forked from bai/curriculum-project-hub
feat(examples): migrate TH-141 sample to declarative layout (WU-6)
Real-content fixture for the end-to-end pipeline. TH-141 (39 parts: 22 segment, 15 lemma, 2 example) migrated from the prototype's typst `#let parts` manifest to ADR-0008: declarative manifest.toml (project+info+ordered parts+targets) + per-element element.toml (kind + scalars; examples carry `source`). Content .typ files copied byte-identical (no math corruption); per-element main.typ + meta.toml dropped (wiring is now generated). Part order matches source exactly; 5 lemmas have no proof.typ (optional); no cross-file imports / paralearn refs / figs. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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kind = "example"
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source = "41 届物理竞赛复赛第三大题(2)"
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假设液体表面张力的存在可以全部归结为表面层内与液体内部每个粒子邻近粒子数目的不同,且表面层内粒子间距与液体内部相同。设表面层每个粒子邻近粒子数是液体内部的 $zeta$ 倍($0 < zeta < 1$)。已知液体摩尔质量 $mu$、摩尔汽化热 $L_m$、质量密度 $rho$、阿伏伽德罗常量 $N_A$,导出液气界面张力系数 $sigma$ 的表达式。
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完整推导见 @缺键一般式。要点为:设体相分子最近邻数 $Z$、单键能 $epsilon$,由共享键计数得 $epsilon = 2 L_m \/ (N_A Z)$;表面分子缺 $(1 - zeta) Z$ 根键,按半键计赔账得亏损能 $Delta U = (1 - zeta) L_m \/ N_A$;分子占体积 $d^3 = mu \/ (rho N_A)$ 给出面密度 $n_s = (rho N_A \/ mu)^(2\/3)$。代入 @骨架公式
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$ sigma = Delta U dot n_s = (1 - zeta) thin L_m thin rho^(2\/3) / (mu^(2\/3) thin N_A^(1\/3)) . $
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