IGCSE Physics: Density and Pressure Core Concepts | IGCSE物理：密度与压强核心考点

📚 IGCSE Physics: Density and Pressure Core Concepts | IGCSE物理：密度与压强核心考点

Density and pressure are two fundamental topics in IGCSE Physics. They appear throughout the syllabus, from solids and liquids to gases and everyday applications such as hydraulic brakes and atmospheric pressure. Mastering these core ideas requires a clear understanding of definitions, formulas, units, and experimental methods.

密度与压强是 IGCSE 物理中的两大基础主题。它们贯穿整个考纲，从固体、液体到气体，再到液压刹车和大气压强等日常应用。掌握这些核心考点需要清楚理解定义、公式、单位以及实验测量方法。

1. What is Density? | 什么是密度？

Density is a measure of how much mass is packed into a given volume. It tells us whether a material is “light” or “heavy” for its size. The equation is:

密度是表示“一定体积内包含多少质量”的物理量。它告诉我们一种材料是“轻”还是“重”。其公式为：

ρ = m / V

where ρ (rho) is density, m is mass, and V is volume.

其中 ρ（rho，希腊字母）是密度，m 是质量，V 是体积。

In SI units, mass is measured in kilograms (kg) and volume in cubic metres (m³), so density is measured in kilograms per cubic metre (kg/m³). In many experiments, however, we use grams and cubic centimetres, giving density in g/cm³.

在国际单位制中，质量的单位是千克（kg），体积的单位是立方米（m³），因此密度的单位是千克每立方米（kg/m³）。不过在实验中我们常用克和立方厘米，因此密度的单位也会写作 g/cm³。

You need to be able to convert between these two common units:

你需要掌握这两种常用单位之间的换算：

1 g/cm³ = 1000 kg/m³

For example, the density of water is 1.0 g/cm³, which is the same as 1000 kg/m³.

例如，水的密度是 1.0 g/cm³，也就等于 1000 kg/m³。

2. Measuring Density of Solids and Liquids | 测量固体和液体的密度

For a regularly shaped solid, such as a cube, cuboid, or sphere, you can calculate volume from its dimensions using the appropriate formula. For a cuboid, V = length × width × height. Use a ruler or vernier callipers for accurate measurements, and measure mass using an electronic balance. Then calculate density using ρ = m / V.

对于形状规则的固体，例如立方体、长方体或球体，你可以通过相应的几何公式计算体积。长方体体积 V = 长 × 宽 × 高。用刻度尺或游标卡尺测量尺寸，用电子天平测量质量，然后运用 ρ = m / V 计算密度。

For an irregularly shaped solid, you cannot easily measure its dimensions. Instead, use a displacement method. Place the solid in a measuring cylinder containing water; the rise in water level equals the volume of the object. A Eureka can (displacement can) can also be used to collect the displaced water.

对于形状不规则的固体，你很难直接测量其尺寸。此时可用排液法：把固体放入装有水的量筒中，水面上升的体积就等于物体的体积。也可以使用溢水杯（排水杯）收集溢出的水。

For a liquid, measure the mass of an empty measuring cylinder, then add a known volume of liquid and measure the total mass. The mass of the liquid is the difference between the two readings. Then divide by the volume.

对于液体，先测量空量筒的质量，然后倒入已知体积的液体并测量总质量。液体的质量等于两次读数之差，再用质量除以体积即可得到密度。

Always record the unit with every measurement.
Repeat measurements to reduce random error.
Read the meniscus at eye level for accurate volume reading.

每次测量都要写出单位。
重复测量以减小偶然误差。
读数时视线应与凹液面最低处齐平。

3. Pressure in Solids | 固体中的压强

Pressure in a solid is defined as the force acting perpendicularly per unit area. The formula is:

固体中的压强定义为单位面积上所受的垂直力。公式为：

p = F / A

where p is pressure, F is the force (perpendicular to the surface), and A is the area of contact.

其中 p 是压强，F 是垂直于表面的力，A 是接触面积。

The SI unit of pressure is the pascal (Pa). 1 Pa = 1 N/m². So one pascal is a very small pressure, equivalent to one newton spread over one square metre.

压强的国际单位是帕斯卡（Pa）。1 Pa = 1 N/m²。因此 1 帕斯卡是极小的压强，相当于一牛顿的力均匀分布在 1 平方米的面积上。

Correct use of area is crucial. For example, a block standing on a flat surface presses on the surface with the area that is actually in contact. Identify that contact area carefully in exam questions.

在解题时正确判断受力面积至关重要。例如，一个长方体放在水平面上，它对桌面的压强取决于实际接触的面积。考试中一定要仔细判断接触面的面积。

Real-life examples include sharp knives creating high pressure with a small edge, snowshoes reducing pressure by increasing area, and tractor tyres being wide to avoid sinking into soft ground.

生活实例包括：刀刃锋利、接触面积小，从而产生高压强；雪鞋通过增大面积减小压强，避免陷进雪里；拖拉机轮胎宽大，是为了减小对松软地面的压强。

4. Pressure in Liquids | 液体中的压强

In a liquid, pressure is caused by the weight of the liquid above the point of interest. As you go deeper, there is more liquid above, so pressure increases with depth.

液体内部的压强是由液体的重力产生的。深度越深，上方液体越多，压强就越大。

The equation for liquid pressure due to a column of liquid is:

液柱产生的压强公式为：

p = hρg

where h is the height (depth) of the liquid column, ρ is the density of the liquid, and g is the gravitational field strength (approximately 10 N/kg on Earth).

其中 h 是液柱的高度（深度），ρ 是液体密度，g 是重力场强度（地球上约为 10 N/kg）。

This equation shows that liquid pressure depends on three factors only: density, depth, and gravitational field strength. It does not depend on the shape or width of the container.

该公式表明液体压强只取决于三个因素：液体密度、深度和重力场强度。它不取决于容器的形状或宽度。

Liquid pressure acts in all directions.
Liquid pressure increases with density.
Liquid pressure increases with depth.
At the same depth, the pressure is the same in any direction.

液体向各个方向都有压强。
液体密度越大，同一深度的压强越大。
液体深度越深，压强越大。
在同一深度，液体向各个方向的压强大小相等。

A useful exam version of the formula is the pressure difference between two points in a liquid:

一个有用的考试公式是液体中两点间的压强差：

Δp = hρg

where Δp is the difference in pressure between the two points and h is the vertical separation between them.

其中 Δp 是两点之间的压强差，h 是两点间的竖直高度差。

5. Hydraulic Systems | 液压系统

Liquids are nearly incompressible. If you apply pressure to a liquid in a sealed container, the pressure is transmitted equally to every part of the liquid. This principle is used in hydraulic machines.

液体几乎不可压缩。如果你对密封容器中的液体施加压强，这个压强会被大小不变地传递到液体的每个部分。这一原理被用于液压机械中。

In a simple hydraulic system, there are two pistons of different areas. The pressure applied on the small piston is transmitted to the large piston:

在简单的液压系统中，有两个面积不同的活塞。作用于小活塞上的压强会被传递到大活塞上：

p₁ = F₁ / A₁ = F₂ / A₂

Since the pressure is the same on both pistons, a small force on a small area produces a large force on a larger area. This allows a hydraulic machine to act as a force multiplier.

由于两活塞上的压强相等，所以小面积上的小力能在大面积上产生大力。因此液压机械可以起到“力的放大”作用。

For example, if A₁ = 0.01 m² and A₂ = 0.5 m², then a force of 100 N on the small piston exerts 100/0.01 = 10,000 Pa of pressure. The large piston experiences 10,000 × 0.5 = 5000 N of force.

例如，若 A₁ = 0.01 m²，A₂ = 0.5 m²，在小活塞上施加 100 N 的力，产生的压强为 100 ÷ 0.01 = 10,000 Pa。大活塞上方则会受到 10,000 × 0.5 = 5000 N 的力。

Applications include hydraulic car lifts, hydraulic brakes, and dentist chairs.

常见的应用包括液压汽车升降机、液压刹车系统和牙医升降椅。

6. Pressure in Gases and Atmospheric Pressure | 气体压强与大气压强

Gas pressure is caused by gas molecules colliding with the walls of their container. Each collision exerts a small force, and billions of collisions per second create a continuous overall pressure.

气体压强是由气体分子与容器壁碰撞产生的。每次碰撞都会施加一个很小的力，而每秒钟无数次的碰撞合起来就形成了持续的气体压强。

Atmospheric pressure is the pressure exerted by the weight of the air in Earth’s atmosphere. At sea level, atmospheric pressure is about 101 kPa, or approximately 100,000 Pa.

大气压强是地球大气层的空气重力所产生的压强。在海平面处，大气压约为 101 kPa，大约等于 100,000 Pa。

As altitude increases, the atmosphere becomes thinner and the air density decreases, so atmospheric pressure decreases. This is why breathing at very high altitudes becomes harder, and also why sealed packages may bulge when taken up a mountain.

随着海拔升高，空气越来越稀薄，空气密度减小，因此大气压强也随之减小。这就是为什么在高海拔地区呼吸更困难，也解释了为什么密封包装袋在上山时会鼓起来。

Gas pressure can also be changed by changing volume or temperature. In IGCSE-level problems, you may be asked to compare pressures using the idea that pressure and volume are related for a fixed mass of gas at constant temperature (Boyle’s law: p₁V₁ = p₂V₂). However, density and pressure questions often simply require p = F/A or p = hρg.

气体压强也会随体积或温度而变化。在 IGCSE 考题中，你可能会遇到“一定质量、温度不变的情况下，压强与体积成反比”的玻意耳定律：p₁V₁ = p₂V₂。不过，密度与压强部分的题目通常只要求运用 p = F/A 或 p = hρg。

7. Manometers and Barometers | 压力计与气压计

A manometer is a U-shaped tube containing a liquid, usually water or mercury. It is used to measure the pressure of a gas by comparing it to atmospheric pressure.

压力计是一种装有液体（通常是水或水银）的 U 形管。它通过比较气体压强与大气压来测量气体压强。

One end of the manometer is connected to the gas supply, and the other end is open to the atmosphere. If the gas pressure is higher than atmospheric pressure, the liquid level is higher on the open side. The pressure difference is given by:

U 形管的一端连接待测气体，另一端开口通向大气。如果气体压强高于大气压，则开口一侧的液面会更高。压强差由以下公式给出：

p_gas = p_atm + hρg

where h is the difference in liquid levels in metres, ρ is the liquid density, and g is the gravitational field strength.

其中 h 是两侧液面的高度差（单位米），ρ 是液体密度，g 是重力场强度。

If the gas pressure is lower than atmospheric pressure, then p_gas = p_atm − hρg.

如果气体压强低于大气压，则 p_gas = p_atm − hρg。

A barometer is used to measure atmospheric pressure. A mercury barometer is a tube filled with mercury, inverted in a mercury reservoir. The height of the mercury column is a direct measure of atmospheric pressure:

气压计用于测量大气压强。水银气压计是一根装满水银的玻璃管，倒插在水银槽中。水银柱的高度可以直接测量大气压强：

p_atm = hρg

At standard atmospheric pressure, mercury rises about 760 mm in the tube.

在标准大气压下，水银柱的高度约为 760 mm。

8. Worked Examples | 例题讲解

Example 1: Calculating density of a cuboid

例 1：计算长方体的密度

A metal cuboid has dimensions 0.20 m × 0.10 m × 0.05 m and a mass of 2.4 kg. Calculate its density.

一个金属长方体的大小为 0.20 m × 0.10 m × 0.05 m，质量为 2.4 kg。求它的密度。

Solution:

解题步骤：

V = 0.20 × 0.10 × 0.05 = 0.001 m³

ρ = m / V = 2.4 / 0.001 = 2400 kg/m³

Therefore, the density of the metal is 2400 kg/m³.

因此，该金属的密度为 2400 kg/m³。

Example 2: Pressure at depth in a liquid

例 2：液体中某深度的压强

A diver is 20 m below the surface of freshwater. The density of freshwater is 1000 kg/m³ and g = 10 N/kg. Calculate the pressure exerted by the water on the diver.

一名潜水员位于淡水水面下方 20 m 深处。淡水密度为 1000 kg/m³，取 g = 10 N/kg。求水对潜水员施加的压强。

p = hρg = 20 × 1000 × 10 = 200,000 Pa

So the water pressure at that depth is 200,000 Pa, which is equal to 200 kPa.

因此该深度处的水压为 200,000 Pa，即 200 kPa。

Note that this is the gauge pressure due to the water only. The total absolute pressure would include atmospheric pressure above the water surface, adding about 101 kPa.

注意这里仅指水产生的压强。如果要求绝对压强，还需要加上水面上方的大气压，约为 101 kPa。

Example 3: Hydraulic force multiplication

例 3：液压力的放大

In a hydraulic system, the small piston has an area of 0.02 m² and the large piston has an area of 1.00 m². A force of 40 N is applied to the small piston. What force is exerted by the large piston?

在某一液压系统中，小活塞面积为 0.02 m²，大活塞面积为 1.00 m²。在小活塞上施加 40 N 的力，大活塞能产生的力是多少？

Pressure on small piston:

小活塞上的压强：

p = F / A = 40 / 0.02 = 2000 Pa

This pressure is transmitted equally, so force on large piston:

该压强等值传递，因此大活塞上的力为：

F = p × A = 2000 × 1.00 = 2000 N

Thus the hydraulic system multiplies the force from 40 N to 2000 N.

因此该液压系统将 40 N 的力放大到了 2000 N。

9. Common Mistakes and Exam Tips | 常见错误与考试技巧

One common mistake is mixing up grams and kilograms, or cubic centimetres and cubic metres. Always convert all values to consistent SI units before substituting into a formula.

常见错误之一是将克和千克、立方厘米和立方米混用。在代入公式之前，应把所有数据统一为一致的国际单位。

Another frequent error is forgetting that pressure in liquids depends on vertical depth, not on the distance along a slanted pipe. Always use the perpendicular depth from the surface.

另一个常见错误是忘记液体压强只取决于竖直深度，而不取决于斜管中的液柱长度。一定要使用从液面到该点的竖直深度。

When calculating pressure as p = F/A, remember that the force F must be perpendicular to the surface. If a force is applied at an angle, only the perpendicular component produces pressure.

计算 p = F/A 时，力 F 必须垂直于受力面。如果力是斜着施加的，只有垂直于接触面的分量才能产生压强。

In density experiments, remember to subtract the mass of the empty container when finding the mass of a liquid. Do not include the container.

在密度测量实验中，求液体质量时一定要减去空容器的质量，不能把容器质量算进去。

Exam tip: when a question gives a graph of mass against volume, the gradient represents density. A steeper line means a higher density.

考试技巧：如果题目给出“质量–体积”图像，则斜率代表密度。直线越陡，密度越大。

Write the formula first, then substitute numbers with units, then give the final answer with a unit.
Check whether your answer is reasonable. Water has a density of 1000 kg/m³, so most solids are between 500 and 8000 kg/m³.
For pressure in liquids, if asked “total pressure at depth”, remember to add atmospheric pressure if it acts on the liquid surface.

先写公式，再代入带单位的数据，最后给出带单位的答案。
检查答案是否合理。水的密度为 1000 kg/m³，大多数固体的密度在 500 到 8000 kg/m³ 之间。
若题目要求“某深处的总压强”，且液面上有大气压作用，记得加上大气压。

10. Summary: Key Equations and Units | 总结：核心公式与单位

Quantity	Equation	SI Unit
Density	ρ = m / V	kg/m³
Pressure in solids	p = F / A	Pa 或 N/m²
Pressure in liquids	p = hρg	Pa
Pressure difference	Δp = hρg	Pa
Hydraulic pressure transmission	F₁/A₁ = F₂/A₂	Pa

Remember that 1 g/cm³ = 1000 kg/m³, and 1 Pa = 1 N/m².

请记住：1 g/cm³ = 1000 kg/m³，且 1 Pa = 1 N/m²。

11. Final Revision Checklist | 考前最终检查清单

Before your exam, make sure you can confidently do the following:

考试之前，请确保你能自信地完成以下内容：

Define density and recall the equation ρ = m / V.
Describe methods for measuring density of solids and liquids.
Convert between kg/m³ and g/cm³.
Define pressure and recall p = F / A.
Explain why pressure in liquids increases with depth and density.
Use p = hρg to solve problems involving liquid pressure.
Explain how hydraulic systems produce a large force from a small force.
Describe how gas pressure arises from molecular collisions.
Interpret the height difference in a manometer.
Use correct significant figures and units throughout.

定义密度并正确运用公式 ρ = m / V。
描述测量固体和液体密度的实验方法。
能在 kg/m³ 与 g/cm³ 之间进行换算。
定义压强并正确运用公式 p = F / A。
解释液体压强随深度和密度增大而增大的原因。
使用 p = hρg 求解液体压强问题。
解释液压系统如何将小力放大为大力。
描述气体压强如何由气体分子碰撞产生。
读懂压力计中液面高度差的意义。
全程使用正确的有效位数和单位。

Density and pressure are not only exam topics; they are also powerful tools for understanding the physical world. Once you can visualise what density and pressure really mean, many problems become much simpler. Keep practising past paper questions, and always check your units carefully.

密度与压强不仅是考试重点，也是理解物理世界的有力工具。一旦你真正理解密度和压强的物理意义，许多题目都会变得简单。请多练习真题，并始终仔细检查单位。

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IGCSE Physics: Density and Pressure Core Concepts | IGCSE物理：密度与压强核心考点