forked from bai/curriculum-project-hub
hongjr03
9927d38c18
ADR-0029 — nested outline manifest, supersedes ADR-0008's flat [[parts]]:
- cph-model: recursive loader over manifest.toml containers / element.toml
leaves; Lesson.parts (pure elements, DFS order) + Lesson.outline (elements
interleaved with section headings at their DFS-open position); rejects
ambiguous/incomplete folders and root-vs-container table misplacement
- cph-diag: new DiagCode::ManifestMalformed for carrier-document structure
errors (discharges an existing TODO)
- cph-typst: augmented manifest now serializes the outline (element/section
entries) instead of a flat parts array
- render/lib.typ: render-lesson renders section headings at their depth
- examples/TH-141 migrated to 5 nested section containers + 3 root segments,
byte-identical element order; smoke-verified via cph check/build + pdftotext
ADR-0030 — batch & combined export, extends ADR-0009/0011:
- cph build with no --target batches every declared target (repeatable
--target for an explicit subset); any target failure => non-zero exit,
per-target ledger, independent per-target execution
- cph-model: bundle.toml loader (directory + [info]/[targets.*]/ordered
lessons with per-lesson target overrides)
- cph-typst: augmented bundle manifest (path-prefixed member outlines),
Engine::{compile_check_bundle,build_bundle_pdf}
- render/lib.typ: render-bundle assembles member lessons under per-lesson
headings, depth-shifts their own section headings, resets example/lemma
counters at each lesson boundary by default
- cph-cli: `cph bundle <path> --target <name>` subcommand, same batching
contract as `cph build`
- new bundle fixtures/tests (cph-model unit + cph-typst through-template PDF
compile), smoke-verified via a real 2-lesson merged PDF
Verification: cargo fmt/clippy/test clean across the workspace (68 tests);
real cph check/build/bundle runs against TH-141 and a bundle fixture, PDF
content inspected via pdftotext.
28 lines
1.2 KiB
Typst
28 lines
1.2 KiB
Typst
参考态满足 $p = beta T$。混合过程总体积不变，仍属等容过程，故混合后亦满足 $p = beta T$。即整个过程始终有 $p = beta T$。
|
||
|
||
代入 $sigma(T, p)$，令 $tau equiv T \/ "K"$，得 $sigma$ 退化为 $tau$ 的单变量函数
|
||
|
||
$ sigma(tau) \/ (10^(-3) "N/m") = 60 + 0.065 tau - 24.0 thin (beta tau) + 3.15 thin (beta tau)^2 . $
|
||
|
||
代入 $beta = 7.28 times 10^(-3)$，注意 $24.0 times 7.28 times 10^(-3) = 0.1747$、$3.15 times (7.28 times 10^(-3))^2 = 1.670 times 10^(-4)$：
|
||
|
||
$ sigma(tau) \/ (10^(-3) "N/m") = 60 - 0.1097 tau + 1.670 times 10^(-4) tau^2 . $
|
||
|
||
对 $tau$ 求导取零：
|
||
|
||
$ tau_("mix") = 0.1097 / (2 times 1.670 times 10^(-4)) approx 328.4 , $
|
||
|
||
即 $T_("mix") approx 328.4 thin "K" approx 55.3 thin "℃"$。
|
||
|
||
混合的热平衡。设参考态石油温度 $T_0 = 373.15 thin "K"$、密度 $rho_0 = 0.8 rho_w$、比热容 $c_0 = 0.6 c_w$；注入水温度 $T_w$、密度 $rho_w$、比热容 $c_w$。等体积混合且绝热给出
|
||
|
||
$ rho_0 c_0 (T_0 - T_("mix")) = rho_w c_w (T_("mix") - T_w) , $
|
||
|
||
代入 $rho_0 c_0 = 0.48 thin rho_w c_w$，
|
||
|
||
$ 0.48 (T_0 - T_("mix")) = T_("mix") - T_w , $
|
||
|
||
解出
|
||
|
||
$ T_w = T_("mix") - 0.48 (T_0 - T_("mix")) approx 306.9 thin "K" approx 33.7 thin "℃" . $
|