Particles of a Gas | 气体的粒子

📚 Particles of a Gas | 气体的粒子

In A-level physics, the behaviour of a gas is explained by considering the motion of its particles. This article reviews the kinetic theory model, the origin of gas pressure, the link between temperature and molecular kinetic energy, and the conditions under which the ideal gas model breaks down.

在 A-level 物理中，气体的行为通过粒子的运动来解释。本文回顾分子动理论模型、气体压强的来源、温度与分子平均动能之间的联系，以及理想气体模型失效的条件。

1. The Particle Model of a Gas | 气体的粒子模型

A gas consists of a very large number of tiny particles, usually atoms or molecules, in continuous random motion. The particles are much smaller than the distances between them, so a gas is mostly empty space.

气体由大量微小的粒子（通常是原子或分子）组成，它们处于持续的无规则运动之中。粒子本身远小于粒子间的距离，因此气体的大部分体积是空的。

Because the particles move freely and only interact during collisions, a gas has no fixed shape or volume. It expands to fill any container and exerts a pressure on the container walls.

由于粒子自由运动，只在碰撞时发生相互作用，气体没有固定的形状和体积。气体会膨胀并充满任何容器，同时对容器壁施加压强。

2. Assumptions of Kinetic Theory | 分子动理论的基本假设

The kinetic theory model of an ideal gas is based on several simplifying assumptions. The gas contains a large number of identical particles moving in random directions with a range of speeds.

理想气体的分子动理论模型建立在若干简化假设之上。气体包含大量相同的粒子，它们沿随机方向运动，速率分布广泛。

Collisions between particles and with the container walls are perfectly elastic, so kinetic energy is conserved in collisions. The volume of the particles themselves is negligible compared with the volume of the container.

粒子之间以及粒子与容器壁之间的碰撞是完全弹性的，因此碰撞中动能守恒。粒子本身的体积与容器体积相比可以忽略不计。

Except during collisions, there are no intermolecular forces acting between particles. The duration of each collision is also negligible compared with the time between collisions.

除碰撞瞬间外，粒子之间不存在分子间作用力。每次碰撞持续的时间与两次碰撞之间的时间相比也可以忽略不计。

Newtonian mechanics can be applied to the motion of the particles, and the gas is in thermal equilibrium with its surroundings.

牛顿力学可以应用于粒子的运动，并且气体与周围环境处于热平衡状态。

3. Pressure from Molecular Collisions | 分子碰撞产生的压强

Gas pressure arises from the rate of change of momentum of the particles as they strike the container walls. Each collision exerts a small force, and the average effect of enormous numbers of collisions produces a steady pressure.

气体压强源于粒子撞击容器壁时动量的变化率。每次碰撞施加一个微小的力，大量碰撞的平均效果产生稳定的压强。

Consider a single particle of mass m moving with velocity component vₓ perpendicular to a wall. When it rebounds elastically, its momentum changes by 2mvₓ.

考虑一个质量为 m 的粒子以垂直于壁面的速度分量 vₓ 运动。当它发生弹性反弹时，动量变化为 2mvₓ。

In a cube of side L, the time between successive collisions with the same wall is 2L/vₓ, so the average force on that wall is mvₓ²/L. Summing over all particles gives the total force.

在边长为 L 的立方体中，同一粒子与同一壁面连续两次碰撞的时间间隔为 2L/vₓ，因此作用在该壁面上的平均力为 mvₓ²/L。对所有粒子求和即可得到总力。

Using the mean square speed ⟨c²⟩ and the isotropy of motion, ⟨vₓ²⟩ = (1/3)⟨c²⟩. The pressure is therefore given by:

利用方均速率 ⟨c²⟩ 以及运动的各向同性，⟨vₓ²⟩ = (1/3)⟨c²⟩。因此压强为：

p = (1/3)(Nm/V)⟨c²⟩ = (1/3)ρ⟨c²⟩

This expression links the macroscopic pressure to the microscopic mean square speed of the particles and the gas density ρ.

该表达式将宏观压强与粒子的微观方均速率以及气体密度 ρ 联系起来。

4. Relationship between Pressure and Volume | 压强与体积的关系

For a fixed mass of gas at constant temperature, the product pV is constant, which is Boyle’s law. This follows from the kinetic theory because reducing the volume increases the collision rate with the walls.

对于一定质量的气体，在温度不变时，pV 为常数，这就是玻意耳定律。分子动理论可以解释该定律：体积减小会使粒子与器壁的碰撞频率增大。

If the volume is halved while the temperature and the number of

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