\[p_1V_1 = p_2V_2 \quad (T, n\ \text{一定})\]\[p_1V_1 = p_2V_2 \quad (T, n\ \text{const.})\]
含义Meaning
温度和气体的量一定时，压强与体积成反比。
At fixed temperature and amount, pressure is inversely proportional to volume.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(p\) | 压强pressure | Pa |
| \(V\) | 体积volume | m³ |
推导Derivation
玻意耳（1662）用 J 形管封闭空气、加注水银改变压强，发现 \(pV\) 近似为常数。
Boyle (1662) compressed air trapped in a J-tube with mercury and found \(pV\) nearly constant.
从 \(pV = nRT\) 看：T、n 不变时右边为常数，故 \(pV\) = 常数。
From \(pV = nRT\): with T and n fixed the right side is constant, so \(pV\) = const.
在 p–V 图上为双曲线（等温线）；温度越高，等温线离原点越远。
On a p–V diagram it is a hyperbola (an isotherm); hotter isotherms lie further out.
适用条件与局限Assumptions & limitations
理想气体行为；高压下分子体积和吸引力使 \(pV\) 偏离常数。
Ideal-gas behaviour; at high pressure molecular size and attraction make \(pV\) drift.
压缩必须足够慢以保持等温（否则温度升高）。
Compression must be slow enough to stay isothermal.