📚 Edexcel IAL Physics Unit 5: Thermodynamics, Radiation, Oscillations and Cosmology | Edexcel IAL 物理 Unit 5：热力学、辐射、振动与宇宙学
This revision guide covers the core ideas in Unit 5 of the Edexcel International A Level Physics specification. It brings together thermal physics, ideal gases, nuclear decay, oscillations, gravitational fields and cosmology. Use the paired explanations and quick-check tables to build confidence before your exam.
本复习指南涵盖 Edexcel 国际 A Level 物理第五单元的核心内容，包括热物理、理想气体、核衰变、振动、引力场和宇宙学。每个要点都配有中英对照解释与速查表格，帮助你在考前建立清晰的知识框架。
1. Internal Energy, Temperature and Heat | 内能、温度与热量
In kinetic theory, all matter is made of particles in constant random motion. The internal energy U of a system is the sum of the random kinetic energy of its particles and the potential energy stored in the bonds between them. Temperature is not the same as heat: temperature is a measure of the average kinetic energy of the particles, while heat is the transfer of internal energy from a hotter body to a colder body.
在分子动理论中，一切物质都由不断做无规则运动的粒子组成。系统的内能 U 是粒子无规则动能与粒子间势能之和。温度不等于热量：温度是粒子平均动能的量度，而热量是由于温差引起的能量传递。
One key idea is that a change in temperature is associated with a change in the random kinetic energy of particles. During a change of state, however, the temperature stays constant even though energy is still being transferred. The energy supplied during melting or boiling increases the potential energy between particles, not their average kinetic energy.
一个关键概念是，温度变化对应粒子无规则动能的变化。但在物态变化过程中，即使能量仍在传递，温度却保持不变。熔化或沸腾时供给的能量增加了粒子间的势能，而不是增加其平均动能。
- Internal energy = total random kinetic energy + intermolecular potential energy.
- 内能 = 分子无规则动能 + 分子间势能。
- Absolute zero: 0 K = −273.15 °C, the lowest possible temperature.
- 绝对零度：0 K = −273.15 °C，是理论上的最低温度。
- Temperature is proportional to average translational kinetic energy for an ideal gas.
- 对于理想气体，温度与分子的平均平动动能成正比。
U = KE_random + PE_intermolecular
2. Specific Heat Capacity and Specific Latent Heat | 比热容与比潜热
The specific heat capacity c of a material is the energy required to raise the temperature of 1 kg of the substance by 1 K without a change of state. It is calculated using Q = mcΔθ, where Q is the thermal energy transferred, m is the mass and Δθ is the temperature change.
比热容 c 是指在不发生物态变化时，使 1 kg 物质温度升高 1 K 所需的能量。计算公式为 Q = mcΔθ，其中 Q 为传递的热能，m 为质量，Δθ 为温度变化。
The specific latent heat L is the energy required to change the state of 1 kg of a substance at constant temperature. The latent heat of fusion is for melting or freezing, and the latent heat of vaporisation is for boiling or condensing. The relevant equation is Q = mL.
比潜热 L 是指使 1 kg 物质在温度不变时发生物态变化所需的能量。熔化潜热用于熔化或凝固，汽化潜热用于沸腾或液化。相关公式为 Q = mL。
Experimental methods often use an electrical heater and a joulemeter or voltmeter-ammeter arrangement. Good insulation is needed to reduce energy loss to the surroundings, and stirring ensures a uniform temperature throughout the sample.
实验方法通常使用电加热器和焦耳计或伏安法电路。良好的隔热措施可以减少热量散失，搅拌则能使样品温度分布均匀。
Q = mcΔθ and Q = mL
| Quantity | Equation | What changes |
|---|---|---|
| Specific heat capacity | Q = mcΔθ | Kinetic energy |
| Specific latent heat | Q = mL | Potential energy |
When interpreting heating curves, flat sections represent changes of state where potential energy is increasing but temperature is constant. Sloping sections represent temperature changes where kinetic energy is increasing.
解释加热曲线时，平台段表示物态变化，势能增加而温度不变；斜线段表示温度变化，动能增加。
3. Kinetic Theory of Gases and the Ideal Gas Equation | 气体动理论及理想气体方程
The ideal gas model assumes a large number of identical, randomly moving point particles. Collisions between particles and the container walls are perfectly elastic, there are no intermolecular forces except during collisions, and the volume of the gas particles themselves is negligible compared with the volume of the container.
理想气体模型假设大量相同、随机运动的点粒子组成气体；粒子之间以及粒子与容器壁的碰撞是完全弹性的；除碰撞瞬间外没有分子间作用力；气体粒子本身的体积相对于容器体积可忽略不计。
The macroscopic behaviour of an ideal gas is summarised by the equation of state pV = nRT, where n is the number of moles and R is the molar gas constant. This can also be written as pV = NkT, where N is the number of molecules and k is the Boltzmann constant.
理想气体的宏观行为可由状态方程 pV = nRT 概括，其中 n 为摩尔数，R 为摩尔气体常数。该方程也可写成 pV = NkT，其中 N 为分子数，k 为玻尔兹曼常数。
Kinetic theory also gives a microscopic link between pressure, volume and molecular speed. The root mean square speed c_rms is found from the relationship pV = ⅓ N m ⟨c²⟩, where m is the mass of one molecule. The average translational kinetic energy of a molecule is ½ m ⟨c²⟩ = (3/2) kT.
动理论还在微观上给出了压强、体积与分子速率之间的联系。均方根速率 c_rms 可通过 pV = ⅓ N m ⟨c²⟩ 求得，其中 m 为单个分子的质量。分子的平均平动动能为 ½ m ⟨c²⟩ = (3/2) kT。
pV = nRT = NkT and ½ m ⟨c²⟩ = (3/2) kT
For a fixed mass of ideal gas, you can apply pV/T = constant. At higher temperatures, the average molecular kinetic energy increases, so the root mean square speed increases. This explains why gas pressure rises at constant volume when temperature rises.
对于一定质量的理想气体，可以运用 pV/T = 常量。温度升高时，分子平均动能增大，均方根速率增大。这正是定容条件下温度升高导致气体压强增大的原因。
4. The First Law of Thermodynamics | 热力学第一定律
The first law of thermodynamics is a statement of energy conservation applied to a thermodynamic system. It can be written as ΔU = Q − W, where ΔU is the change in internal energy of the system, Q is the heat added to the system, and W is the work done by the system on its surroundings. Some specifications use ΔU = Q + W with W defined as work done on the system, so always check the sign convention used in your course.
热力学第一定律是能量守恒定律在热力学系统中的体现。可写作 ΔU = Q − W，其中 ΔU 为系统内能的变化，Q 为系统吸收的热量，W 为系统对外界做的功。某些课程使用 ΔU = Q + W，并把 W 定义为外界对系统做的功，因此务必确认你课程采用的符号约定。
There are four key processes to recognise: isothermal processes occur at constant temperature with ΔU = 0; adiabatic processes occur without heat transfer so Q = 0; isochoric processes occur at constant volume so W = 0; and isobaric processes occur at constant pressure. Each process has a distinct curve on a p–V diagram.
需要识别四种关键过程：等温过程温度不变，ΔU = 0；绝热过程不传热，Q = 0；等容过程体积不变，W = 0；等压过程压强不变。每种过程在 p–V 图上都有独特的曲线。
- Isothermal: ΔU = 0, so Q = W.
- 等温：ΔU = 0，因此 Q = W。
- Adiabatic: Q = 0, so ΔU = −W.
- 绝热：Q = 0，因此 ΔU = −W。
- Isochoric: W = 0, so ΔU = Q.
- 等容：W = 0，因此 ΔU = Q。
- Isobaric: pressure remains constant while volume changes.
- 等压：压强保持不变，体积发生变化。
ΔU = Q − W
In a gas expansion, the gas does work on its surroundings, so its internal energy may decrease unless heat is absorbed. In a rapid compression, the process is approximately adiabatic: work is done on the gas, increasing its internal energy and therefore its temperature.
气体膨胀时对外做功，如果不吸收热量，内能就会减小。在快速压缩过程中，过程近似绝热：外界对气体做功，使内能增大，温度随之升高。
5. Nuclear Decay, Activity and Half-Life | 核衰变、活度与半衰期
Radioactive decay is a random and spontaneous process in which an unstable nucleus emits radiation. Activity A is the number of decays per second and is measured in becquerels. It is related to the number of undecayed nuclei N by the equation A = λN, where λ is the decay constant.
放射性衰变是一种自发的随机过程，不稳定原子核会放出辐射。活度 A 表示每秒发生衰变的次数，单位是贝克勒尔。它与未衰变原子核数目 N 的关系为 A = λN，其中 λ 为衰变常数。
The number of undecayed nuclei follows an exponential decay law: N = N₀ e^(−λt), where N₀ is the original number of nuclei. Activity follows the same form: A = A₀ e^(−λt). The half-life t½ is the time taken for half of the original nuclei to decay, and it is given by t½ = ln 2 / λ.
未衰变核的数量遵循指数衰减规律：N = N₀ e^(−λt)，其中 N₀ 为初始核数。活度也遵循相同形式：A = A₀ e^(−λt)。半衰期 t½ 是初始核数衰变一半所需的时间，由 t½ = ln 2 / λ 给出。
A = λN and t½ = ln 2 / λ
There are three main types of radiation: alpha particles are helium nuclei, beta-minus particles are fast electrons, and gamma rays are high-energy photons. Alpha particles are the most ionising but least penetrating, while gamma rays are the most penetrating but least ionising.
辐射主要有三种类型：α 粒子是氦核，β⁻ 粒子是高速电子，γ 射线是高能光子。α 粒子的电离能力最强但穿透能力最弱，γ 射线的穿透能力最强但电离能力最弱。
| Radiation | Nature | Ionising power | Penetration |
|---|---|---|---|
| Alpha α | Helium nucleus | High | Stopped by paper or skin |
| Beta β⁻ | Fast electron | Medium | Stopped by thin aluminium |
| Gamma γ | Electromagnetic photon | Low | Reduced by thick lead |
Exponential decay is widely used in radioactive dating. Carbon-14 dating, for example, compares the remaining carbon-14 activity in a sample with the activity in living material to estimate the age of archaeological objects.
指数衰变广泛用于放射性测年。例如碳-14 测年法通过比较样品中剩余的碳-14 活度与活体中的活度，来估算考古文物的年代。
6. Simple Harmonic Motion Basics | 简谐运动基础
Simple harmonic motion is an oscillation in which the acceleration is directly proportional to the displacement from a fixed equilibrium position and always directed towards that equilibrium. The defining equation is a = −ω²x, where ω is the angular frequency and x is the displacement.
简谐运动是一种振动，其加速度与离开固定平衡位置的位移成正比，且总是指向平衡位置
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