\[\frac{V_1}{T_1} = \frac{V_2}{T_2}\ (p\ \text{一定}), \qquad \frac{p_1}{T_1} = \frac{p_2}{T_2}\ (V\ \text{一定})\]\[\frac{V_1}{T_1} = \frac{V_2}{T_2}\ (p\ \text{const.}), \qquad \frac{p_1}{T_1} = \frac{p_2}{T_2}\ (V\ \text{const.})\]
含义Meaning
压强一定时体积与热力学温度成正比；体积一定时压强与热力学温度成正比。
At constant pressure volume is proportional to absolute temperature; at constant volume pressure is.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(T\) | 热力学温度（必须用 K）absolute temperature (must be K) | K |
| \(V\) | 体积volume | m³ |
| \(p\) | 压强pressure | Pa |
推导Derivation
查理（1787）和盖-吕萨克（1802）发现：每升温 1 °C，气体体积增加其 0 °C 体积的约 1/273。
Charles (1787) and Gay-Lussac (1802): each 1 °C rise expands a gas by about 1/273 of its 0 °C volume.
\[V = V_0\left(1 + \frac{t}{273.15}\right) = V_0\,\frac{273.15 + t}{273.15}\]令 \(T = t + 273.15\)，即 \(V \propto T\)。外推到 \(V = 0\) 得到绝对零度 −273.15 °C，这是开尔文温标的由来之一。
With \(T = t + 273.15\), \(V \propto T\). Extrapolating to \(V = 0\) gives absolute zero, −273.15 °C — one origin of the Kelvin scale.
同理可由 \(pV = nRT\) 直接得到两种形式。
Both forms also follow directly from \(pV = nRT\).
适用条件与局限Assumptions & limitations
温度必须用开尔文；用摄氏度会得到错误结果。
Temperatures must be in kelvin.
低温下真实气体在到达 0 K 前已液化，直线外推只是理想化。
Real gases liquefy long before 0 K; the extrapolation is idealised.