Pure Geometric Reformulation

ABSTRACTThis paper introduces a purely geometric reformulation of classical gas thermodynamics (the Mendeleev-Clapeyron Ideal Gas Law and barometric scale height relations) by eliminating mass, moles, and nucleon counts as primary variables. Within an elastic vacuum lattice framework characterized by a universal tension force (F_lattice = 1.210256 * 10^44 N) and structural stiffness (6.732955 * 10^26 kg/m), any physical body or gas envelope is represented solely by its geometric deformation radius (Schwarzschild indentation, Rs). We demonstrate that surface atmospheric pressure is governed by the elastic compression of the atmospheric indentation (Rs_atm) against the planetary indentation (Rs_planet) across the spherical surface area, while surface temperature and atmospheric layer thickness (scale height, H) are determined by the interaction of planetary and single-molecule indentations (Rs_mol) with stellar lattice wave decay. Step-by-step arithmetic verifications for Earth (H = 8.31 - 8.50 km, P = 99,153 Pa, T = 292.96 K), Mars (P = 645.55 Pa, T = 217.27 K), Venus (P = 9.25 MPa, T = 742.41 K), and Saturn's moon Titan (P = 146,318 Pa, T = 90.57 K, sound speed = 194.73 m/s) match observational data with 94% to 99.9% accuracy. Finally, we provide a standalone geometric prediction for the nitrogen-dominated atmosphere of exoplanet TRAPPIST-1e.