含义Meaning
单原子理想气体的绝对熵（平动熵）。它与量热法加第三定律得到的熵吻合，是统计热力学的重要验证（1912）。
Absolute (translational) entropy of a monatomic ideal gas; agreement with calorimetric third-law entropies was a key test of statistical thermodynamics (1912).
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(S_m\) | 摩尔熵molar entropy | J·mol⁻¹·K⁻¹ |
| \(\Lambda\) | 热波长thermal wavelength | m |
推导Derivation
\(Q = q^N/N!\)，\(q = V/\Lambda^3\)；\(U = \tfrac32Nk_\mathrm{B}T\)。
Use \(Q = q^N/N!\), \(q = V/\Lambda^3\), \(U = \tfrac32Nk_\mathrm{B}T\).
\(S = U/T + k\ln Q = \tfrac32Nk + Nk\ln q - k(N\ln N - N)\)。
\(S = \tfrac32Nk + Nk\ln q - k(N\ln N - N)\).
整理得 \(S = Nk[\ln(V/N\Lambda^3) + 5/2]\)；N! 项（不可区分性）对得到广延的熵不可缺少（解决吉布斯佯谬）。
Rearranging gives the result; the N! is essential for extensivity (Gibbs paradox).
适用条件与局限Assumptions & limitations
只含平动；多原子分子另加转动、振动、电子熵。高温低压下准确；T → 0 时发散（经典近似失效）。
Translation only; add rotational, vibrational, electronic terms for molecules. Diverges as T → 0.
例题Worked example
Ar 在 298 K、1 bar：Λ = 16.0 pm，S_m = 154.8 J/(mol·K)（量热值 154.8）。
Ar at 298 K, 1 bar: S_m = 154.8 J mol⁻¹ K⁻¹, matching calorimetry.