定义Definition
气体分子运动论用大量做无规则运动的分子来解释气体的宏观性质:气体压强来自分子对器壁的碰撞,温度反映分子的平均平动动能。理想气体状态方程可以从它推导出来。
The kinetic theory of gases explains the bulk properties of gases in terms of huge numbers of molecules in random motion: pressure comes from molecules striking the container walls, and temperature measures their average translational kinetic energy. The ideal gas equation can be derived from it.
基本假设Assumptions
气体由大量做无规则直线运动的分子组成;分子本身的体积与容器体积相比可忽略;除碰撞外分子之间没有作用力;碰撞是完全弹性的;分子的平均动能与热力学温度成正比,Ē = (3/2)kT。满足这些假设的气体称为理想气体。
A gas consists of many molecules moving randomly in straight lines; their own volume is negligible compared with the container; there are no forces between them except in collisions; collisions are perfectly elastic; and their average kinetic energy is proportional to the thermodynamic temperature, Ē = (3/2)kT. A gas meeting these assumptions is ideal.
实际气体的偏离Real gases
高压时分子本身体积不可忽略,低温时分子间吸引力变得重要,实际气体偏离理想行为。范德华方程通过修正体积和压强描述实际气体。分子小、分子间作用力弱的气体(如 He、H₂)在高温低压下最接近理想气体。
At high pressure the molecules' own volume matters, and at low temperature intermolecular attractions become important, so real gases deviate from ideal behaviour. The van der Waals equation corrects the volume and pressure to describe them. Gases with small molecules and weak forces, such as He and H₂, behave most ideally at high temperature and low pressure.
分子速率分布Distribution of speeds
麦克斯韦–玻尔兹曼分布给出了气体分子速率的统计分布:温度升高时分布曲线变宽、峰值右移,高速分子比例增大,这也解释了升温使反应加快的原因。
The Maxwell–Boltzmann distribution gives the statistical spread of molecular speeds: as temperature rises the curve broadens and its peak moves to higher speed, with more fast molecules, which also explains why reactions speed up when heated.
年表Timeline
- 1738
丹尼尔·伯努利用分子碰撞解释气体压强
Daniel Bernoulli explains gas pressure by molecular impacts
- 1857
克劳修斯系统发展气体分子运动论
Clausius develops the kinetic theory systematically
- 1860
麦克斯韦推导出分子速率分布
Maxwell derives the distribution of molecular speeds
- 1872
玻尔兹曼发展统计理论并推广速率分布
Boltzmann extends the statistical theory and the speed distribution
相关公式Formulas
例题Worked example
25 °C 时 N₂:u_rms = √(3×8.314×298/0.028) = 515 m/s,接近声速的 1.5 倍。
N₂ at 25 °C: u_rms = 515 m/s, about 1.5 × the speed of sound.