含义Meaning
能斯特热定理（1906）与普朗克表述：完美晶体在绝对零度熵为零。由此可通过量热测定物质的“绝对”（规定）熵，列成标准摩尔熵表。
The Nernst heat theorem (1906) and Planck’s statement: a perfect crystal has zero entropy at 0 K. Calorimetry then gives absolute (third-law) entropies tabulated as standard molar entropies.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(S_m^\circ\) | 标准摩尔熵standard molar entropy | J·mol⁻¹·K⁻¹ |
推导Derivation
完美晶体在 0 K 只有一个微观状态（W = 1），由 S = k ln W 得 S = 0。
A perfect crystal at 0 K has W = 1.
从 0 K 起逐段积分 Cp/T 并加上各相变熵；最低温区用德拜 T³ 律外推。
Integrate Cp/T from 0 K, adding transition entropies; extrapolate with T³ at the lowest temperatures.
推论：绝对零度不可能通过有限步骤达到。
Corollary: absolute zero is unattainable in finitely many steps.
适用条件与局限Assumptions & limitations
取向无序的晶体（CO、N₂O、冰）在 0 K 仍有残余熵。
Orientationally disordered crystals (CO, N₂O, ice) keep residual entropy.
例题Worked example
298 K 标准摩尔熵：金刚石 2.4，石墨 5.7，H₂O(l) 70.0，H₂O(g) 188.8 J/(mol·K)。
S°(298 K): diamond 2.4, graphite 5.7, liquid water 70.0, steam 188.8 J mol⁻¹ K⁻¹.