含义Meaning
恒温恒压下判断反应方向的状态函数（吉布斯，1876）：ΔG < 0 自发，= 0 平衡，> 0 非自发。它综合了焓（能量）与熵（混乱度）两方面的趋势，−ΔG 等于可做的最大非体积功。
The state function that decides direction at constant T and p (Gibbs, 1876): ΔG < 0 spontaneous, 0 at equilibrium, > 0 non-spontaneous. It combines enthalpy and entropy, and −ΔG is the maximum non-expansion work.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(G\) | 吉布斯自由能Gibbs energy | J |
| \(\Delta S\) | 体系熵变entropy change of the system | J·K⁻¹ |
推导Derivation
总熵变 \(\Delta S_\text{总} = \Delta S + \Delta S_\text{环}\)；恒温恒压下环境吸热 −ΔH，\(\Delta S_\text{环} = -\Delta H/T\)。
Total entropy change with ΔS_surr = −ΔH/T at constant T, p.
\(\Delta S_\text{总} = -(\Delta H - T\Delta S)/T = -\Delta G/T\)，所以总熵增等价于 ΔG < 0。
So ΔS_total = −ΔG/T: entropy increase ⇔ ΔG < 0.
四种情形：ΔH < 0、ΔS > 0 总自发；ΔH > 0、ΔS < 0 总不自发；其余两种取决于温度。
Four sign combinations; two are temperature-dependent.
适用条件与局限Assumptions & limitations
只判断热力学可能性，不说明速率（金刚石转化为石墨 ΔG < 0 但极慢）。
Says nothing about rate (diamond → graphite is spontaneous but imperceptibly slow).
ΔH、ΔS 随温度变化不大时才能用 298 K 数据估算其他温度。
Using 298 K ΔH, ΔS at other T is approximate.
例题Worked example
CaCO₃ → CaO + CO₂：ΔH° = +178 kJ/mol，ΔS° = +161 J/(mol·K)，T_转向 ≈ 1106 K（约 833 °C）以上自发。
CaCO₃ decomposition becomes spontaneous above ~1106 K.