diatomicModesHighTemp
plain-language theorem explainer
The high-temperature quadratic mode count for diatomic molecules is set to seven under Recognition Science mode counting. Researchers computing classical heat capacities for diatomic gases cite this when applying equipartition to translational, rotational, and vibrational contributions. The declaration is a direct constant assignment that aligns with the eight-tick octave structure.
Claim. In the high-temperature limit a diatomic molecule has seven quadratic modes: three translational, two rotational, and two vibrational, so that $C_V = (7/2) R$.
background
The module derives heat capacity formulas from 8-tick mode counting. Classical equipartition assigns $kT/2$ to each quadratic mode, and mode counting determines the total energy $U$ and thus $C_V = (∂U/∂T)_V$ and $C_P = (∂H/∂T)_P$ in RS-native units. The eight-tick octave (T7) supplies the discrete mode structure underlying the count.
proof idea
This is a direct definition that assigns the constant 7, matching the classical sum of three translational, two rotational, and two vibrational quadratic terms once temperature excites all modes.
why it matters
The value supplies the mode count required for the high-temperature diatomic heat-capacity formula derived from 8-tick counting. It closes the classical limit step in the thermodynamics module and is consistent with the eight-tick octave (T7) and the overall forcing chain from T0 to T8.
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