CAIE IGCSE物理 能量 功 功率 效率 能源
剑桥 IGCSE 物理 0625 把能量、功与功率放在 Topic 1 的 1.7 节，编号从 1.7.1 到 1.7.4，四小节分别是能量、功、能源与功率。这一节的分值来源不集中：选择题里常有一到两道判断能量储存与转移的题，结构题里则常有一道给图和数据进行计算的小题。Core 与 Extended 在这里的差别不在概念，而在动能公式与重力势能公式只写在 Supplement 里，Core 考生的计算题只走到功与功率。文中所有编号、卷面分值、公式口径都以 Cambridge 官方 0625 syllabus（2026、2027、2028 年考试适用，version 1，2023 年 9 月发布）为准，阅卷侧的常见错误引 CAIE 2026 年 3 月 Principal Examiner Report。
Topic 1.7 of Cambridge IGCSE Physics 0625 covers energy, work, energy resources and power as four consecutive sub-sections, and the marks arrive in two different shapes: a multiple-choice item that asks you to classify a store or a transfer, and a structured part that hands you a diagram and a set of numbers. The tier difference is narrow but real, because the kinetic and gravitational potential energy equations sit in the Supplement while work and power are examined at both tiers. Codes, mark weights and equation wording below follow the Cambridge 0625 syllabus for exams in 2026, 2027 and 2028, with examiner observations taken from the March 2026 Principal Examiner Report.
1.7 在三张卷上的位置与分值
1.7 不占任何一张独立的卷子，它落在选择题与结构题里，而且两级考生的卷面结构一样。所有考生考三张卷：Core 考生考 Paper 1（45 分钟、40 分、40 道四选一、占 30%）与 Paper 3（1 小时 15 分钟、80 分、占 50%），Extended 考生考 Paper 2 与 Paper 4，时长与分值完全相同，只是内容含 Supplement。剩下的 20% 来自 Paper 5 实验卷（1 小时 15 分钟、40 分）或 Paper 6 笔答替考（1 小时、40 分），二选一。整科的评估目标权重是 AO1 占 50%、AO2 占 30%、AO3 占 20%，而在 Paper 1 与 Paper 2 内部 AO1 占 63%、AO2 占 37%，Paper 5 与 Paper 6 则是 100% 的 AO3。这意味着同一道能量题，选择题考的是判断，结构题考的是代入与单位。很多学生以为 1.7 只出计算，实际上能源取舍的描述题也挂在编号之下。Core 考生最高只能拿到 C 等级，Extended 考生从 A* 到 G 都有。
The energy block does not own a paper of its own; it is spread across the multiple-choice component and the theory component, and the shape of the assessment is identical at both tiers. All candidates sit three papers: Core candidates take Paper 1 (45 minutes, 40 marks, 40 four-option questions, 30%) and Paper 3 (1 hour 15 minutes, 80 marks, 50%), while Extended candidates take Paper 2 and Paper 4 with the same timings and weights; the final 20% comes from either Paper 5 (1 hour 15 minutes, 40 marks) or Paper 6 (1 hour, 40 marks). Inside Papers 1 and 2 the objectives split as AO1 63% and AO2 37%, and the practical papers are entirely AO3, so the same energy topic is tested once as a judgement and once as a substitution with units. Core candidates are eligible for grades C to G, Extended candidates for A* to G.
七类能量储存与四种转移方式
大纲 1.7.1 列出七类能量储存：动能、重力势能、化学能、弹性（应变）能、核能、静电能与内能（热能）。判断一道题在考储存还是转移，看动词：说某物体 possesses 或 stored as，问的是储存；说 transferred from A to B，问的是转移。1.7.1 同时给出四种转移方式：力做功（机械功）、电流做功（电功）、加热，以及电磁波、声波和其他波。很多学生以为电池里存的是电能，CAIE 2026 年 3 月的报告里明确写了考生最常见的误解就在这里，电池里存的是化学能，转移出去以后才是电能。放射线与声波在城市噪声里都属于波的形式转移能量，而摩擦生热属于力做功之后的加热。做题时先给每个物体贴一个储存标签，再判断两两之间发生的是哪一种转移，比直接猜答案稳得多。
Section 1.7.1 lists seven stores, namely kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic and internal (thermal), and the wording of the question separates a store from a transfer. Four transfers are examined: mechanical work done by a force, electrical work done by a current, heating, and waves such as electromagnetic, sound and other wave types. In the March 2026 report examiners noted that candidates who called the battery store electrical rather than chemical lost the mark, and the same report recorded light energy described as going to the surroundings where only thermal transfer took place.
能量守恒与流程图读法
1.7.1 的第三条要求是知道能量守恒原理，并能用它解释简单的能量流程图。守恒的意思不是能量总量在某个装置里保持不变，而是总能量在转移与转化过程中不会消失，只是分成了有用输出与耗散输出两部分。读流程图时先看输入框的气泡大小，气泡大的一方分到的能量多，再看输出框分成几个箭头，箭头数量就是耗散渠道的数量。Sankey 图在 Extended 才要求解释，Core 只需要处理简单的流程图。常见的错误是把流程图里的箭头方向读反，把从装置流向环境的耗散能量当成输入。题面给 500 J 输入、320 J 有用输出时，剩下的 180 J 全部属于耗散，不需要再减一次。
The conservation principle in 1.7.1 is applied through flow diagrams rather than stated as a slogan: total energy is not lost, it is shared between a useful output and one or more dissipated outputs. Reading a diagram starts with the width of each band and ends with the number of outgoing arrows, because each extra arrow is another dissipation route. Sankey diagrams are only required in the Supplement, and the usual slip is to read a dissipation arrow as an input.
动能 Ek = 1/2 m v^2 的两级差别
动能公式 Ek = 1/2 m v^2 排在 1.7.1 的 Supplement 里，也就是说 Core 考生不需要用它算题，但 Extended 考生必须会用。公式里速度取平方，所以速度翻倍时动能变成四倍：1200 kg 的汽车以 15 m/s 行驶时动能是 135000 J，以 30 m/s 行驶时是 540000 J，正好四倍，这也是高速公路限速与刹车距离讨论里最常用的一组数字。算一个 0.15 kg 的球以 8.0 m/s 飞行，代入后是 0.5 乘 0.15 乘 64，得 4.8 J，单位写 J 不写 m/s。学生最常把 v^2 当成 v 乘 2，或者忘记先换成 kg 与 m/s 再平方。阅卷时公式分与答案分分开给，写出 Ek = 1/2 m v^2 并标明 m 与 v 的取值，即使最后一步算错也能保住前面的分。
Kinetic energy sits in the Supplement, so Extended candidates are expected to recall and use Ek = 1/2 m v squared while Core candidates are not examined on it. The square matters more than the halving, since doubling the speed quadruples the energy; a 1200 kg car carries 135000 J at 15 m/s and 540000 J at 30 m/s, which is exactly the four-fold jump the equation predicts. A 0.15 kg ball at 8.0 m/s gives 4.8 J, and the mark scheme rewards the substituted equation before it rewards the number.
重力势能 ΔEp = mgΔh 与 g 的取值
重力势能的变化量 ΔEp = mgΔh 同样在 Supplement 里，注意符号是变化量，所以要用高度的差值而不是高度本身。g 在 0625 里取 9.8 m/s^2，这是 syllabus 1.1 节写明的自由落体加速度近似值，题目给了 10 就用 10，没给就按 9.8 算。把 2.0 kg 的物体举高 1.5 m，代入 2.0 乘 9.8 乘 1.5 得 29.4 J；一个 60 kg 的学生爬上 3.0 m 高的平台，势能增加 1764 J。很多学生以为向下运动时势能公式不能用，实际上下落时 Δh 取负值，算出来是负的势能变化，与动能增加正好对上。常见的错误是把 h 写成物体的总高度而不是前后高度差，斜面题里尤其明显。错得最多的是把质量当成重量，报告里就记录了考生把 mass 说成 the weight of the object 而丢分的例子。
The change in gravitational potential energy follows the same pattern: it is a difference, so the height in the equation is the vertical change rather than the final height. The syllabus gives g near the Earth as approximately constant at 9.8 m/s squared, so a 2.0 kg object raised 1.5 m gains 29.4 J, and a 60 kg student climbing 3.0 m gains 1764 J; the March 2026 report shows mass and weight descriptions are still confused, with mass defined as the weight of the object and weight described merely as gravity acting on it.
功 W = Fd = ΔE 与没有位移就没有功
1.7.2 的定义很短：机械功或电功等于转移的能量，公式 W = Fd = ΔE，两个等号都要求会写。用 40 N 的水平力把物体沿力的方向推动 2.5 m，做功 100 J，这 100 J 同时就是物体获得的能量。判断有没有做功，看力与位移是否同向：把书包提在手里站在原地，力有、位移没有，做功为零；把书包提起来沿直线走，竖直方向的力与水平位移垂直，那一段竖直力也不做功。很多学生以为只要用力就一定做功，于是把静止托举算成做了功。题目里出现斜面时，先分解出沿斜面的分力再乘位移，否则 F 会用错。阅卷时单位写 N m 与写 J 都算对，但把功写成 W 会与功率混淆。
Work done is defined as the energy transferred, written W = Fd = ΔE, and the equality of the two forms is itself examined. A 40 N push along 2.5 m transfers 100 J, while holding a bag still transfers nothing because the displacement is zero and a vertical force carried along a horizontal path transfers nothing either. On a slope the force must be resolved along the direction of travel before it is multiplied by the distance.
功率 P = W / t = ΔE / t
1.7.4 把功率定义为每单位时间所做的功，也定义为每单位时间转移的能量，两条公式 P = W / t 与 P = ΔE / t 要能互换使用。100 J 的功在 5 s 内完成，功率是 20 W；把 1764 J 的势能在 6 s 内交出去，平均功率是 294 W。功率单位是瓦特，1 W 等于 1 J/s，所以看到 kW 要记得乘 1000 再代。电功场景里 2000 W 的电水壶工作 180 s，消耗 360000 J，折合 0.1 kWh，1 kWh 等于 3.6 乘 10^6 J。学生最常把功率与能量混着写，题目问功率却交出焦耳。阅卷时 2 分的功率题通常一分给公式、一分给答案与单位，单位漏写会停在 1 分。
Power is defined twice in 1.7.4, once as work done per unit time and once as energy transferred per unit time, and the two equations convert freely into each other. Doing 100 J of work in 5 s gives 20 W, and releasing 1764 J of potential energy over 6 s gives an average 294 W; a 2000 W kettle running for 180 s transfers 360000 J, which is 0.1 kWh because one kilowatt-hour equals 3.6 million joules. Marks in a two-mark power question are normally split between the equation and the answer with its unit.
效率的两条公式与百分数写法
1.7.3 把效率定义成有用输出与总输入之比再乘 100%，并且给了能量与功率两个版本：(% efficiency) = (useful energy output) / (total energy input) 乘 100%，以及 (% efficiency) = (useful power output) / (total power input) 乘 100%。两个版本都要求 recall and use，也就是公式本身不会印在卷面上。CAIE 2026 年 3 月报告里有一道太阳能板题，考生用输出的 0.40 A 与 7.0 V 相乘得到功率输出 2.8 W，这一步做对的人不少，卡住的人把电压除以电流。若同一块板的总输入功率是 8.0 W，效率就是 2.8 除以 8.0 再乘 100%，得 35%，写 0.35 会被扣掉百分号那一步。60 W 的白炽灯换成 9 W 的 LED，同样亮度下只用 15% 的功率。常见的错误是把效率算成输出比输入加输出，或者把百分数写成小数后忘记乘 100。
Efficiency is defined in 1.7.3 as useful output divided by total input, expressed as a percentage, and both the energy and the power versions must be recalled rather than read from the paper. In the March 2026 solar panel question candidates who multiplied 0.40 A by 7.0 V reached the 2.8 W output, while those who divided voltage by current did not; against an 8.0 W input that output gives 35%, and a 9 W LED replacing a 60 W filament lamp uses 15% of the power for the same light.
七类能源与锅炉、汽轮机、发电机
1.7.3 要求能用七类来源获得有用能量或发出电：化石燃料里的化学能、生物燃料里的化学能、水（包括波浪、潮汐与水电大坝储存的能量）、地热、核燃料、用太阳光发电的太阳能电池，以及用红外与其他电磁波加热水的太阳能热水器并作为风能的来源。Core 要求提到锅炉、汽轮机与发电机，也就是燃料或热源把水变成蒸汽，蒸汽推动汽轮机，汽轮机带动发电机。同一套装置在不同能源下差别只在热源：化石燃料烧锅炉，核燃料用裂变放热，地热直接取地下热。波浪与潮汐用水的运动推动涡轮，太阳能电池则跳过锅炉直接把光变成电。很多学生以为太阳能热水器也发电，实际上它只把水加热。写装置链条时把三个词按顺序写全，缺一个就少一个给分点。
Seven energy sources are listed for producing useful energy or generating electricity: chemical energy in fossil fuels, chemical energy in biofuels, water including waves, tides and hydroelectric dams, geothermal resources, nuclear fuel, solar cells converting sunlight to electricity, and solar panels using infrared and other electromagnetic waves to heat water, with wind treated as a consequence of solar heating. The Core wording expects the boiler, turbine and generator chain, in which a heat source raises steam that drives a turbine coupled to a generator. Nuclear fuel substitutes fission heat for combustion, geothermal takes heat from the ground, and solar cells skip the boiler entirely.
取舍五个维度与阅卷措辞
1.7.3 的第二条要求是按五个维度比较各方法的优缺点：renewability（可再生性）、availability（可获得性）、reliability（可靠性）、scale（规模）与环境影响。这五个词就是评分方案里的关键词，答案要落到具体装置上，写 environmental friendly 或 eco-friendly 太笼统。CAIE 2026 年 3 月报告里那道理太阳能板题，得分的答案都在谈这块板本身的可再生性与环境负担，丢分的答案要么写成泛泛的环保，要么挑了一个与图中装置无关的缺点，例如占地太大。风能与太阳能的可获得性受天气限制，水电与潮汐的亮点是稳定输出。化石燃料与核燃料属于不可再生，后者的问题是废料处置。常见的错误是把可靠性说成可再生性，两者的判据完全不同。
The advantages and disadvantages of each method are compared on five named grounds: renewability, availability, reliability, scale and environmental impact, and those five words are the ones the mark scheme looks for. In the March 2026 solar panel question the credited answers discussed the renewability and the environmental burden of that specific panel, while responses that offered only environmentally friendly or eco-friendly gained little, and a disadvantage unrelated to the panel shown, such as land area, gained nothing. Reliability and renewability are separate judgements, since a renewable source can still be intermittent.
太阳是几乎所有能源的源头与三类例外
Supplement 里有一条容易被忽略的要求：来自太阳的辐射是所有能源的主要来源，例外只有地热、核能与潮汐三类。原因是化石燃料、生物燃料、风、波浪与太阳能本身都由太阳的能量驱动，而潮汐来自月球与太阳的引力作用加上地球自转。同一节还要求知道太阳的能量来自核聚变，并知道目前正在研究如何把聚变释放的能量大规模用来发电，也就是说聚变发电还没有进入商业运行。很多学生以为核燃料的能量也来自太阳，核裂变与聚变都不依赖太阳。写理由时把三类例外一次写全，比只写一个地热更容易拿满分。常见的错误是把潮汐算进太阳能驱动的一类，因为月亮才是潮汐的主要推手。
The Supplement adds one statement that is easy to skip: radiation from the Sun is the main source of energy for all our energy resources except geothermal, nuclear and tidal. Fossil fuels, biofuels, wind, waves and solar devices all trace back to solar radiation, while tides come from the gravitational pull of the Moon and the Sun acting on a rotating Earth. The same section states that the Sun releases energy by nuclear fusion and that research continues into producing electrical energy from fusion on a large scale, which confirms fusion power is not yet in commercial use.
阅卷常见错误与三周复习排期
CAIE 2026 年 3 月报告在 1.7 相关的几道题里记录了四类失分动作：把电池的储存写成电能而不是化学能，把功率算成电压除以电流，用太笼统的词描述能源优缺点，以及把质量说成重量。复习时第一周把七类储存与四种转移各写一张对照表，把电池、弹簧、水坝、食物四类物品的储存标签写准；第二周练功、功率与效率三组计算，每道题都写出公式、代入与单位三行；第三周做能源取舍的短答题，每道题强制写满五个维度中的两个具体点。很多学生把三周全花在计算上，描述题的措辞分反而一直没捡。每天十分钟读一遍自己做错的题，比再刷一套新卷有效。把 2.8 W、294 W、35% 这三个数字记牢，它们在真题里反复出现。
The March 2026 report records four recurring losses on this block: calling the battery store electrical, dividing voltage by current to find power, describing energy resources with vague words, and defining mass as weight. A three-week plan assigns the first week to the seven stores and four transfers, the second to worked calculations in work, power and efficiency, and the third to resource-comparison answers that name at least two of the five grounds each time.
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