📚 Ideal Gases | 理想气体
An ideal gas is a theoretical model used to simplify the study of gases. It obeys the ideal gas laws exactly under all conditions of temperature and pressure. The model assumes that gas particles have negligible volume and exert no intermolecular forces on each other except during elastic collisions. Real gases approach ideal behaviour at low pressures and high temperatures.
理想气体是一种用于简化气体研究的理论模型。它在所有温度和压力条件下都严格遵守理想气体定律。该模型假设气体分子自身的体积可以忽略不计，且分子之间除弹性碰撞外没有相互作用力。实际气体在低压和高温条件下接近理想气体行为。
1. Introduction to Ideal Gases | 理想气体简介
In the study of thermodynamics, the macroscopic properties of a gas—pressure p, volume V, and thermodynamic temperature T—are related by simple experimental laws when the gas is kept at low density. The ideal gas model provides a framework that links these properties precisely. For a fixed mass of an ideal gas, any change in one variable can be predicted if the other two are known.
在热力学研究中，当气体处于低密度时，其宏观性质——压强 p、体积 V 和热力学温度 T——可通过简单的实验定律关联起来。理想气体模型提供了一个精确联系这些性质的框架。对于一定质量的理想气体，如果已知其中两个变量，就可以预测第三个变量的变化。
The key idea is that an ideal gas consists of a large number of identical, point-like particles in constant random motion. The behaviour of the gas is entirely determined by the average kinetic energy of its particles, which depends only on temperature. This allows us to connect the microscopic world of molecules with measurable macroscopic quantities.
其核心思想是：理想气体由大量完全相同的、可视为质点的粒子组成，它们持续进行无规则运动。气体的行为完全由其粒子的平均动能决定，而平均动能只取决于温度。这就使我们能够将微观分子世界与可测量的宏观量联系起来。
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 p is inversely proportional to the volume V. This can be written as:
玻意耳定律指出：对于一定质量的气体，在温度保持不变的条件下，压强 p 与体积 V 成反比。可用下式表示：
p ∝ 1/V or pV = constant
s is reduced by half while the temperature remains the same, the pressure doubles. Mathematically, for two states of the same gas, Boyle' pts 1 and 2 refer to initial and final states. The product pV is constant only if T is held fixed and the mass of gas does not change.
实验上，若在温度不变时将气体体积减半，压强便会加倍。用数学表达，对于同种气体的两个状态，玻意耳定律给出 p₁V₁ = p₂V₂，其中下标 1 和 2 分别代表初始状态与末状态。只要温度不变且气体质量不变，乘积 pV 就是一个常数。
3. Charles's Law | 查理定律
Charles's law states that at constant pressure, the volume V of a fixed mass of gas is directly proportional to its absolute temperature T. The relationship is expressed as:
查理定律指出：在压强不变的条件下，一定质量气体的体积 V 与其绝对温度 T 成正比。此关系可表达为：
V ∝ T or V / T = constant
temperature is measured in kelvin (K) because the proportionality holds only on the absolute scale. A plot of V against T for an ideal gas yields a straight line passing through the origin.
对于在相同压强下的任意两个状态，有 V₁/T₁ = V₂/T₂。必须使用开尔文 (K) 温度，因为只有采用绝对温标时比例关系才成立。理想气体的 V–T 图是一条通过原点的直线。
4. The Pressure Law (Gay–Lussac's Law) | 压力定律（盖–吕萨克定律）
The pressure law states that for a fixed mass of gas at constant volume, the pressure p is directly proportional to its absolute temperature T. In equation form:
压力定律指出：对于一定质量的气体，在体积保持不变的条件下，压强 p 与其绝对温度 T 成正比。可用方程表示为：
p ∝ T or p / T = constant
so requires temperatures to be in kelvin. When a sealed container of gas is heated, the increase in average molecular kinetic energy leads to more frequent and more forceful collisions with the walls, raising the pressure.
因此，在体积不变时的两个状态之间，有 p₁/T₁ = p₂/T₂。该定律同样要求温度以开尔文为单位。当密封容器中的气体被加热时，分子平均动能的增加导致与器壁的碰撞更加频繁且更剧烈，从而使压强升高。
5. Combining the Gas Laws | 气体定律的综合
By combining Boyle's law, Charles's law and the pressure law, we obtain a general relationship for a fixed mass of ideal gas:
将玻意耳定律、查理定律和压力定律结合起来，便得到定量理想气体的通用关系式：
pV / T = constant or p₁V₁ / T₁ = p₂V₂ / T₂
This equation holds for any change in the state of a fixed amount of gas, provided the gas behaves ideally. It shows that the quantity pV/T remains unchanged as long as the number of particles does not change. This combined law is the foundation for introducing the mole and the universal gas constant.
只要气体行为接近理想气体，该方程便适用于一定量气体状态的任何变化。它表明只要粒子数不变，pV/T 这个量就保持不变。这个综合定律为引入摩尔和普适气体常量奠定了基础。
6. The Ideal Gas Equation (pV = nRT) | 理想气体方程 (pV = nRT)
ests that the constant depends on the amount of gas. By introducing the number of moles n, we obtain the ideal gas equation:
综合定律 pV/T = 常数表明，该常数取决于气体的量。引入摩尔数 n 后，就得到了理想气体方程：
pV = nRT
stant, R = 8.31 J mol⁻¹ K⁻¹. The amount n is measured in moles. One mole contains Avogadro' ascals, V in cubic metres, n in moles, and T in kelvin, the product pV equals nRT exactly.
式中 R 是摩尔气体常数，R = 8.31 J mol⁻¹ K⁻¹。n 是以摩尔为单位的物质的量。1 摩尔含有阿伏加德罗常数个粒子，Nₐ = 6.02 × 10²³ mol⁻¹。该方程适用于任何理想气体：若 p 以帕斯卡为单位，V 以立方米为单位，n 以摩尔为单位，T 以开尔文为单位，则 pV 恰好等于 nRT。
The ideal gas equation allows us to calculate any one variable if the other three are known. It also shows that at a given temperature and pressure, equal volumes of any ideal gas contain the same number of molecules, which is consistent with Avogadro's law.
理想气体方程使我们能在已知三个变量的前提下计算第四个变量。它还表明，在相同温度和压强下，相同体积的任何理想气体含有相同数量的分子，这与阿伏加德罗定律一致。
7. The Equation of State (pV = NkT) | 状态方程 (pV = NkT)
Instead of using moles, we can describe the gas in terms of the total number of molecules N. The equation of state then becomes:
除了用摩尔描述外，我们也可以用分子总数 N 来描述气体。此时状态方程为：
pV = NkT
larly useful when linking macroscopic pressure to microscopic molecular motion, because N represents the actual number of particles in the container.
式中 k 是玻尔兹曼常数，k = 1.38 × 10⁻²³ J K⁻¹。R 与 k 的关系为 R = Nₐ k。当需要将宏观压强与微观分子运动联系起来时，这一形式尤其有用，因为 N 表示容器中实际的粒子数目。
The equation of state emphasises that the product pV is directly proportional to the absolute temperature for a given number of molecules. It provides the bridge towards the kinetic theory of gases.
该状态方程强调，对于一定数量的分子，乘积 pV 与绝对温度成正比。它为气体分子运动论搭建了桥梁。
8. Basic Assumptions of the Kinetic Theory | 分子运动论的基本假设
The kinetic theory of gases explains the macroscopic properties of an ideal gas by considering the motion of its molecules. The theory is built on the following simplifying assumptions:
气体分子运动论通过考虑分子的运动来解释理想气体的宏观性质。该理论建立在以下简化假设之上：
(1) A gas consists of a very large number of identical molecules, each moving randomly in all directions with a range of speeds.
(1) 气体由极大量完全相同的分子组成，每个分子沿各个方向作无规则运动，速率各异。
(2) The volume of the molecules themselves is negligible compared with the total volume occupied by the gas; they are treated as point particles.
(2) 分子本身的体积与气体所占的总体积相比可以忽略；它们被当作质点处理。
(3) All collisions between molecules and between molecules and the walls of the container are perfectly elastic, so no kinetic energy is lost.
(3) 所有分子之间以及分子与容器壁之间的碰撞都是完全弹性的，因此无动能损失。
(4) The time during which a collision takes place is negligible compared with the time between collisions, so intermolecular forces act only during collisions.
(4) 碰撞持续的时间与两次碰撞之间的时间相比可忽略不计，因此分子间作用力仅在碰撞瞬间存在。
(5) Outside collisions, no intermolecular forces act; the molecules move in straight lines at constant speed.
(5) 碰撞之外，分子间没有作用力；分子作匀速直线运动。
(6) The laws of Newtonian mechanics apply to the motion of the molecules.
(
Published by TutorHao | A-Level Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图