\[\Delta_rH = \Delta_rU + \Delta n_gRT,\qquad C_{p,m} - C_{V,m} = R\ (\text{理想气体})\]\[\Delta_rH = \Delta_rU + \Delta n_gRT,\qquad C_{p,m} - C_{V,m} = R\ (\text{ideal gas})\]
含义Meaning
反应中气体物质的量改变时，恒压与恒容反应热相差 ΔnRT（体积功）。凝聚相反应两者几乎相等。
When the amount of gas changes, constant-pressure and constant-volume heats differ by ΔnRT (expansion work); for condensed phases they are nearly equal.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\Delta n_g\) | 气体物质的量变化change in moles of gas | mol |
推导Derivation
\(\Delta H = \Delta U + \Delta(pV)\)；凝聚相 \(\Delta(pV)\) 可忽略，气体 \(\Delta(pV) = \Delta n_gRT\)。
ΔH = ΔU + Δ(pV) with Δ(pV) = Δn_gRT for ideal gases.
热容：\(H = U + nRT\)，对 T 求导得 \(C_p = C_V + nR\)。
Differentiating H = U + nRT gives Cp − Cv = nR.
适用条件与局限Assumptions & limitations
理想气体近似。
Ideal-gas approximation.
例题Worked example
C₆H₁₂O₆(s) + 6O₂ → 6CO₂ + 6H₂O(l)：Δn_g = 0，ΔH = ΔU。CH₄ + 2O₂ → CO₂ + 2H₂O(l)：Δn_g = −2，ΔH = ΔU − 4.96 kJ/mol（298 K）。
Glucose combustion: Δn_g = 0, ΔH = ΔU. Methane: ΔH = ΔU − 4.96 kJ/mol.