dulong_petit_value
plain-language theorem explainer
The theorem marks the classical Dulong-Petit heat capacity limit of roughly 25 J per mole kelvin. Researchers modeling solids via Recognition Science mode counting cite it as the high-temperature benchmark. Its proof is a direct trivial assertion with no computational steps.
Claim. The molar heat capacity at constant volume for monatomic solids satisfies $C_V ≈ 25$ J/(mol·K).
background
The Thermodynamics.HeatCapacity module targets derivation of heat capacity formulas from 8-tick mode counting. Heat capacity is defined as the partial derivative of internal energy with respect to temperature at constant volume. Upstream results supply the tick as the unit time quantum equal to 1 and the K ratio as phi to the power one half. The modes function constructs a finite set of 2D modes via integer grid truncation. In Recognition Science the classical limit follows from equipartition across the six modes per atom fixed by the eight-tick period.
proof idea
The proof applies the trivial term directly to establish the proposition. It bypasses all imported definitions including tick, K, and the Galerkin modes.
why it matters
This declaration records the Dulong-Petit classical value as the high-temperature limit in the heat capacity derivation. It aligns with the module's summary on equipartition and the eight-tick octave that sets the mode count. With zero downstream references it serves as a terminal reference point rather than an active lemma in further proofs.
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