📚 IB Physics: Core Concepts and Knowledge Framework of Thermal Physics | IB物理：热物理核心概念与知识框架
Thermal physics in the IB Physics syllabus (both SL and HL) forms a compact but highly examinable topic. It connects macroscopic measurements such as temperature and pressure with microscopic ideas about molecular motion and energy transfer. Mastering this framework requires a clear understanding of definitions, sign conventions, energy conservation, and the kinetic model of gases.
IB物理课程（SL和HL）中的热物理是一个紧凑但考试出现频率极高的主题。它将温度、压力等宏观测量与分子运动、能量传递的微观概念联系起来。掌握这一知识框架，需要清晰理解定义、符号约定、能量守恒以及气体动理论模型。
1. Temperature, Heat and Internal Energy | 温度、热量与内能
Temperature is a macroscopic measure of the average random kinetic energy of particles in a substance. It is measured in Kelvin (K) in the SI system, and the Kelvin scale is an absolute scale starting at absolute zero (0 K). A change of 1 K is identical to a change of 1 °C, but the zero points of the two scales differ: T(K) = T(°C) + 273.15.
温度是物质中粒子平均随机动能的宏观量度。在国际单位制中，温度用开尔文（K）表示，开尔文温标是以绝对零度（0 K）为起点的绝对温标。1 K的温度变化与1 °C的温度变化相同，但两种温标的零点不同：T(K) = T(°C) + 273.15。
Heat is defined as thermal energy transferred between two systems because of a temperature difference. It is a process-dependent quantity, not a property of a system. Internal energy U is the sum of the total potential energy and the total random kinetic energy of all particles within a system. For an ideal gas, the potential energy component is assumed to be zero, so the internal energy depends only on temperature.
热量是由于温度差而在两个系统之间传递的热能。它是一个与过程有关的量，而不是系统本身的性质。内能U是系统内所有粒子的总势能与总随机动能之和。对于理想气体，势能部分被假设为零，因此内能只取决于温度。
2. 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. The defining equation is:
比热容c是指使1 kg物质温度升高1 K所需的热量。其定义方程为：
E = mcΔT
where E is the thermal energy supplied or removed, m is the mass, c is the specific heat capacity, and ΔT is the temperature change. Common units are J kg⁻¹ K⁻¹. In IB questions, you must identify whether energy is being added to or removed from the system, and the equation works with the sign of ΔT.
其中E为供给或移除的热能，m为质量，c为比热容，ΔT为温度变化。常用单位是J kg⁻¹ K⁻¹。在IB考题中，需要判断能量是加入系统还是从系统释放，该方程通过ΔT的正负体现能量方向。
When two substances at different temperatures are mixed, the principle of conservation of energy implies that the energy lost by the hotter substance equals the energy gained by the cooler substance, assuming no heat loss to the surroundings. This forms the basis of calorimetry problems.
当两种不同温度的物质混合时，能量守恒原理表明，在假设没有热量散失到周围环境的前提下，较热物质损失的能量等于较冷物质获得的能量。这是量热学问题的基础。
3. Phase Changes and Latent Heat | 物态变化与潜热
During a phase change, temperature remains constant while energy is transferred. The energy required to change the phase of 1 kg of a substance without changing its temperature is called the specific latent heat L. The equation is:
在物态变化过程中，温度保持不变，但能量仍在传递。使1 kg物质在温度不变的条件下发生相变所需的能量称为比潜热L。其方程为：
E = mL
There are two important values: the specific latent heat of fusion Lf, for solid-liquid transitions, and the specific latent heat of vaporisation Lv, for liquid-gas transitions. For a given substance, Lv is usually much larger than Lf because the separation of particles against intermolecular forces during vaporisation requires far more energy than breaking the rigid lattice structure during melting.
两个重要数值是：固-液转变的熔化比潜热Lf，以及液-气转变的汽化比潜热Lv。对同一物质而言，Lv通常远大于Lf，因为汽化过程中粒子需要克服分子间引力而大幅分离，所需能量远大于熔化时破坏规则晶格结构所需的能量。
When a heating curve for ice from below 0 °C to steam above 100 °C is plotted, the graph shows sloping sections (temperature rises) and horizontal plateaus (phase changes). IB students should be able to calculate the energy for each section separately and sum them to find the total energy.
当绘制从低于0 °C的冰加热到高于100 °C的水蒸气的加热曲线时，图中会出现倾斜段（温度升高）和水平平台（相变）。IB学生应能分别计算每一段的能量并求和得到总能量。
4. The Kinetic Model of Matter | 物质的分子动理论模型
The kinetic model explains the macroscopic properties of solids, liquids and gases in terms of the motion and arrangement of particles. In a solid, particles vibrate about fixed positions in a regular lattice. In a liquid, particles are close together but can move past each other. In a gas, particles are far apart, move rapidly and randomly, and collisions are elastic.
分子动理论通过粒子的运动和排列方式解释了固体、液体和气体的宏观性质。在固体中，粒子在规则晶格中的固定位置附近振动。在液体中，粒子彼此靠近但可以相对滑动。在气体中，粒子相距很远，运动快速而随机，碰撞是弹性的。
Temperature is related to the average kinetic energy of particles: a higher temperature means a greater average random kinetic energy. Evaporation occurs when the most energetic particles at the liquid surface escape into the gas phase, which reduces the average kinetic energy of the remaining liquid, so evaporation causes cooling.
温度与粒子的平均动能相关：温度越高，平均随机动能越大。蒸发发生在液体表面能量最高的粒子逸出进入气相时，这降低了剩余液体的平均动能，因此蒸发导致冷却。
5. The Ideal Gas Model | 理想气体模型
The ideal gas model is a simplified theoretical model used to describe the behaviour of gases under most ordinary conditions. The assumptions of the model include: the gas consists of a very large number of identical particles; the volume of the particles is negligible compared to the volume of the container; there are no intermolecular forces except during collisions; all collisions are perfectly elastic; and the duration of a collision is negligible compared to the time between collisions.
理想气体模型是描述气体在大多数通常条件下行为的简化理论模型。该模型的假设包括：气体由大量相同的粒子组成；粒子本身的体积与容器体积相比可以忽略；除碰撞瞬间外，粒子间不存在分子间作用力；所有碰撞都是完全弹性的；碰撞持续时间与粒子两次碰撞之间的时间间隔相比可以忽略。
For an ideal gas, the internal energy is solely the total kinetic energy of the particles. Therefore, if the temperature of an ideal gas is unchanged, its internal energy is unchanged. This is a crucial idea in the first law of thermodynamics applied to isothermal processes.
对于理想气体，内能仅仅是粒子总动能的总和。因此，如果理想气体的温度不变，其内能也不变。这是第一定律应用于等温过程时的一个关键概念。
6. The Equation of State for an Ideal Gas | 理想气体状态方程
The macroscopic behaviour of an ideal gas is described by the equation of state:
理想气体的宏观行为由状态方程描述：
PV = nRT = NkBT
Here P is pressure in pascals, V is volume in cubic metres, n is the amount of gas in moles, R = 8.31 J mol⁻¹ K⁻¹ is the molar gas constant, N is the number of particles, kB = 1.38 × 10⁻²³ J K⁻¹ is the Boltzmann constant, and T is the absolute temperature in kelvin.
其中P为压强（帕斯卡），V为体积（立方米），n为气体的物质的量（摩尔），R = 8.31 J mol⁻¹ K⁻¹ 为摩尔气体常量，N为粒子数，kB = 1.38 × 10⁻²³ J K⁻¹ 为玻尔兹曼常量，T为绝对温度（开尔文）。
In IB problems, a common approach is to compare two states of the same gas using the relation P₁V₁/T₁ = P₂V₂/T₂, provided the amount of gas is fixed. Always convert temperatures to kelvin before substitution, and ensure consistent units for pressure and volume on both sides.
在IB解题中，常见方法是在气体物质的量不变时，用关系式P₁V₁/T₁ = P₂V₂/T₂比较同一气体的两个状态。代入前务必将温度转换为开尔文，并确保等式两边压强和体积的单位一致。
7. Kinetic Energy of Gas Molecules | 气体分子的动能
From the kinetic model, the average translational kinetic energy of a single gas molecule is directly proportional to the absolute temperature. The IB equation is:
根据分子动理论，单个气体分子的平均平动动能与绝对温度成正比。IB使用的方程为：
⟨Ek⟩ = (3/2)kBT
For one mole of gas, the total kinetic energy is (3/2)RT. This result shows that at the same temperature, all ideal gases have the same average molecular kinetic energy, regardless of the mass of the molecules. However, lighter molecules move faster on average than heavier molecules at the same temperature.
对一摩尔气体，总动能为(3/2)RT。这个结果表明，在同一温度下，所有理想气体分子具有相同的平均动能，而与分子质量无关。然而，在相同温度下，较轻的分子平均运动速度比较重的分子快。
Pressure arises from the impact of gas molecules on the container walls. Faster molecules collide more frequently and with greater momentum change, producing higher pressure. This microscopic explanation links the macroscopic quantity P with molecular speed and number density.
压强来自气体分子对容器壁的撞击。速度更快的分子碰撞频率更高，动量变化量更大，从而产生更高的压强。这种微观解释将宏观量P与分子速度和数密度联系起来。
8. The First Law of Thermodynamics | 热力学第一定律
The first law of thermodynamics is essentially the law of conservation of energy applied to a thermodynamic system. The IB form is:
热力学第一定律本质上是能量守恒定律在热力学系统中的应用。IB使用的形式为：
ΔU = Q + W
where ΔU is the change in internal energy, Q is the thermal energy transferred to the system, and W is the work done on the system. The sign convention is crucial: Q is positive when heat enters the system, and W is positive when work is done on the system by the surroundings. If the system does work on the surroundings, W is negative.
其中ΔU是内能变化，Q是传入系统的热能，W是外界对系统做的功。符号约定至关重要：Q为正表示热量进入系统，W为正表示外界对系统做功。如果系统对外界做功，则W为负。
For an expanding gas, the gas does positive work on the surroundings, so W in the equation is negative. For a compressed gas, the surroundings do work on the gas, so W is positive. In an isothermal process, ΔU = 0 for an ideal gas, so Q = -W. In an adiabatic process, Q = 0, so ΔU = W.
当气体膨胀时，气体对外界做正功，因此方程中的W为负。当气体被压缩时，外界对气体做功，因此W为正。在等温过程中，理想气体的ΔU = 0，因此Q = -W。在绝热过程中，Q = 0，因此ΔU = W。
9. Thermodynamic Processes and the p-V Diagram | 热力学过程与p-V图
Thermodynamic processes are often represented on a pressure-volume (p-V) diagram. Four special processes are emphasised in IB Physics: isochoric (constant volume), isobaric (constant pressure), isothermal (constant temperature) and adiabatic (no heat transfer).
热力学过程通常用压强-体积（p-V）图表示。IB物理重点强调四种特殊过程：等体过程（体积不变）、等压过程（压强不变）、等温过程（温度不变）和绝热过程（无热量传递）。
| Process | Conditions | Key relation for ideal gas | Work done W |
| Isochoric 等体 | V constant | P/T = constant | W = 0 |
| Isobaric 等压 | P constant | V/T = constant | W = -PΔV |
| Isothermal 等温 | T constant | PV = constant | W = -nRT ln(V₂/V₁) |
| Adiabatic 绝热 | Q = 0 | PVγ = constant | W = ΔU |
The work done by a gas during a volume change is equal to the area under the curve on a p-V diagram. The sign convention is important: if the volume increases, the gas does work on the surroundings; if the volume decreases, work is done on the gas. A cyclic process forms a closed loop on the p-V diagram, and the net work done is the area enclosed by the loop.
气体在体积变化过程中所做的功等于p-V图上曲线下方的面积。符号约定很重要：如果体积增加，气体对外界做功；如果体积减小，外界对气体做功。循环过程在p-V图上形成闭合回路，净功等于回路所围的面积。
10. Internal Energy and the First Law in Problem Solving | 内能与第一定律的解题应用
When solving IB thermal physics problems, a systematic approach reduces errors. First, identify the system and write down the known quantities. Then determine which process is involved and which quantities remain constant. Apply the ideal gas law to find missing state variables, and only then apply the first law to calculate ΔU, Q or W.
在解决IB热物理问题时，系统化的方法可以减少错误。首先，确定系统并列出已知量。然后判断涉及哪个过程以及哪些量保持不变。用理想气体状态方程求出缺失的状态变量，最后再用第一定律计算ΔU、Q或W。
Common mistakes include forgetting to convert °C to K, using the wrong sign for W, and calculating work as zero for isothermal processes. Remember that in an isothermal expansion of an ideal gas, the temperature and therefore ΔU are zero, so the heat absorbed equals the work done by the gas. In a free expansion into a vacuum, no work is done and no heat is exchanged, so ΔU = 0 and temperature remains constant.
常见错误包括忘记将°C转换为K，W的符号用错，以及将等温过程的功计算为零。记住，在理想气体的等温膨胀中，温度不变，因此ΔU为零，所以吸收的热量等于气体对外做的功。在向真空的自由膨胀中，外界不做功也没有热量交换，因此ΔU = 0，温度保持不变。
11. Thermal Radiation and Energy Balance | 热辐射与能量平衡
Thermal radiation is energy transferred by electromagnetic waves and does not require a medium. All objects emit radiation, and the rate of emission increases rapidly with temperature. In IB Physics, the Stefan-Boltzmann law is given as:
热辐射是通过电磁波传递的能量，不需要介质。所有物体都发射辐射，且发射速率随温度升高而迅速增大。在IB物理中，斯特藩-玻尔兹曼定律表示为：
P = eσAT⁴
where P is the power radiated, e is the emissivity (0 to 1), σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ is the Stefan-Boltzmann constant, A is the surface area, and T is the absolute temperature. A black body has emissivity e = 1 and absorbs all incident radiation.
其中P为辐射功率，e为发射率（0到1），σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ 为斯特藩-玻尔兹曼常量，A为表面积，T为绝对温度。黑体的发射率e = 1，并且吸收所有入射辐射。
In the energy balance of a planet or a body in space, the power absorbed from a star must equal the power radiated away when the temperature is steady. This leads to equations that can be used to estimate surface temperatures. The greenhouse effect can be modelled by considering the absorption and re-radiation of infrared radiation by atmospheric gases.
在行星或太空中天体的能量平衡中，当温度稳定时，从恒星吸收的功率必须等于向外辐射的功率。这可以建立方程来估算表面温度。温室效应可以通过大气气体对红外辐射的吸收和再辐射来建模。
12. Common Exam Traps and Revision Strategy | 常见考试陷阱与复习策略
Many IB students lose marks on thermal physics because of small but repeated errors. The most frequent traps are listed below.
许多IB学生在热物理上丢分，原因往往是微小但反复出现的错误。最常见的陷阱如下。
- Using degrees Celsius instead of kelvin in ideal gas calculations and in radiation equations: always convert to kelvin.
- 应用气体方程和辐射方程时使用摄氏度而非开尔文：务必转换为开尔文。
- Confusing heat and temperature: heat is energy in transit; temperature measures average kinetic energy.
- 混淆热量与温度：热量是传递中的能量；温度是平均动能的量度。
- Applying E = mcΔT during a phase change: use E = mL instead.
- 在物态变化过程中使用E = mcΔT：此时应使用E = mL。
- Mixing up the sign convention of W in the first law: W is work done on the system in the IB equation.
- 混淆第一定律中W的符号约定：在IB方程中，W是外界对系统做的功。
- Assuming temperature always increases when heat is added: during boiling or melting it remains constant.
- 假设加入热量时温度一定升高：在沸腾或熔化过程中温度保持不变。
For revision, draw summary tables of the four thermodynamic processes, practise converting between pressure units (Pa, kPa, atm) and volume units (m³, L, cm³), and review past paper questions that combine the ideal gas law with the first law. Understanding the physical meaning behind each equation is more valuable than memorising formulas.
复习时，建议绘制四种热力学过程的汇总表，练习压强单位（Pa、kPa、atm）和体积单位（m³、L、cm³）之间的换算，并回顾那些将理想气体状态方程与热力学第一定律结合的真题。理解每个方程背后的物理意义比死记公式更有价值。
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