\[\Delta_rH(T_2) = \Delta_rH(T_1) + \int_{T_1}^{T_2}\Delta_rC_p\,dT,\qquad \left(\frac{\partial\Delta_rH}{\partial T}\right)_p = \Delta_rC_p\]
含义Meaning
反应焓随温度的变化由产物与反应物热容之差决定（1858）。由 298 K 数据可推算其他温度下的反应焓。
The temperature dependence of reaction enthalpy is set by the heat-capacity difference between products and reactants (1858), allowing 298 K data to be extrapolated.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\Delta_rC_p\) | 产物与反应物定压热容之差heat-capacity difference | J·mol⁻¹·K⁻¹ |
推导Derivation
沿两条路径：先在 T₁ 反应再把产物加热到 T₂，或先把反应物加热到 T₂ 再反应。
Compare two routes between the same states.
焓是状态函数，两路径相等，整理得积分式。
Equate them (Hess).
适用条件与局限Assumptions & limitations
温度区间内不能有相变（否则加入相变焓）；Cp 随温度变化时用多项式 \(a + bT + c/T^2\) 积分。
No phase changes in the interval; use polynomial Cp.
例题Worked example
N₂ + 3H₂ → 2NH₃：ΔCp ≈ −45 J/(mol·K)，ΔH(298) = −92.2 → ΔH(700) ≈ −92.2 − 0.045×402 = −110 kJ/mol（实测约 −106）。
Ammonia: ΔH ≈ −110 kJ/mol at 700 K by this estimate (tables ≈ −106).