📚 IB WJEC Physics: Thermodynamics Key Points | IB WJEC 物理：热力学 考点精讲
Thermodynamics is the branch of physics that deals with heat, work, and energy. In the IB and WJEC syllabi, you are expected to master core concepts such as temperature scales, internal energy, the first and second laws, ideal gas behaviour, and the underlying kinetic theory. This article breaks down the essential points, clarifies common pitfalls, and provides a structured revision guide in both English and Chinese.
热力学是物理学中研究热、功和能量的分支。在 IB 和 WJEC 考纲中，你需要掌握温度标度、内能、热力学第一和第二定律、理想气体行为以及背后的动理论等核心概念。本文以中英双语梳理必考要点，明确常见误区，提供结构化的复习指南。
1. Temperature and Thermal Equilibrium | 温度与热平衡
Temperature is a measure of the average kinetic energy of particles in a substance. Two objects are in thermal equilibrium when they are at the same temperature and there is no net heat flow between them. The zeroth law of thermodynamics states that if A and B are each in thermal equilibrium with C, then A and B are in thermal equilibrium with each other.
温度是物质内粒子平均动能的量度。当两个物体温度相同且它们之间没有净热传递时，就处于热平衡。热力学第零定律表明，如果 A 和 B 分别与 C 处于热平衡，那么 A 和 B 彼此也处于热平衡。
The Celsius scale is based on the freezing point (0 °C) and boiling point (100 °C) of water at standard atmospheric pressure. The absolute temperature scale (Kelvin) is defined such that 0 K is absolute zero, the temperature at which particle motion theoretically ceases. The conversion is: T (K) = T (°C) + 273.15.
摄氏温标基于标准大气压下水的冰点 (0 °C) 和沸点 (100 °C)。绝对温标（开尔文）定义 0 K 为绝对零度，理论上此时粒子运动停止。换算关系为：T (K) = T (°C) + 273.15。
Thermometers rely on a physical property that changes with temperature, such as the expansion of a liquid, the resistance of a metal, or the pressure of a gas at constant volume. In an ideal gas thermometer, temperature is directly proportional to pressure at constant volume: T ∝ p.
温度计依赖于随温度变化的物理性质，例如液体膨胀、金属电阻变化或等容条件下气体压强变化。在理想气体温度计中，等容条件下温度与压强成正比：T ∝ p。
2. Heat and Internal Energy | 热量与内能
Heat (Q) is the energy transferred from a hotter object to a colder one due to a temperature difference. It is not a property of a system; a body does not ‘contain’ heat. Internal energy (U) is the total sum of the random kinetic and potential energies of all particles within a system.
热量 (Q) 是因温差而从高温物体传递到低温物体的能量。它不是系统的属性，物体并不“含有”热量。内能 (U) 是系统内所有粒子无规则运动的动能和势能之和。
For an ideal gas, the internal energy depends only on temperature, because there are no intermolecular forces and thus no potential energy contribution. For real gases, liquids, and solids, both kinetic and potential energies matter, so internal energy depends on both temperature and phase.
对于理想气体，内能只取决于温度，因为分子间无作用力，没有势能贡献。对于真实气体、液体和固体，动能和势能都很重要，因此内能取决于温度和物态。
When heat is supplied to a system, the internal energy may increase and the system may do work on its surroundings. The relationship is formalised in the first law of thermodynamics.
当系统吸热时，内能可能增加，同时系统可能对外做功。这个关系由热力学第一定律精确描述。
3. Specific Heat Capacity | 比热容
Specific heat capacity (c) is the energy required to raise the temperature of 1 kg of a substance by 1 K (or 1 °C) without a change of state. The formula is: Q = mcΔT, where m is mass and ΔT is the temperature change.
比热容 (c) 是使 1 kg 物质温度升高 1 K（或 1 °C）所需能量且不发生相变。公式为：Q = mcΔT，其中 m 为质量，ΔT 为温度变化。
The unit of specific heat capacity is J kg⁻¹ K⁻¹. Water has a high specific heat capacity (about 4200 J kg⁻¹ K⁻¹), which makes it excellent for thermal regulation in both nature and engineering applications.
比热容的单位是 J kg⁻¹ K⁻¹。水的比热容很高（约 4200 J kg⁻¹ K⁻¹），这使其在自然界和工程中的热调节非常有效。
In experiments, an electrical heater can supply energy calculated as E = VIt = Pt. The actual temperature rise may be less than theoretical due to heat losses to the surroundings, so insulation and stirring are used to improve accuracy.
在实验中，电加热器提供的能量可通过 E = VIt = Pt 计算。实际温升可能因散热到环境中而低于理论值，因此需用隔热和搅拌来提高精度。
4. Latent Heat and Phase Changes | 潜热与相变
During a change of state (melting, boiling, condensing, etc.), the temperature remains constant even though heat is being supplied or removed. The energy absorbed or released per unit mass during a phase change is called specific latent heat (L). Q = mL.
在物态变化（熔化、沸腾、凝结等）过程中，尽管持续加热或放热，温度保持不变。单位质量物质在相变中吸收或释放的能量称为比潜热 (L)。Q = mL。
Specific latent heat of fusion (Lf) applies to melting/freezing, and specific latent heat of vaporisation (Lv) applies to boiling/condensing. Lv is typically much larger than Lf because breaking all intermolecular bonds to form a gas requires more energy than merely loosening them in a liquid.
熔化比潜热 (Lf) 用于熔化/凝固，汽化比潜热 (Lv) 用于沸腾/凝结。Lv 通常远大于 Lf，因为将分子间所有键打破形成气体所需的能量远大于在液体中仅使键松动。
On a heating curve, temperature plateaus represent phase changes. For impure substances, melting and boiling points are not sharp, and the mixture melts/boils over a range of temperatures.
在加热曲线上，温度平台代表相变。对于不纯物质，熔点和沸点不尖锐，混合物在一个温度范围内熔化/沸腾。
5. The First Law of Thermodynamics | 热力学第一定律
The first law of thermodynamics is a statement of energy conservation: The change in internal energy of a system (ΔU) equals the heat added to the system (Q) minus the work done by the system (W). In IB standard notation: ΔU = Q – W.
热力学第一定律是能量守恒的表述：系统内能的变化 (ΔU) 等于系统吸收的热量 (Q) 减去系统对外做的功 (W)。按 IB 标准记法：ΔU = Q – W。
Sometimes the form ΔU = Q + W is used, where W is the work done on the system. Be careful to identify which sign convention your exam board expects. For IB and WJEC, the convention is ΔU = Q – W with W being work done by the system.
有时也使用 ΔU = Q + W 的形式，其中 W 是外界对系统做的功。务必注意考纲要求的符号规定。对于 IB 和 WJEC，规定是 ΔU = Q – W，其中 W 是系统对外做的功。
For a gas expanding at constant pressure, work done W = pΔV. If a gas is compressed, ΔV is negative, and work is done on the gas, leading to an increase in internal energy (if no heat is transferred).
对于气体在恒压下膨胀，做功 W = pΔV。如果气体被压缩，ΔV 为负，外界对气体做功，若没有热传递则内能增加。
6. Thermodynamic Processes | 热力学过程
An isothermal process occurs at constant temperature. For an ideal gas, ΔU = 0, so Q = W. The gas must expand or compress very slowly so that heat exchange with the surroundings maintains a constant temperature.
等温过程在恒定温度下发生。对于理想气体，ΔU = 0，因此 Q = W。气体必须非常缓慢地膨胀或压缩，以便与环境的热交换维持恒温。
An adiabatic process is one in which no heat enters or leaves the system (Q = 0). Then ΔU = -W. In an adiabatic expansion, the gas does work and its internal energy decreases, causing cooling. Adiabatic compression leads to heating. The relationship pVγ = constant applies, where γ = Cp/Cv.
绝热过程中系统没有热量进出 (Q = 0)。则 ΔU = -W。在绝热膨胀中，气体对外做功，内能减少，导致冷却。绝热压缩则导致升温。满足关系式 pVγ = 常数，其中 γ = Cp/Cv。
An isovolumetric (isochoric) process keeps volume constant (ΔV = 0). No work is done, so ΔU = Q. All heat transfer changes the internal energy and thus temperature. On a p-V diagram, this is a vertical line.
等容过程保持体积不变 (ΔV = 0)。不做功，因此 ΔU = Q。所有热量传递都改变内能和温度。在 p-V 图上是一条竖直线。
An isobaric process occurs at constant pressure. Work done is W = pΔV, and the first law becomes ΔU = Q – pΔV. Many everyday applications, such as heating a gas in a cylinder with a movable piston, approximate isobaric conditions if the piston moves freely.
等压过程在恒压下发生。做功为 W = pΔV，第一定律变为 ΔU = Q – pΔV。许多日常应用，如加热带有可移动活塞的气缸，若活塞自由移动则可近似等压条件。
7. Ideal Gas Laws | 理想气体定律
The behaviour of an ideal gas is described by the equation of state: pV = nRT, where p is pressure (Pa), V is volume (m³), n is the number of moles, R is the universal gas constant (8.31 J K⁻¹ mol⁻¹), and T is absolute temperature (K).
理想气体的行为由状态方程描述：pV = nRT，其中 p 是压强（Pa），V 是体积（m³），n 是摩尔数，R 是普适气体常数（8.31 J K⁻¹ mol⁻¹），T 是绝对温度（K）。
The combined gas law for a fixed mass of gas follows: p₁V₁/T₁ = p₂V₂/T₂. Special cases include Boyle’s law (constant T: p₁V₁ = p₂V₂), Charles’s law (constant p: V₁/T₁ = V₂/T₂), and Gay-Lussac’s law (constant V: p₁/T₁ = p₂/T₂).
对于一定质量的气体，组合气体定律为：p₁V₁/T₁ = p₂V₂/T₂。特例包括玻意耳定律（恒 T：p₁V₁ = p₂V₂）、查理定律（恒 p：V₁/T₁ = V₂/T₂）和盖-吕萨克定律（恒 V：p₁/T₁ = p₂/T₂）。
The ideal gas model assumes that gas particles have negligible volume, exert no forces on each other except during elastic collisions, and move randomly. Real gases deviate at high pressure and low temperature when intermolecular forces and particle volume become significant.
理想气体模型假设气体粒子体积可忽略，除弹性碰撞外彼此无作用力，并做随机运动。真实气体在高压低温下偏离理想行为，此时分子间力和粒子体积变得不可忽略。
8. Kinetic Theory of Gases | 气体动理论
Kinetic theory links the macroscopic properties of a gas to the motion of its particles. The pressure exerted by an ideal gas is given by p = (1/3) (Nm/V) c̄², where N is the number of molecules, m is the mass per molecule, V is volume, and c̄² is the mean square speed.
动理论将气体的宏观性质与分子运动联系起来。理想气体的压强公式为 p = (1/3) (Nm/V) c̄²，其中 N 是分子数，m 是分子质量，V 是体积，c̄² 是方均速率。
The average translational kinetic energy of a molecule is related to absolute temperature: (1/2) m c̄² = (3/2) kT, where k is the Boltzmann constant (1.38 × 10⁻²³ J K⁻¹). This shows that temperature is a direct measure of the average kinetic energy of particles.
分子的平均平动动能与绝对温度的关系为：(1/2) m c̄² = (3/2) kT，其中 k 是玻尔兹曼常数（1.38 × 10⁻²³ J K⁻¹）。这表明温度直接衡量粒子的平均动能。
The root-mean-square speed (crms) = √(c̄²) = √(3RT/M), where M is molar mass in kg mol⁻¹. Lighter molecules have higher rms speeds at a given temperature, explaining diffusion rates.
方均根速率 crms = √(c̄²) = √(3RT/M)，其中 M 是摩尔质量（kg mol⁻¹）。相同温度下，较轻的分子具有更高的方均根速率，这解释了扩散速率的差异。
9. The Second Law of Thermodynamics | 热力学第二定律
The second law states that the entropy of an isolated system never decreases; it either increases for irreversible processes or remains constant for reversible ones. This gives a direction to natural processes: heat flows spontaneously from hot to cold, never the reverse without external work.
热力学第二定律表明，孤立系统的熵永不减少；在不可逆过程中熵增加，在可逆过程中熵保持不变。这为自然过程指明了方向：热量自发地从高温流向低温，没有外界做功不会反向流动。
Another statement of the second law refers to heat engines: it is impossible to convert heat completely into work in a cyclic process with no other effect. Some heat must always be rejected to a cold reservoir (sink).
第二定律的另一种表述针对热机：在循环过程中，不可能将热量完全转化为功而不产生其他影响。总有一部分热量必须排放到低温热库（冷源）。
Entropy (S) is a measure of disorder. When a gas expands freely, entropy increases because the molecules are distributed over a larger volume. The change in entropy is ΔS = Q/T for a reversible isothermal process.
熵 (S) 是系统无序度的量度。气体自由膨胀时，分子分布在更大体积中，熵增加。在可逆等温过程中，熵的变化为 ΔS = Q/T。
10. Heat Engines and Efficiency | 热机与效率
A heat engine operates between a hot reservoir at temperature TH and a cold sink at TC. It absorbs heat QH, does useful work W, and rejects waste heat QC to the cold sink. By conservation of energy: QH = W + QC.
热机工作在高温热库温度 TH 和低温冷源 TC 之间。它吸收热量 QH，做有用功 W，并将废热 QC 排放至冷源。由能量守恒：QH = W + QC。
The thermal efficiency η of a heat engine is defined as η = W/QH = (QH – QC)/QH = 1 – QC/QH. No engine can exceed the efficiency of a Carnot engine operating between the same two temperatures.
热机的热效率 η 定义为 η = W/QH = (QH – QC)/QH = 1 – QC/QH。在相同温度区间工作的任何热机，其效率不能超过卡诺热机。
The Carnot efficiency is the maximum theoretical efficiency: ηCarnot = 1 – TC/TH, with temperatures in Kelvin. To improve efficiency, one should increase TH or decrease TC.
卡诺效率是理论最大效率：ηCarnot = 1 – TC/TH，温度用开尔文。要提高效率，可提高 TH 或降低 TC。
In a p-V diagram, the area enclosed by a cyclic process represents the net work done per cycle. IB students should be able to interpret such cycles and calculate efficiency or work done from given data.
在 p-V 图中，循环过程所围的面积代表每循环的净功。IB 学生应能解释此类循环，并根据给定数据计算效率或做功。
11. Practical Skills and Graphical Analysis | 实验技能与图像分析
Thermodynamics exam questions often involve interpreting graphs. Be familiar with p-V diagrams: isotherms are hyperbolic curves, adiabats are steeper curves, isochoric processes are vertical lines, and isobaric processes are horizontal lines.
热力学考题常涉及图像分析。熟悉 p-V 图：等温线是双曲线，绝热线更陡，等容线为竖直线，等压线为水平线。
To determine specific heat capacity or latent heat, students may need to use electrical methods, cooling curves, or the method of mixtures. Always account for energy losses by using insulation, lagging, and repeating measurements.
测定比热容或潜热时，学生可能需要使用电学方法、冷却曲线或混合法。始终通过使用隔热、包覆和重复测量来减少能量损失。
A common experimental task is determining the specific latent heat of vaporisation of water using a kettle and balance, or measuring specific heat capacity of a metal block with an embedded heater. The key formula is E = mcΔT + heat losses, where heat losses can be minimised or corrected for using a cooling correction.
常见实验任务包括用电水壶和天平测定水的汽化比潜热，或用内置加热器的金属块测量比热容。核心公式为 E = mcΔT + 热损耗，可最小化热损耗或通过冷却校正处理。
12. Exam Tips and Common Pitfalls | 考试技巧与常见错误
Always convert temperatures to Kelvin when using the ideal gas law, kinetic energy formulas, or calculating efficiency. Using Celsius will lead to incorrect results, especially in ratios.
使用理想气体定律、动能公式或计算效率时，始终将温度转换为开尔文。使用摄氏温标会导致错误，尤其是在比值计算中。
Be careful with the sign convention in the first law. The IB data booklet gives ΔU = Q + W, where W is work done on the system. However, many textbooks use ΔU = Q – W with W done by the system. Check which version your teacher uses and stick to it consistently.
注意第一定律的符号规定。IB 数据手册给出 ΔU = Q + W，其中 W 是外界对系统做的功。但许多教材使用 ΔU = Q – W，W 为系统对外做功。确认教师使用的版本并保持一致。
When explaining the kinetic theory, link macroscopic observations such as pressure increase with temperature to microscopic particle behaviour: higher temperature means faster molecules, more frequent and more forceful collisions with the walls.
在用动理论解释现象时，将宏观观察（如压强随温度升高而增大）与微观粒子行为联系起来：温度升高 → 分子运动更快 → 与器壁碰撞更频繁、更有力。
For the second law, be prepared to describe why certain processes are irreversible in terms of entropy, such as free expansion, mixing, or heat flow from hot to cold. A correct answer will mention the increase in the total entropy of the universe.
对于第二定律，要准备用熵解释为何某些过程是不可逆的，例如自由膨胀、混合或热量从高温流向低温。正确答案应提及宇宙总熵的增加。
Finally, practise drawing and annotating p-V diagrams for cyclic processes, clearly labelling heat in, heat out, and work. This is a common multipart question in both IB and WJEC exams.
最后，练习绘制并标注循环过程的 p-V 图，清楚标出吸热、放热和功。这是 IB 和 WJEC 考试中常见的多部分大题。
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