定义Definition
熵是描述体系中能量与粒子分散程度的状态函数，符号 S，单位 J K⁻¹ mol⁻¹（摩尔熵）。从统计角度，S = k ln W，W 为体系可能的微观状态数；微观状态越多，熵越大。
Entropy, S, is a state function measuring how dispersed the energy and particles of a system are, in J K⁻¹ mol⁻¹ for molar entropy. Statistically S = k ln W, where W is the number of possible microstates; the more microstates, the higher the entropy.
比较熵的大小Comparing entropies
同一物质：气态 > 液态 > 固态，如 H₂O(g) 188.8、H₂O(l) 69.9 J K⁻¹ mol⁻¹。温度升高熵增大。粒子越多、结构越复杂，熵越大。反应生成更多气体分子时熵增加，如 CaCO₃(s) → CaO(s) + CO₂(g) 的 ΔS 为正。完美晶体在 0 K 时熵为零（热力学第三定律）。
For one substance, gas > liquid > solid: H₂O(g) 188.8 and H₂O(l) 69.9 J K⁻¹ mol⁻¹. Entropy rises with temperature, and with more particles and more complex structures. Reactions that produce more gas molecules increase entropy, so ΔS for CaCO₃(s) → CaO(s) + CO₂(g) is positive. A perfect crystal at 0 K has zero entropy (the third law).
与自发性的关系Link to feasibility
热力学第二定律：孤立体系的总熵永不减少。判断恒温恒压下反应能否自发，要同时考虑焓变和熵变：ΔG = ΔH − TΔS，ΔG < 0 时反应可自发进行。例如 ΔH > 0、ΔS > 0 的反应在高温下才能自发。
The second law states that the total entropy of an isolated system never decreases. At constant temperature and pressure, feasibility depends on both enthalpy and entropy: ΔG = ΔH − TΔS, and a reaction is feasible when ΔG < 0. A reaction with ΔH > 0 and ΔS > 0, for example, becomes feasible only at high temperature.
计算Calculation
ΔS°(反应) = Σ S°(生成物) − Σ S°(反应物)，注意乘以化学计量数，单位 J K⁻¹ mol⁻¹；代入 ΔG = ΔH − TΔS 时要换算成 kJ。
ΔS°(reaction) = Σ S°(products) − Σ S°(reactants), multiplied by the coefficients, in J K⁻¹ mol⁻¹; convert to kJ before using ΔG = ΔH − TΔS.
年表Timeline
- 1865
克劳修斯提出“熵”的概念并命名
Clausius introduces and names entropy
- 1877
玻尔兹曼给出熵的统计解释 S = k ln W
Boltzmann gives the statistical interpretation S = k ln W
- 1906
能斯特提出热定理，后发展为热力学第三定律
Nernst states his heat theorem, later the third law of thermodynamics
相关公式Formulas
例题Worked example
1 mol 水从 0 °C 加热到 100 °C：ΔS = 75.3×ln(373/273) = 23.5 J/K。
Heating 1 mol of water 0 → 100 °C: ΔS = 23.5 J/K.
例题Worked example
水汽化：ΔS = 40.7×10³/373 = 109 J/(mol·K)；冰融化：6.01×10³/273 = 22.0 J/(mol·K)。
Water: ΔvapS = 109, ΔfusS = 22.0 J mol⁻¹ K⁻¹.