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The historic, classical thermodynamic model of star interiors neglects luminosity (𝐿), and consequently predicts ultrahigh central solar temperatures (𝑇 ~ 15 × 106 K). Modern models yield similar 𝑇 profiles mostly because local thermal equilibrium and multiple free parameters are used. Instead, long-term stability of stars signifies disequilibrium where energy generated equals energy emitted. We assume that heat is generated in a shell defining the core and use Fourier’s model, which describes diffusion of heat, including via radiation, to predict the 𝑇 profile. Under steady-state, power 𝐿 transmitted through each shell is constant above the zone of energy generation. Hence, 𝐿 is independent of spherical radius (𝑠), so the Stefan-Boltzmann law dictates 𝑇(𝑠), and material properties are irrelevant. Temperature is constant in the core and proportional to 𝐿¼𝑠−½ above. A point source core sets the upper limit on 𝑇(𝑠), giving 𝑇average = (6/5)𝑇surface. Core size or convecting regions little affect our results. We also construct a parameter-free model for interior pressure (𝑃) and density (ρ) by inserting our 𝑇(𝑠) formula into an ideal gas law (𝑃/ρ 𝛼 𝑇) while using the equation for hydrostatic gravitational compression. We find 𝑃 𝛼 𝑠−3, ρ 𝛼 𝑠−5/2, and ρaverage = 6 × ρsurface. Another result, 𝐿 𝛼 mass3.3, agrees with accepted empirical rules for main sequence stars, and validates our model. The total solar mass already “burned” suggests that fusion occurs near 𝑠surf/400 where 𝑃 ~ 0.5 × 1012 Pa, in agreement with H-bomb pressure estimates. Implications are discussed. 

Available data on insulating, semiconducting, and metallic solids verify our new model that incorporates steady-state heat flow into a macroscopic, thermodynamic description of solids, with agreement being best for isotropic examples. Our model is based on: (1) mass and energy conservation; (2) Fourier’s law; (3) Stefan–Boltzmann’s law; and (4) rigidity, which is a large, yet heretofore neglected, energy reservoir with no counterpart in gases. To account for rigidity while neglecting dissipation, we consider the ideal, limiting case of a perfectly frictionless elastic solid (PFES) which does not generate heat from stress. Its equation-of-state is independent of the energetics, as in the historic model. We show that pressure-volume work (PdV) in a PFES arises from internal interatomic forces, which are linked to Young’s modulus (Ξ) and a constant (n) accounting for cation coordination. Steady-state conditions are adiabatic since heat content (Q) is constant. Because average temperature is also constant and the thermal gradient is fixed in space, conditions are simultaneously isothermal: Under these dual restrictions, thermal transport properties do not enter into our analysis. We find that adiabatic and isothermal bulk moduli (B) are equal. Moreover, Q/V depends on temperature only. Distinguishing deformation from volume changes elucidates how solids thermally expand. These findings lead to simple descriptions of the two specific heats in solids: ∂ln(cP)/∂P = −1/B; cP = nΞ times thermal expansivity divided by density; cP = cVnΞ/B. Implications of our validated formulae are briefly covered.