WJEC GCSE物理 Energy 能量守恒 比热容 功率
WJEC 的 GCSE Physics 里，energy 不是在某一章讲完的。Unit 1.3 讲热传递与房屋保温的成本效益，Unit 1.4 讲家庭用电的电费与保险丝，Unit 1.8 讲比热容与潜热，Unit 2.3 讲做功、动能与重力势能。很多学生以为 energy 只属于 Unit 1，于是在 Unit 2 的 Work and energy 上丢掉整题的分。公式其实不多，麻烦的是同一个词在不同单元对着不同的公式。这篇按四个位置串起来讲：公式从哪里来、卷面怎么考、单位与有效数字怎么处理，以及每年重复出现的失分点。先把 Unit 1 与 Unit 2 的分工记住，再谈计算。
Energy in WJEC GCSE Physics is not confined to one chapter. Heat transfer and the cost of insulation sit in Unit 1.3, domestic electricity and running costs in Unit 1.4, specific heat capacity and latent heat in Unit 1.8, and work, kinetic energy and gravitational potential energy in Unit 2.3. Many students revise energy for Unit 1 only and then meet the same word again in Unit 2 attached to a different set of formulae. This article follows the topic across those four locations and points out where marks are usually lost.
能量守恒、Sankey 图与效率公式
能量守恒在 spec 2.3(a) 里的说法是：力作用在运动的物体上，能量会被转移，但能量总量保持不变。做题时看到的从来不是能量消失，而是能量转到用处不大的地方，比如摩擦生热、声音、空气阻力。Sankey 图把输入画成一条粗箭头，有用输出画成细箭头，其余分支就是损耗。效率的算法写在 spec 1.2(d)：有用转移的能量或功率，除以总输入，再乘 100%。很多学生以为效率只能算机器，其实保温、发电、输电都能算。常见的错误是分子分母搞反，或者拿功率去除能量，单位没统一就下笔。功率和能量是两个量，比值要成立，两边必须同族。
Efficiency is defined in the specification as the useful energy or power transferred divided by the total energy or power supplied, multiplied by 100. A Sankey diagram makes the losses visible: the wide arrow is the input, the narrower arrow is what the device actually delivers, and the remaining branches are dissipation to thermal energy in the surroundings, sound and air resistance. Many students lose marks by inverting that fraction, or by dividing a power by an energy before converting units, so match the two units first and the arithmetic becomes routine.
传导 对流 辐射：热传递的三条路径
spec 1.3(a) 要求用温度差解释热量的三种传递方式。传导靠分子振动一层层往下传，金属里还有自由电子，所以铜和铝比木头快得多，1.3(c) 专门点名了 mobile electrons 这个模型。对流只发生在液体和气体里：受热部分体积变大、密度变小而上升，冷的部分补位，形成循环。辐射不需要介质，太阳的热量穿过真空落到地面靠的就是它。学生最常把对流的成因说成热空气往上升，而漏掉密度差这个理由，阅卷时这句话拿不到分。把三者的媒介、是否需要流动、能否穿过真空写清楚，比较题就稳。1.3 还有两个指定实验：热传递方式的探究，以及规则与不规则固体、液体的密度测定。
Conduction transfers energy through particle vibrations, and metals do it far better because they also contain mobile electrons, a phrase the specification uses directly; convection happens only in liquids and gases, where the heated region expands, becomes less dense and rises while cooler fluid moves in to take its place. Radiation needs no medium at all, which is why energy from the Sun crosses the vacuum of space. Examiners see the same weak answer every year, hot air rises, with no mention of density even though the density difference is the reason the circulation starts. Two specified practicals belong to this topic, on methods of heat transfer and on determining the density of regular and irregular solids and of liquids.
房屋保温的 payback time 与成本效益
spec 1.3(e) 列了四种常见的家庭保温手段：阁楼保温棉、双层玻璃、空腔墙保温、门窗密封条。1.3(f) 要的不是哪种最省能，而是哪种最划算，做法是用数据算 payback time：安装成本除以每年省下的燃料费，单位是年。很多学生以为材料越贵越值，卷面常给一张成本与年节省费用的表，让你比较四种方案的回收期。算出来的年数越小，回本越快，这跟效率高低是两个问题。常见的错误是拿总节省额去除成本，或者把成本与年节省的单位混掉。1.3(g) 还要求比较不同能源用于供暖与交通的成本，表里通常带一个效率百分比，先把每千瓦时多少钱换算成每有用千瓦时多少钱，口径才可比。计算器按出来的数字要带单位，答案写成 "3.5 年" 而不是 "3.5"。
The specification lists loft insulation, double glazing, cavity wall insulation and draught excluders as the standard ways of cutting heat loss from a house. Unit 1.3 asks which measure is the most cost effective rather than which saves the most energy, and the tool is payback time, installation cost divided by the annual fuel saving, answered in years. A question will usually supply a table of costs and annual savings, and the smallest number of years is the fastest payback, which is a different question from how efficient the measure is. When comparing fuels for heating and transport, apply the efficiency percentage first so that the comparison is made per useful kilowatt hour rather than per kilowatt hour supplied.
做功 动能与重力势能：W = Fd, KE = ½mv², PE = mgh
Unit 2.3 的核心是三个公式：W = Fd、KE = ½mv²、PE = mgh。做功只在力的方向上有位移时才发生，把箱子竖直提起和水平推着走，代入的距离完全不同。动能与速度是平方关系，一辆 1200 kg 的汽车从 10 m/s 加速到 20 m/s，动能从 60000 J 涨到 240000 J，速度翻倍、动能翻四倍。这也是刹车距离随车速迅速拉长的原因。重力势能里的 g 取多少，WJEC 的 spec 2.2(e) 给了明确近似：地球上质量 1 kg 的物体重量约 10 N，所以 W = mg 与 PE = mgh 按 g = 10 N/kg 算。错得最多的是把质量当重量代入，或者算 PE 时用了绝对高度而不是高度变化量。弹簧部分还有 F = kx 与 W = ½Fx，后者只在线性关系下成立，非线性就要数 F-x 图下的格子。
Unit 2.3 supplies the three equations that turn up on every paper: work done equals force times distance moved in the direction of the force, kinetic energy is half times mass times velocity squared, and gravitational potential energy is mass times field strength times change in height. Doubling speed quadruples kinetic energy, so a car braking from 20 m/s has four times the energy to shed compared with one braking from 10 m/s, and that is why stopping distances grow so quickly with speed. For weight and potential energy this specification takes the approximation that a 1 kg mass weighs 10 N at the Earth's surface, so use g = 10 N/kg unless a question states otherwise. Springs add F = kx and W = ½Fx, where the second expression only holds for a linear force-extension graph; when the line bends, count squares under the graph instead.
比热容 Q = mcΔθ 与潜热 Q = mL
比热容出现在 Unit 1.8，公式是 Q = mcΔθ，其中 c 的单位是 J/(kg °C)，Δθ 就是温度变化量。水的比热容是 4200 J/(kg °C)，铜大约 385 J/(kg °C)，同样质量、同样升温，水要吸走十倍以上的热量，所以海边昼夜温差比内陆小。潜热是另一条公式 Q = mL，熔化与沸腾时温度保持不变，吸走的热量全部用于改变状态，这两个量和比热容经常混在一个大题里考。测定比热容是 spec 1.8 的指定实验，卷面会给实验数据让你算 c，再问误差来源，比如热量散失到空气里。常见的错误是 Δθ 用错起点，或者把 mL 里的 L 当成长度。把升温段与状态变化段分开算再相加，这类题就只剩代入。
Specific heat capacity appears in Unit 1.8 as Q = mcΔθ, where c is measured in joules per kilogram per degree Celsius and Δθ is the temperature change. Water requires 4200 J to raise the temperature of 1 kg by 1 °C while copper needs only about 385 J, which is why coastal areas show smaller day to night temperature swings than inland ones. Latent heat is a separate equation, Q = mL, and during melting or boiling the temperature stays constant because the energy supplied changes the state instead of the temperature. The determination of specific heat capacity is one of the specified practicals, so questions often supply experimental data and then ask you to evaluate the method and the losses to the surroundings; two traps catch students here, taking the wrong starting temperature for Δθ and reading L in Q = mL as a length.
家庭用电：kWh 电费与保险丝额定值
家用电器的功率用 kW 表示，电能单位用 kWh，spec 1.4(a)(b) 的两条公式是 units used = power x time 与 cost = units x cost per unit。一只 2000 W 的电水壶烧五分钟，耗电 2 kW 乘 5/60 h，约 0.17 kWh，再乘题目给出的每度电价就是这次烧水的成本。1.4(c) 要求用能耗等级 A 到 G 和功率标牌比较电器的使用成本，买价便宜不等于用起来便宜。保险丝的额定值按电流选，I = P/V：一台 3000 W 的电器接在 230 V 上，电流约 13 A，13 A 的保险丝压线，通常往上取一档。很多学生把 kWh 当成 kW 写进答案，或者算电费时忘记把分钟换成小时。1.4(f) 的环状主干线、火线、零线与地线，考的是某根线断开或接错会出现什么现象，光背结构图没用，要能把现象倒推回接线。
Appliances are rated in kilowatts and the energy they consume is measured in kilowatt hours, so units used equals power in kW times time in hours, and the cost is that figure multiplied by the price per unit given in the question. A 2000 W kettle boiled for five minutes uses 2 kW for one twelfth of an hour, which is about 0.17 kWh. Fuse ratings come from I = P/V, so a 3000 W appliance on a 230 V supply draws roughly 13 A and the next standard rating above that is chosen. Mixing kW with kWh, or forgetting to convert minutes to hours, accounts for a large share of the marks lost here; the ring main question usually asks what happens when the live, neutral or earth wire fails, so learn the symptoms rather than the picture.
三个单元的分工与卷首公式表
WJEC GCSE Physics 由三个单元组成。Unit 1 Electricity Energy and Waves 与 Unit 2 Forces Space and Radioactivity 各占 45%，都是 1 小时 45 分钟、80 分，分 Foundation 与 Higher 两个层级，后者可评 A* 到 D，前者 C 到 G。Unit 3 实践评估占 10%、30 分，由学校在一月到二月组织、WJEC 外部评分，不分层级。这门资格考试从 2016 年起施教、2018 年夏天首次颁奖，由 Qualifications Wales 监管，不对英格兰的学校开放。卷首会附一张公式表，Foundation 层级的考生不需要移项，但公式换个写法要认得出，1.2 那两条效率与功率的写法就经常换。1.3 的热传递与密度、1.8 的比热容、2.3 的弹簧力与伸长量都是指定实验，实验题的答案要落在数据与误差上。WJEC 在 2026 年 2 月的 spec 第 3 版里写明，新的 Unit 3 从 2026 年起施教、2028 年首次颁奖，动手探究被单独拎成一个单元。
The qualification is built from three units: Unit 1 covers electricity, energy and waves and Unit 2 covers forces, space and radioactivity, each worth 45 % of the qualification as a 1 hour 45 minute, 80 mark paper available at foundation and higher tier. Unit 3 is a practical assessment worth 10 % and 30 marks, organised by the centre in January or February and marked externally by WJEC, and it is untiered. A list of equations is printed at the start of every paper, and foundation tier candidates are not expected to change the subject of an equation, only to recognise the same relationship written differently. The specification was first taught in 2016 with first award in summer 2018 and is regulated by Qualifications Wales, so it is not available to centres in England, and the revised Unit 3 on scientific enquiry is taught from 2026 with first award in 2028.
阅卷上重复出现的失分点
阅卷时见得最多的不是算错，而是答非所问。单位丢掉的情况最常见，动能写成 240000 而不写 J，效率算出来是 0.35 又写成 35%，两种写法混在一道题里。有效数字也常被忽略，题目给的是两位有效数字的数据，答案就该留两位。公式背对了却代入错的量同样可惜，用质量代替重量、用绝对高度代替高度变化，结果数量级就跑偏。解释题更容易丢分，很多学生以为写两句就能得分，实际上阅卷按点给分，只说双层玻璃好、没写空气层抑制了传导与对流，那个机制点就是空的。解释题按机制加结果两句话来写，比多写三行形容词管用。
What examiners see most often is not wrong arithmetic but an answer to a different question. Units are dropped, kinetic energy written as 240000 with no J, or an efficiency of 0.35 written as 35 % on one line and 0.35 on the next. Significant figures are ignored even though the data in the question are given to two figures, and marks also disappear when a correct formula is fed the wrong quantity, such as a mass where a weight is needed or an absolute height where a change in height belongs; explanation questions suffer most, because marks are awarded for the mechanism, so writing that double glazing works without mentioning that the trapped air reduces conduction and convection leaves the point unclaimed.
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