\[\frac{dp}{dT} = \frac{\Delta_\text{trs}H}{T\,\Delta_\text{trs}V}\]
含义Meaning
任意两相平衡线（相图上的相界线）的斜率（1834）。冰的熔化 ΔV < 0，所以加压使冰的熔点降低——水是少数固液线斜率为负的物质。
The slope of any two-phase coexistence line (1834). Ice melts with ΔV < 0, so pressure lowers its melting point — water is one of few substances with a negative solid–liquid slope.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\Delta_\text{trs}V\) | 相变体积变化volume change on transition | m³·mol⁻¹ |
推导Derivation
两相共存时 \(\mu_\alpha(T,p) = \mu_\beta(T,p)\)；沿相界线移动 \(d\mu_\alpha = d\mu_\beta\)。
Along the coexistence line dμ_α = dμ_β.
\(-S_\alpha dT + V_\alpha dp = -S_\beta dT + V_\beta dp\)，得 \(dp/dT = \Delta S/\Delta V\)。
Hence dp/dT = ΔS/ΔV.
代入 \(\Delta S = \Delta H/T\)。
Substitute ΔS = ΔH/T.
适用条件与局限Assumptions & limitations
严格成立（无近似）；积分时需知 ΔH、ΔV 随温度、压强的变化。
Exact; integration needs ΔH and ΔV.
例题Worked example
冰：ΔfusH = 6.01 kJ/mol，ΔV = −1.63 cm³/mol：dp/dT = 6010/(273×(−1.63×10⁻⁶)) = −1.35×10⁷ Pa/K，即加压约 135 bar 熔点降低 1 K。
Ice: dp/dT ≈ −135 bar/K.