目 次

第 0章 熱力学の目的 1

第 1章 熱力学の諸概念 5

1.1 状態量 ·········································································································· 51.1.1 示量性，示強性 ···················································································· 8

1.2 エネルギー，熱，仕事 ··················································································· 101.2.1 内部エネルギー ·················································································· 101.2.2 熱 ···································································································· 101.2.3 仕事 ································································································· 121.2.4 状態量でない量 ·················································································· 13

1.3 熱平衡 ········································································································ 171.3.1 熱的相互作用 ····················································································· 171.3.2 熱力学第 0法則 ·················································································· 181.3.3 温度スケール ····················································································· 21

1.4 単位 ··········································································································· 22●Topics さまざまなエネルギー資源の比較 ···························································· 31

第 2章 簡単な物質の性質 33

2.1 理想気体の状態方程式 ··················································································· 332.2 熱運動 ········································································································ 34

2.2.1 エネルギー等分配則 ············································································ 342.3 理想気体の内部エネルギー ············································································· 37

2.3.1 内部エネルギー ·················································································· 372.3.2 状態方程式の微視的理論 ······································································ 392.3.3 物質の静的性質 ·················································································· 402.3.4 比熱 ································································································· 41

2.4 理想気体における種々の熱力学的過程 ······························································ 432.5 ファン・デル・ワールス気体（＊） ·································································· 452.6 物質の相（＊） ····························································································· 46

2.6.1 水の相転移 ························································································ 472.6.2 蒸気圧 ······························································································ 48

2.7 動的性質（＊） ····························································································· 51

viii 目 次

2.7.1 乱雑な運動とエネルギー緩和 ································································ 512.7.2 物質の動的性質 ·················································································· 54

●Topics 熱雑音 ································································································ 65●Topics 生物におけるゆらぎ ·············································································· 68

第 3章 熱力学第一法則 71

3.1 第一法則 ····································································································· 713.2 準静的過程 ·································································································· 75

3.2.1 状態量が定義できる条件 ······································································ 753.3 定常状態（＊） ····························································································· 79

3.3.1 パワーのつりあい ··············································································· 793.3.2 熱伝導 ······························································································ 80

3.4 エンタルピー ······························································································· 833.5 開放系（＊） ································································································ 86

3.5.1 開放系でのエンタルピーの役割 ····························································· 863.5.2 流れのある系 ····················································································· 893.5.3 絞り過程—ジュール・トムソン効果 ····················································· 913.5.4 工業的応用例 ····················································································· 95

●Topics 反応温度 ···························································································· 112

第 4章 熱力学第二法則 115

4.1 熱機関 ······································································································· 1154.1.1 熱機関の必要性 ················································································· 1154.1.2 熱機関の例 ······················································································· 1184.1.3 熱効率 ····························································································· 121

4.2 可逆過程，不可逆過程 ·················································································· 1224.2.1 熱力学的可逆性 ················································································· 1224.2.2 可逆性，不可逆性についてのさらなる議論 ············································· 127

4.3 第二法則 ···································································································· 1314.3.1 カルノー機関 ···················································································· 1314.3.2 第二法則の表し方 ·············································································· 1354.3.3 冷凍機関 ·························································································· 1424.3.4 実際の熱効率と内的可逆機関（＊） ······················································· 143

●Topics スピーカーで冷凍？ ············································································· 152

第 5章 エントロピー 155

5.1 エントロピー ······························································································ 1555.1.1 状態量としてのエントロピー ······························································· 155

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5.1.2 エントロピー増大則 ··········································································· 1575.1.3 エントロピーによる過程の記述 ···························································· 158

5.2 エントロピーの計算 ····················································································· 1635.2.1 可逆過程で結ぶ ················································································· 1635.2.2 エントロピーのつりあい（＊） ····························································· 170

5.3 理想気体の計算 ··························································································· 1755.3.1 同種分子からなる気体 ········································································ 1755.3.2 混合エントロピー ·············································································· 178

5.4 エントロピーの物理的意味 ············································································ 180●Topics ナノテクノロジー—ゆらぎを制する爪歯 ·················································· 190

第 6章 第二法則の発展（＊） 193

6.1 エントロピー増大則とエネルギー極値の法則 ···················································· 1936.1.1 U の最小化 ······················································································· 1956.1.2 F の最小化 ······················································································· 1976.1.3 Gの最小化 ······················································································· 198

6.2 化学ポテンシャル ························································································ 1996.2.1 2つの相の平衡 ·················································································· 1996.2.2 化学平衡 ·························································································· 2036.2.3 反応熱，親和力 ················································································· 2076.2.4 反応の濃度依存 ················································································· 2106.2.5 ファン・デル・ワールス気体のエントロピー ·········································· 213

6.3 平衡状態への回復 ························································································ 2136.3.1 エントロピー生成の最小化 ·································································· 2146.3.2 電流分布の問題 ················································································· 215

6.4 熱力学第三法則 ··························································································· 2166.4.1 ネルンストの定理 ·············································································· 2166.4.2 第三法則の証拠 ················································································· 2186.4.3 第三法則の破れ ················································································· 220

6.5 エントロピーの絶対値 ·················································································· 2226.5.1 エントロピーの測定 ··········································································· 2226.5.2 具体例 ····························································································· 223

●Topics CO2 問題 ··························································································· 235

第 7章 第二法則の工学的応用 237

7.1 最大仕事の原理 ··························································································· 2377.1.1 不可逆性の評価 ················································································· 242

7.2 熱機関の第二法則からの解析（＊） ································································· 247

x 目 次

7.2.1 ランキン機関はなぜカルノー機関にしないのか？ ···································· 2477.2.2 ランキン機関の詳細検討 ····································································· 248

7.3 化学反応における可逆過程 ············································································ 2507.3.1 燃料電池 ·························································································· 2517.3.2 電気化学反応によるΔGの測定 ··························································· 253

7.4 濃度差の利用（＊） ······················································································ 2567.4.1 混合過程 ·························································································· 2567.4.2 浸透による仕事 ················································································· 2567.4.3 分離・精練過程 ················································································· 259

●Topics デジタルコンピュータの限界 ································································· 269

第 8章 統計力学序論（＊） 273

8.1 孤立系の統計 ······························································································ 2738.1.1 微視的状態を数える ··········································································· 2738.1.2 統計力学の基本的仮定 ········································································ 275

8.2 熱浴と相互作用する系 ·················································································· 2778.2.1 ボルツマンの原理 ·············································································· 277

8.3 エントロピーの統計力学的解釈 ······································································ 2818.4 エネルギー等分配則 ····················································································· 2828.5 エネルギーのゆらぎ ····················································································· 2848.6 水素分子の回転運動 ····················································································· 284

参考文献 291

付録 A 物理定数表 293

付録 B 多変数関数解析 295

付録 C 数値テーブル 301

索 引 306

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