Two centuries after Carnot defined thermodynamics as a scientific discipline based on work by engineers like James Watt, can we learn more from Carnot’s perceptive analysis of maximum power from heat engines? Using action mechanics, the rate of work in Carnot’s heat engine cycle can be integrated as external pressure-volume work, sustained by internal quantum field work, equal to changes in Gibbs free energy that was called caloric by Carnot. His treatise of 1824 even gave equations that express the work potential as a function of temperature and the logarithm of the change in volume. To answer this question, we apply Carnot’s principle defined by Clausius as entropy, to atmospheric heat-work cycles, such as in anticyclones. We show using Lagrange’s virial theorem how Carnot’s thermodynamic states as Gibbs potential become entangled with gravitational potential states. The effective capacitance of greenhouse gases for energy in the troposphere enable recycling of heat emitted from the Earth’s hot surface, thermally setting tropospheric air masses in action. By delaying irreversible emission of long wavelength quanta to space, this recycling process extends the residence time of solar energy in the troposphere as work, maximising troposphere entropy to the tropopause. The virial theorems of Lagrange and Clausius, governed on the principle of least action, provide a more accurate lapse rate in temperature with temperature in the atmosphere, replacing the paradigm of adiabatic expansion. Reversible 4-stage Carnot cycles, based on Lagrangian least variation in action, raise surface temperature and pressure from turbulent heat release, sustaining the weight of the atmosphere. New lessons for understanding climate dynamics are emerging from this virial-action analysis.

A testable hypothesis with quantitative predictions is put forward, proposing that strong acids produced on land at a rate correlated with global population are an increas-ing cause of increasing atmospheric CO2 pressure (pCO2). This hypothesis widens the imbalance assumed between the global uptake of CO2 by photosynthesis and emissions of CO2 from all sources, including the combustion of fossil fuels, causing greater atmos-pheric pCO2. Our modelling tests for reactions of dissolved inorganic carbon show that increasing atmospheric CO2 is caused thermodynamically by falling land surface pH values, but only with bicarbonate present. Strong acids generated by oxygen from re-duced inorganic compounds of nitrogen and sulphur emit CO2 almost stoichiometrically from dissolved bicarbonate in the pH range of most global soils, between 6 to above 8. We show that each decrease of aqueous pH value of 0.01 units from acidification of sur-face water near pH 8 potentially increases the pCO2 in the atmosphere by about 7 ppmv. The surface pH value of the ocean near 8.10 in 2000 has been shown to decrease at this rate, a result of equilibrating with the rising atmospheric pCO2. Therefore, our qualita-tive estimates of increasing atmospheric CO2 driven by irreversible acidification on land are critical and need broad scale validation. Unfortunately, these acidifying processes on land from excessive nitrogen fertiliser, export of alkaline produce from farmlands and other processes were not considered by previous biogeochemical reviews. However, several very recent research studies showing CO2 emissions from soil during nitrifica-tion are consistent with our hypothesis. Despite counter measures to curb excessive CO2 emissions, including carbon capture and geological storage, the increasing Keeling curve for pCO2 may continue to rise because zero carbon policies do not address these causes. We recommend that this hypothesis be further tested by in situ experiments in neutral soils and water, designed to compare CO2 emissions under the acidifying conditions de-scribed in this article. Corrective counter measures can then be designed and applied.

Atmospheric climate science lacks the capacity to integrate thermodynamics with the gravitational potential of air in a classical quantum theory. To what extent can we identify Carnot’s ideal heat engine cycle in reversible isothermal and isentropic phases between dual temperatures partitioning heat flow with coupled work processes in the atmosphere? Using statistical action mechanics to describe Carnot’s cycle, the maximum rate of work possible can be integrated for the working gases as equal to variations in the absolute Gibbs energy, estimated as sustaining field quanta consistent with Carnot’s definition of heat as caloric. His treatise of 1824 even gave equations expressing work potential as a function of differences in temperature and the logarithm of the change in density and volume. Second, Carnot’s mechanical principle of cooling caused by gas dilation or warming by compression can be applied to tropospheric heat–work cycles in anticyclones and cyclones. Third, the virial theorem of Lagrange and Clausius based on least action predicts a more accurate temperature gradient with altitude near 6.5–6.9 °C per km, requiring that the Gibbs rotational quantum energies of gas molecules exchange reversibly with gravitational potential. This predicts a diminished role for the radiative transfer of energy from the atmosphere to the surface, in contrast to the Trenberth global radiative budget of ≈330 watts per square metre as downwelling radiation. The spectral absorptivity of greenhouse gas for surface radiation into the troposphere enables thermal recycling, sustaining air masses in Lagrangian action. This obviates the current paradigm of cooling with altitude by adiabatic expansion. The virial-action theorem must also control non-reversible heat–work Carnot cycles, with turbulent friction raising the surface temperature. Dissipative surface warming raises the surface pressure by heating, sustaining the weight of the atmosphere to varying altitudes according to latitude and seasonal angles of insolation. New predictions for experimental testing are now emerging from this virial-action hypothesis for climate, linking vortical energy potential with convective and turbulent exchanges of work and heat, proposed as the efficient cause setting the thermal temperature of surface materials.