diatomicModesRoomTemp
plain-language theorem explainer
Diatomic gases activate five quadratic modes at room temperature, three translational plus two rotational. Researchers computing heat capacities from Recognition Science mode counting cite this integer to recover the classical C_V = (5/2)R result. The declaration is a direct constant assignment with no computation or lemmas.
Claim. A diatomic molecule possesses five active quadratic degrees of freedom at room temperature, yielding the classical heat capacity per mole $C_V = (5/2)R$.
background
The module derives heat capacities from 8-tick mode counting. Classical equipartition assigns $kT/2$ per quadratic mode, so $C_V = (f/2)R$ where $f$ is the number of active modes. In Recognition Science each 8-tick mode contributes to the energy storage; the eight-tick octave (period $2^3$) supplies the discrete counting grid. The supplied doc-comment states the physical breakdown: three translational modes plus two rotational modes for N2, O2, H2, with vibration frozen out at room temperature.
proof idea
One-line definition that directly assigns the integer 5.
why it matters
The value supplies the room-temperature mode count that enters the diatomic heat-capacity formulas downstream in the same module. It implements the T7 eight-tick octave landmark by fixing the active-mode tally before vibrational modes activate at higher temperature, consistent with the Recognition Composition Law and the classical-to-quantum transition built from 8-tick discreteness.
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