slower abiogenic calcification is more likely in warmer water.