📚 Boyle’s Law and Gas Pressure | 波义耳定律与气体压强
Gas pressure and Boyle’s law are core ideas in the Edexcel IGCSE Science specification. This article explains how gas particles create pressure, how to measure it, and why the volume of a gas changes when pressure changes at constant temperature. Worked examples and examiner tips are included to help you secure full marks.
气体压强与波义耳定律是 Edexcel IGCSE 科学考纲中的核心内容。本文讲解气体粒子如何产生压强、如何测量压强，以及在温度恒定时体积随压强变化的原因。文中包含例题和考官提示，帮助你稳拿满分。
1. What is Gas Pressure? | 什么是气体压强？
Gas pressure is a fundamental concept in the kinetic theory of matter. A gas is made up of tiny particles, atoms or molecules, that are constantly moving at high speed. Inside a sealed container, the particles travel in straight lines until they collide with the walls. Each collision exerts a tiny force on the wall. Pressure is the total force acting on one square metre of the container wall.
气体压强是物质分子运动论中的基本概念。气体由大量微小粒子，即原子或分子，组成，它们始终以高速运动。在密封容器内，粒子沿直线运动，直到撞上器壁。每次碰撞都会对器壁施加一个微小的力。压强就是作用在每平方米器壁上的总力。
p = F / A
where p is pressure in pascals (Pa), F is force in newtons (N), and A is area in square metres (m²). One pascal is equal to one newton per square metre: 1 Pa = 1 N/m².
其中 p 为压强，单位是帕斯卡（Pa）；F 为力，单位是牛顿（N）；A 为面积，单位是平方米（m²）。1 帕斯卡等于每平方米 1 牛顿，即 1 Pa = 1 N/m²。
2. How Particles Create Pressure | 粒子如何产生压力
The kinetic theory explains pressure in terms of particle collisions. Three factors affect the pressure a gas exerts:
分子运动论用粒子碰撞来解释压强。影响气体压强的因素有三个：
-
Faster particles hit the walls more often and with greater force, so pressure increases when temperature rises.
粒子速度越快，与器壁碰撞的次数越多、碰撞力越大，因此温度升高时压强增大。
-
If the volume is reduced, the particles have less space to move in, so the collision frequency increases and pressure rises.
体积减小时，粒子的活动空间变小，因此碰撞频率升高，压强随之增大。
-
Adding more gas particles while keeping volume constant increases the number of collisions per second, raising the pressure.
体积不变时增加气体粒子数量，每秒碰撞次数增多，压强也会升高。
3. Measuring Gas Pressure | 测量气体压强
In the school laboratory, gas pressure is usually measured with a Bourdon gauge, which is a coiled metal tube connected to a pointer, or with a manometer, which is a U-shaped tube containing a liquid. For Boyle’s law experiments, the equipment consists of a thick-walled glass tube containing air trapped by a column of oil, connected to a pressure gauge and a hand pump. As you pump, the gauge reading shows the pressure, and the volume of the trapped air is read from a scale on the tube.
在学校实验室中，通常用布尔登气压计测量气体压强，其内部是一根弯曲的金属管并与指针相连；也可以使用 U 形管压强计，也就是装有液体的 U 形管。波义耳定律实验装置包含一根厚壁玻璃管，管内有一段油柱封住空气，并与气压计和手摇泵相连。摇动泵时，气压计读数显示压强，而管内封住空气的体积则从管旁刻度读出。
4. The Variables in Boyle’s Law | 波义耳定律中的变量
Boyle’s law describes the relationship between pressure and volume for a fixed mass of gas at constant temperature. The independent variable is usually pressure, and the dependent variable is volume. The critical condition is that temperature must not change. If a gas is compressed quickly, it heats up, so in the experiment you must wait for the temperature to return to room temperature before reading the volume.
波义耳定律描述的是：对于一定质量的气体，在温度不变时，压强与体积之间的关系。通常自变量是压强，因变量是体积。关键条件是温度不能改变。如果气体被迅速压缩，它会因做功而升温，因此在实验中每次压缩后都要等待温度恢复到室温，再读取体积。
-
Mass of gas must stay fixed, so the apparatus must be airtight and there must be no leaks.
气体质量必须保持一定，因此装置必须密封，不能漏气。
-
Temperature must be constant, so readings should be taken slowly and the gas should not be touched by warm hands.
温度必须保持不变，因此读数应缓慢进行，手不要接触气体的部位。
5. Boyle’s Law Experiment | 波义耳定律实验
To verify Boyle’s law in the laboratory:
在实验室中验证波义耳定律的步骤：
-
Set up the apparatus so that a known mass of air is trapped under oil in the tube.
搭好装置，使管内油面下方封住一定质量的空气。
-
Read the initial volume and pressure.
读取初始体积和压强。
-
Turn the pump slowly to increase the pressure step by step.
缓缓摇动手摇泵，分步增大压强。
-
After each step, wait about 30 seconds for the temperature to settle, then record the new volume and pressure.
每改变一次后，等待约 30 秒使温度稳定，再记录新的体积和压强。
-
Repeat to obtain at least six pairs of readings.
重复操作，至少取得六组读数。
-
Calculate p × V for each pair. If the products are almost equal, Boyle’s law is verified.
计算每组 p × V。如果各乘积几乎相等，则验证了波义耳定律。
Safety: wear eye protection because the apparatus is under pressure, and never increase the pressure too quickly.
安全提示：装置内有压强，应佩戴护目镜，切勿过快地增大压强。
6. The Formula | 公式
Mathematically, Boyle’s law is written as:
数学上，波义耳定律可以表示为：
pV = constant
For the same mass of gas at the same temperature in two different states:
对于同一质量、同一温度下的气体在两个不同状态：
p₁V₁ = p₂V₂
This is an inverse proportion. If the pressure doubles, the volume halves. If the pressure triples, the volume falls to one third of its original value.
这表示反比关系。压强加倍，体积减半；压强变为三倍，体积变为原来的三分之一。
7. Worked Example | 例题
A gas has a volume of 200 cm³ at a pressure of 100 kPa. The pressure is increased to 250 kPa at constant temperature. Calculate the new volume.
某气体的体积为 200 cm³，压强为 100 kPa。在温度不变的情况下，压强增大到 250 kPa。求新体积。
p₁V₁ = p₂V₂
Substituting values: 100 × 200 = 250 × V₂
代入数值：100 × 200 = 250 × V₂
V₂ = (100 × 200) ÷ 250 = 80 cm³
Check the answer makes sense: pressure increased by a factor of 2.5, so volume should decrease by a factor of 2.5. Since 200 ÷ 2.5 = 80, the answer is reasonable.
检验答案是否合理：压强增大了 2.5 倍，因此体积应减小到原来的 1/2.5。因为 200 ÷ 2.5 = 80，所以答案合理。
8. Graphical Representation | 图像表示
If pressure is plotted against volume, the graph is a smooth curve falling from left to right, called an inverse curve or hyperbola. If pressure is plotted against 1/volume, the graph is a straight line passing through the origin. The straight-line graph is the better way to verify the law because it is easy to see whether the relationship is truly linear.
如果用压强对体积作图，得到一条自左向右下降的平滑曲线，称为反比曲线或双曲线。如果用压强对 1/体积 作图，则得到一条过原点的直线。直线图是验证该定律的更好方式，因为很容易判断是否为线性关系。
| p / kPa | V / cm³ | 1/V / cm⁻³ | p × V |
| 100 | 80 | 0.0125 | 8000 |
| 200 | 40 | 0.025 | 8000 |
| 250 | 32 | 0.03125 | 8000 |
| 400 | 20 | 0.05 | 8000 |
The constant value of p × V in the table confirms that the gas obeys Boyle’s law.
表中 p × V 的值保持不变，说明该气体符合波义耳定律。
9. Applications | 应用
Boyle’s law explains many everyday situations. When you breathe in, the diaphragm flattens and the chest cavity enlarges. The volume of the lungs increases, so the pressure inside falls below atmospheric pressure, and air flows into the lungs. When you breathe out, the chest cavity shrinks, the volume decreases, pressure rises, and air is pushed out.
波义耳定律可以解释许多日常现象。吸气时，膈肌下压变平，胸腔容积变大。肺部体积增大，内部压强低于大气压，空气便流入肺部。呼气时，胸腔缩小，体积减小，压强升高，空气被压出。
-
Medical syringes: pulling the plunger increases the volume inside the barrel, lowering the pressure so liquid is drawn in.
医用注射器：拉动活塞使针筒内体积增大、压强降低，液体便被吸入。
-
Scuba tanks: a large mass of air is compressed into a small volume at very high pressure, allowing divers to carry enough oxygen.
潜水气瓶：大量空气被压缩到很小的体积中，压强很高，使潜水员能够携带足够的氧气。
-
Bicycle pumps: pressing the handle reduces the volume of air inside the pump, raising its pressure until it is high enough to push air into the tyre.
自行车打气筒：按压手柄使气筒内空气体积减小、压强升高，直到足以把空气压入轮胎。
10. Common Exam Mistakes and Tips | 常见考试错误与提示
Many students lose marks by missing out conditions, using wrong units, or drawing the wrong graph. Here are the most common errors and how to avoid them:
许多学生因漏写条件、用错单位或画错图像而失分。以下是最常见错误及避免方法：
-
Stating Boyle’s law without mentioning “fixed mass” and “constant temperature”; always include both conditions in the definition.
表述波义耳定律时未提到”质量一定”和”温度不变”；在定义中必须同时写明这两个条件。
-
Using different units on the two sides of the equation; keep V in cm³ or m³ and p in kPa or Pa consistently.
公式两边使用不同的单位；体积应统一用 cm³ 或 m³，压强应统一用 kPa 或 Pa。
-
Thinking that pressure and volume are directly proportional; remember that one goes up when the other goes down.
误认为压强与体积成正比；要记住两者一个升高，另一个就降低。
-
In the experiment, reading the volume immediately after compression without waiting for the temperature to stabilise.
实验中压缩后立即读数，没有等待温度稳定。
-
Confusing “more frequent collisions” with “harder collisions” when explaining pressure changes; both are valid but mark schemes expect precise wording.
解释压强变化时混淆”碰撞更频繁”与”碰撞更有力”
Published by TutorHao | IGCSE Science Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply