monatomic_cv_value
plain-language theorem explainer
Monatomic gases show a constant-volume heat capacity of roughly 12.5 J per mole per kelvin from three translational modes under eight-tick counting. A physicist matching classical limits in Recognition Science to noble-gas experiments would cite this result. The proof reduces directly to the trivial proposition True as a placeholder for the numerical claim.
Claim. For a monatomic ideal gas the constant-volume molar heat capacity satisfies $C_V = (3/2) R$ and therefore $C_V$ is approximately 12.5 J mol$^{-1}$ K$^{-1}$.
background
Recognition Science obtains heat capacities by counting active modes in the eight-tick framework. Classical equipartition assigns $kT/2$ to each quadratic mode, so $C_V = (f/2) R$ where $f$ is the number of modes. The module states that monatomic gases activate only the three translational modes, producing the classical value 1.5 R. The local setting is the derivation of heat-capacity formulas from 8-tick mode counting, with $C_V$ defined as the partial derivative of internal energy with respect to temperature at fixed volume. Upstream results supply the finite set of truncated modes, the dimensionless bridge ratio $K = phi^{1/2}$, and period definitions used for mode enumeration.
proof idea
The proof is a term-mode reduction that applies the trivial tactic to the proposition True, serving as a one-line placeholder for the numerical claim stated in the comment.
why it matters
This declaration supplies the monatomic base case for heat-capacity formulas derived from eight-tick mode counting (T7). It anchors the classical equipartition step before extensions to diatomic gases that add rotational modes and before quantum corrections from phi-ladder discreteness. No downstream theorems are recorded yet; the result closes the three-mode counting that aligns with D = 3 spatial dimensions in the forcing chain.
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