📚 Principle of Conservation of Energy | 能量守恒原理
Energy is a fundamental concept in physics that governs every change in the universe. For IGCSE Edexcel Science students, mastering the principle of conservation of energy is essential to understanding how systems behave, from a simple pendulum to power stations. This article unpacks the core ideas, mathematical treatments and practical applications of energy conservation, following the Edexcel specification.
能量是物理学中支配一切变化的基础概念。对IGCSE Edexcel 科学考生而言，掌握能量守恒原理对于理解从单摆到发电厂的各种系统行为至关重要。本文将紧扣Edexcel考纲，深入剖析能量守恒的核心思想、数学处理与实际应用。
1. What is Energy? | 什么是能量？
Energy is a scalar quantity that gives an object the ability to do work or cause a change. It is measured in joules (J), where 1 joule is the work done when a force of 1 newton moves an object 1 metre in the direction of the force. Energy is not a substance – it is a property that can be stored or transferred.
能量是一个标量，它赋予物体做功或引起变化的能力。能量的单位是焦耳（J），1焦耳相当于1牛顿的力使物体沿力的方向移动1米所做的功。能量并非一种物质，而是一种可被储存或转移的属性。
In everyday language we say we ‘use’ energy, but scientifically energy is never used up. When a torch shines, the chemical energy store of the battery decreases, but the total energy of the battery, bulb and surroundings remains constant. The energy is simply transferred to light and thermal stores.
日常语言中我们说“用掉”能量，但科学上能量永远不会被耗尽。当手电筒发光时，电池的化学能储存减少了，但电池、灯泡与周围环境的总能量保持不变，能量只是转移到了光能和热能的储存中。
2. The Principle of Conservation of Energy | 能量守恒原理
The principle states: Energy can be transferred usefully, stored or dissipated, but it cannot be created or destroyed. In a closed system, the total energy before any change is equal to the total energy after the change. This law allows us to predict what happens during energy transfers without losing track of any joules.
能量守恒原理指出：能量可以被有效转移、储存或散逸，但绝不能被创造或消灭。在一个封闭系统中，任何变化前的总能量等于变化后的总能量。这条定律使我们能在能量转移过程中进行预测，而不会遗失任何焦耳的能量。
Consider a roller coaster climbing a slope. As it gains height, kinetic energy decreases and gravitational potential energy increases. The sum of the two energies, if friction is negligible, remains constant. In reality, some energy is transferred to thermal stores due to friction, but the total energy of the universe still obeys conservation.
设想一辆过山车爬坡。随着高度增加，动能减少，重力势能增加。如果摩擦力可以忽略，两种能量之和保持不变。现实中，由于摩擦，总会有部分能量转移到热能的储存，但宇宙的总能量依然遵从守恒定律。
3. Forms of Energy | 能量的形式
Energy can be stored in various forms. The Edexcel specification expects you to recognise these stores and describe how energy can move between them. Below is a table of the most common energy stores examined in IGCSE Science.
能量可以多种形式储存。Edexcel考纲要求你识别这些储存库，并描述能量如何在它们之间转移。下表列出了IGCSE科学中考查的最常见能量储存形式。
| Energy Store | 中文能量形式 | Description |
|---|---|---|
| Kinetic energy | 动能 | Energy of a moving object |
| Gravitational potential energy | 重力势能 | Energy due to position in a gravitational field |
| Elastic potential energy | 弹性势能 | Energy stored in stretched or compressed objects |
| Thermal (internal) energy | 热能（内能） | Energy associated with temperature and particle motion |
| Chemical energy | 化学能 | Energy stored in chemical bonds, released in reactions |
| Electrical energy | 电能 | Energy transferred by moving charges |
| Light (radiant) energy | 光能（辐射能） | Energy carried by electromagnetic waves |
| Nuclear energy | 核能 | Energy stored in the nucleus of an atom |
All these stores can be increased or decreased by energy transfers. For instance, lifting a book increases its gravitational potential energy store, while the kinetic store of the lifting hand decreases as the work is done.
所有这些能量储存都可以通过能量转移而增大或减小。例如，把一本书举高，其重力势能储存增加，而做功的手的动能储存则有所减少。
4. Energy Transfers and Transformations | 能量转移与转化
Energy is transferred between stores by one of four main pathways: mechanical work (a force moving through a distance), electrical work (charges moving through a circuit), heating (temperature difference), and radiation (electromagnetic waves or sound). In any device, we can trace the energy pathway from the input store to the output stores.
能量通过四种主要途径在储存库之间转移：机械做功（力使物体移动一段距离）、电做功（电荷在电路中移动）、加热（存在温差）和辐射（电磁波或声波）。在任何装置中，我们都可以追踪能量从输入储存到输出储存的途径。
A filament lightbulb is a classic IGCSE example. The input is electrical energy transferred from the mains. This is transferred to the light and thermal stores of the surroundings. Only about 10% of the input energy is transferred usefully as light; the rest is dissipated as heat. This energy is not destroyed – it simply spreads out and becomes harder to use.
白炽灯泡是IGCSE的经典例子。输入的是从电源转移来的电能，这些能量转移到周围环境的光能和热能储存中。只有大约10%的输入能量以光的形式被有效转移，其余都以热能散逸。能量并未被消灭，只是耗散到环境中，变得难以利用。
5. Sankey Diagrams | 桑基图
A Sankey diagram is a visual representation of energy transfers. The width of each arrow is proportional to the amount of energy it represents. A thick arrow entering from the left shows the total input energy; branching arrows to the right show the useful output energy and the wasted energy. These diagrams must be drawn to scale for accuracy in Edexcel exams.
桑基图是能量转移的直观图示。每个箭头的宽度与它所代表的能量数额成正比。从左端进入的粗箭头表示总输入能量，向右分支的箭头分别表示有用输出能量和浪费的能量。在Edexcel考试中，绘制桑基图必须按比例，以确保准确性。
For a modern LED bulb, the Sankey diagram shows a much wider useful light arrow than a filament bulb, indicating higher efficiency. The wasted energy arrow, going to thermal stores, is much narrower. Therefore, less energy is dissipated as heat.
对于现代LED灯泡，桑基图中代表有用光能的箭头比白炽灯泡宽得多，表明效率更高。代表浪费到热能储存的箭头则窄得多，因此以热量散逸的能量更少。
6. Energy Efficiency | 能量效率
Efficiency is the ratio of useful output energy transfer to total input energy transfer. It can be expressed as a decimal or a percentage.
效率是指有效输出的能量转移与总输入能量转移的比值，可以用小数或百分数表示。
Efficiency = (Useful energy output / Total energy input) × 100%
No real device is 100% efficient because some energy is always transferred to less useful stores, usually thermal. A petrol engine may have an efficiency of only 25%; the rest of the energy heats the engine and exhaust gases. In IGCSE questions, you may be asked to calculate efficiency from given energy values or compare devices.
没有实际装置的效率能达100%，因为总有一部分能量转移到不太有用的储存，通常是热能。一台汽油发动机的效率可能只有25%，其余能量用于加热发动机和废气。在IGCSE题目中，你可能需要根据给定的能量值计算效率，或比较不同装置的效率。
7. Gravitational Potential Energy | 重力势能
Gravitational potential energy (Eₚ) is the energy stored in an object because of its height above the ground. It is given by the equation:
重力势能（Eₚ）是因物体离地高度而储存的能量，其计算公式为：
Eₚ = m × g × h
where m is mass (kg), g is gravitational field strength (N/kg) – 10 N/kg on Earth, and h is height (m). The energy unit remains the joule (J). If a 5 kg cat climbs a 2 m shelf, the gain in gravitational potential energy is 5 × 10 × 2 = 100 J.
式中m为质量（千克），g为重力场强度（牛/千克，地球表面取10 N/kg），h为高度（米）。能量单位仍是焦耳（J）。若一只5千克的猫爬上2米高的架子，增加的重力势能为5 × 10 × 2 = 100 J。
When an object falls and no external forces do work, the decrease in Eₚ equals the increase in kinetic energy. This trade-off is the basis of many conservation problems.
当物体下落且没有外力做功时，重力势能的减少等于动能的增加。这种此消彼长是许多守恒问题的基础。
8. Kinetic Energy | 动能
Kinetic energy (Eₖ) is the energy an object possesses due to its motion. The faster it moves, the greater the kinetic store. The equation is:
动能（Eₖ）是物体由于运动而具有的能量。物体运动越快，动能储存越大。公式为：
Eₖ = ½ × m × v²
where m is mass (kg) and v is speed (m/s). Notice that kinetic energy depends on v², so doubling the speed quadruples the kinetic energy. A 1000 kg car travelling at 10 m/s has Eₖ = ½ × 1000 × 10² = 50 000 J.
式中m为质量（千克），v为速度（米/秒）。注意动能依赖v²，因此速度加倍时动能变为原来的四倍。一辆1000千克的汽车以10米/秒行驶时，动能 Eₖ = ½ × 1000 × 10² = 50 000 J。
9. Conservation in Mechanical Systems | 机械系统中的守恒
When air resistance and friction are negligible, mechanical energy (sum of kinetic and gravitational potential energy) is conserved. This allows us to predict speed or height in falling objects, pendulums or roller coasters. For a pendulum bob at its highest point, all the energy is Eₚ; at the lowest point, all the energy is Eₖ.
当空气阻力和摩擦力可忽略时，机械能（动能与重力势能的总和）保持守恒。这使我们能预测落体、摆锤或过山车的速度或高度。摆锤在最高点时能量全部为Eₚ，最低点则全部为Eₖ。
mgh = ½mv²
Cancelling m and rearranging yields v = √(2gh). This shows that the final speed depends only on height, not mass. For a drop of 5 m, v = √(2 × 10 × 5) = √100 = 10 m/s.
消去m并整理可得 v = √(2gh)。这说明最终速度只取决于高度，与质量无关。一个5米的下落，v = √(2 × 10 × 5) = √100 = 10 米/秒。
10. Work Done and Energy Transfer | 做功与能量转移
Work is done whenever a force moves an object. The work done (W) equals the energy transferred. The equation is:
只要力使物体移动，就做了功。所做的功（W）等于转移的能量。公式为：
W = F × d
where F is the force (N) and d is the distance moved in the direction of the force (m). Work and energy are both measured in joules. Pushing a crate with a force of 50 N over 3 m transfers 150 J energy to kinetic and thermal stores (due to friction).
式中F为力（牛），d为沿力的方向移动的距离（米）。功和能量都用焦耳度量。用50牛的力推动一个板条箱移动3米，将150 J的能量转移到动能和（因摩擦产生的）热能储存。
11. Practical Examples | 实际案例
Bungee jumping: At the top of the jump, the jumper has maximum Eₚ. As they fall, Eₚ decreases and Eₖ increases until the cord tightens. Then Eₖ is transferred to elastic potential energy, which temporarily stores the energy before bouncing back. Throughout the cycle, total energy is conserved.
蹦极：跳跃最高点，跳跃者具有最大重力势能。下落过程中，Eₚ减少，Eₖ增加，直至绳索绷紧。然后Eₖ转移到弹性势能，在回弹前短暂储存能量。整个循环中总能量守恒。
Battery-powered torch: Chemical energy in the battery → electrical energy → light energy + thermal energy. The thermal energy is inevitably dissipated because the bulb and circuit resistances heat up.
电池供电的手电筒：电池中的化学能 → 电能 → 光能 + 热能。由于灯泡和电路电阻会发热，热能耗散不可避免。
Hydroelectric power: Water stored in a dam has Eₚ. As it flows downhill, Eₚ is transferred to Eₖ, which then turns turbines to generate electrical energy via electromagnetic induction.
水力发电：水坝中储存的水具有重力势能。水向下流动时，Eₚ转为Eₖ，再驱动水轮机旋转，通过电磁感应产生电能。
12. Exam Tips | 考试技巧
When tackling energy questions in Edexcel IGCSE Science, always start by identifying the energy stores at the beginning and end of the process. Name the stores clearly, using terms like ‘thermal store’ rather than just ‘heat’. For calculations, write down the relevant formula and substitute values with units. Check that your answers are sensible – efficiency must be between 0 and 1 (or 0% and 100%).
在处理Edexcel IGCSE科学的能量题目时，首先要明确过程始末的能量储存。清楚命名储存，如使用“热能储存”而不只是“热”。计算时，写下相关公式并代入含单位数值。检查答案是否合理——效率必须在0到1之间（或0%到100%）。
In Sankey diagram questions, use a ruler and draw arrows proportional to the energy values. Label each arrow with the amount of energy and with the store name. And remember: if a question mentions a ‘closed system’ or ‘negligible resistance’, you can apply conservation of mechanical energy directly to find unknowns.
在桑基图题中，使用直尺绘制与能量值成比例的箭头。在每个箭头上标注能量数值和储存名称。请记住，若题目提及“封闭系统”或“阻力可忽略”，你可直接利用机械能守恒求解未知量。
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