📚 IB Physics: Complete Guide to Gas Laws | IB物理：气体定律全解析
Gas laws are a core topic in the IB Physics Thermal Physics section. They connect the macroscopic variables of pressure, volume, temperature, and amount of gas, and they also link to the microscopic motion of molecules through kinetic theory. This guide covers every gas law you need for your IB exams, including the ideal gas equation, kinetic theory calculations, and real-gas limitations.
气体定律是 IB 物理热学部分的核心内容。它将气体的宏观变量——压强、体积、温度和物质的量——联系起来，并通过气体动理论将宏观规律与分子的微观运动相结合。本指南涵盖你在 IB 考试中需要掌握的所有气体定律，包括理想气体方程、动理论计算以及真实气体的局限性。
1. The Ideal Gas Model | 理想气体模型
The ideal gas is a theoretical model built on several assumptions: gas molecules have negligible volume compared to the container; there are no intermolecular forces except during brief elastic collisions; all collisions are perfectly elastic; the molecules are in constant random motion; and the time spent in collisions is negligible compared with the time between collisions.
理想气体是一种理论模型，它建立在若干假定之上：与容器的体积相比，气体分子本身的体积可以忽略；除短暂弹性碰撞外，分子间没有相互作用力；所有碰撞都是完全弹性的；分子处于永不停息的无规则运动中；碰撞的持续时间远小于两次碰撞之间的时间。
These assumptions simplify the mathematics greatly and give accurate predictions for real gases at high temperature and low pressure. Under other conditions, real gases deviate from ideal behaviour, as discussed in Section 10.
这些假定极大地简化了数学推导，并且能在高温低压条件下对真实气体作出准确的预测。在其他条件下，真实气体则会偏离理想行为，这将在第 10 节中讨论。
A real gas behaves most ideally when its temperature is high and its pressure is low. Raising the temperature increases molecular speeds and weakens the effect of intermolecular attractions; lowering the pressure makes the molecular volume even more negligible relative to the container.
当温度较高、压强较低时，真实气体的行为最接近理想气体。升高温度会使分子速度增大，从而削弱分子间引力的影响；降低压强则使分子本身体积相对于容器更加可以忽略。
2. Boyle’s Law | 玻意耳定律
Boyle’s law states that for a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume. The mathematical form is p₁V₁ = p₂V₂, where p is pressure and V is volume.
玻意耳定律指出：对于质量一定的气体，在温度不变时，其压强与体积成反比。其数学形式为 p₁V₁ = p₂V₂，其中 p 是压强，V 是体积。
Halving the volume doubles the concentration of molecules, so the frequency of collisions with the container walls doubles, which doubles the pressure. On a p-V graph, each constant-temperature curve is a hyperbola called an isotherm. A graph of p against 1/V is instead a straight line through the origin.
体积减半会使分子浓度加倍，分子与容器壁碰撞的频率翻倍，从而使压强也加倍。在 p-V 图上，每一条等温曲线都是双曲线，称为等温线；而 p 对 1/V 的图像则是一条过原点的直线。
Boyle’s law applies only to isothermal processes. In IB exams, you may be asked to sketch two isotherms; a higher temperature corresponds to a curve further from the origin because the product pV increases with temperature.
玻意耳定律只适用于等温过程。在 IB 考试中，你可能会被要求画出两条等温线；温度越高，对应的曲线越远离原点，因为 pV 的乘积随温度升高而增大。
3. Charles’s Law | 查理定律
Charles’s law states that for a fixed mass of gas at constant pressure, the volume is directly proportional to the absolute temperature: V₁/T₁ = V₂/T₂. The temperature must always be in kelvin.
查理定律指出：对于质量一定的气体，在压强不变时，体积与绝对温度成正比：V₁/T₁ = V₂/T₂。温度必须始终使用开尔文单位。
Using Celsius degrees in this ratio gives incorrect results. If the absolute temperature doubles from 300 K to 600 K, the volume doubles; but if the Celsius temperature changes from 27 °C to 327 °C, the ratio is not 1:2.
在此比例式中使用摄氏度会得到错误结果。若绝对温度从 300 K 升高到 600 K，体积会加倍；但若摄氏温度从 27 °C 变为 327 °C，其比值并不是 1:2。
On a V-T graph plotted in kelvin, the line passes through the origin. At constant pressure, heating a gas increases the average kinetic energy of its molecules, so they push the piston outward and the volume expands.
在以开尔文为单位的 V-T 图上，直线经过原点。在等压条件下加热气体，分子平均动能增大，分子推着活塞向外运动，体积膨胀。
4. Gay-Lussac’s Law | 盖-吕萨克定律
Gay-Lussac’s law, sometimes called the pressure-temperature law, states that for a fixed mass of gas at constant volume, the pressure is directly proportional to the absolute temperature: p₁/T₁ = p₂/T₂.
盖-吕萨克定律又称压强-温度定律，它指出：对于质量一定的气体，在体积不变时，压强与绝对温度成正比：p₁/T₁ = p₂/T₂。
When the temperature rises, the average speed of the molecules increases, so they strike the walls more often and with greater average force. Both effects increase the pressure the gas exerts on the container.
当温度升高时，分子的平均速率增大，它们撞击器壁更频繁，每次撞击的平均作用力也更大。这两种效应都会增大气体对容器施加的压强。
This law explains why sealed aerosol cans may explode when heated: the volume is approximately fixed, so the pressure rises dangerously with temperature. In IB questions, this law is often combined with the ideal gas equation to find missing quantities.
该定律解释了密封气雾罐受热后可能爆炸的原因：体积近似不变，因此压强随温度升高而危险地增大。在 IB 题目中，这条定律常与理想气体方程结合，用来求解未知量。
5. Avogadro’s Law and the Mole | 阿伏伽德罗定律与摩尔
Avogadro’s law states that equal volumes of all gases at the same temperature and pressure contain the same number of molecules. One mole of any ideal gas contains N_A = 6.02 × 10²³ particles, known as the Avogadro constant.
阿伏伽德罗定律指出：在相同的温度和压强下，相同体积的任何气体都含有相同数量的分子。任何理想气体的 1 摩尔所含的粒子数为 N_A = 6.02 × 10²³，称为阿伏伽德罗常数。
At standard temperature and pressure (273 K and 1.01 × 10⁵ Pa), one mole of an ideal gas occupies 2.24 × 10⁻² m³, which is 22.4 L. This molar volume is a useful conversion factor in stoichiometry problems.
在标准温度和压强下（273 K 和 1.01 × 10⁵ Pa），1 摩尔理想气体占据的体积为 2.24 × 10⁻² m³，即 22.4 L。这个摩尔体积是化学计量问题中常用的换算因子。
In calculations, the number of moles n can be found from n = N/N_A or n = m/M, where N is the number of molecules, m is the mass of the gas, and M is its molar mass in kilograms per mole. Master these conversions because they appear in most ideal gas questions.
在计算中，物质的量 n 可用 n = N/N_A 或 n = m/M 求得，其中 N 是分子数，m 是气体质量，M 是以千克每摩尔为单位的摩尔质量。掌握这些换算很重要，因为大多数理想气体问题都会用到它们。
6. The Ideal Gas Equation | 理想气体方程
The ideal gas equation combines Boyle’s law, Charles’s law, Gay-Lussac’s law, and Avogadro’s law into one expression:
理想气体方程把玻意耳定律、查理定律、盖-吕萨克定律和阿伏伽德罗定律合并为一个表达式：
pV = nRT
Here, p is the pressure in pascals, V is the volume in cubic metres, n is the number of moles, T is the absolute temperature in kelvin, and R = 8.31 J mol⁻¹ K⁻¹ is the molar gas constant.
其中 p 是以帕斯卡为单位的压强，V 是以立方米为单位的体积，n 是物质的量，T 是以开尔文为单位的绝对温度，R = 8.31 J mol⁻¹ K⁻¹ 是摩尔气体常量。
An equivalent form uses N, the total number of molecules: pV = NkT, where k = 1.38 × 10⁻²³ J K⁻¹ is the Boltzmann constant. The two constants are related by R = N_A k. Use the second form when quantities involve individual molecules rather than moles.
另一个等价形式使用分子总数 N：pV = NkT，其中 k = 1.38 × 10⁻²³ J K⁻¹ 是玻尔兹曼常量。两个常量之间的关系为 R = N_A k。当问题涉及单个分子而非摩尔时，使用第二种形式更方便。
Worked example: A cylinder of volume 2.0 × 10⁻³ m³ contains 0.10 mol of an ideal gas at 300 K. The pressure is p = nRT/V = 0.10 × 8.31 × 300 / (2.0 × 10⁻³) = 1.25 × 10⁵ Pa. Notice how all quantities were already in SI units.
例题：一个体积为 2.0 × 10⁻³ m³ 的气缸装有 0.10 mol 的理想气体，温度为 300 K。压强为 p = nRT/V = 0.10 × 8.31 × 300 / (2.0 × 10⁻³) = 1.25 × 10⁵ Pa。注意所有物理量都已使用国际制单位。
7. Kinetic Theory of Gases | 气体动理论
Kinetic theory connects the macroscopic pressure of a gas to the microscopic motion of its molecules. Starting from Newton’s laws and averaging over all molecules, the pressure satisfies the relation:
气体动理论将气体的宏观压强与分子微观运动联系起来。从牛顿定律出发并对所有分子求平均，压强满足如下关系：
pV = ⅓Nm⟨v²⟩
In this equation, m is the mass of one molecule, N is the number of molecules, and ⟨v²⟩ is the mean square speed of the molecules. The angle brackets denote an average over all molecules.
在这个方程中，m 是一个分子的质量，N 是分子总数，⟨v²⟩ 是分子的均方速率
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