📚 Thermal Physics Fundamentals | 热学基础知识梳理
Thermal physics is one of the core topics in IB Physics, covering the macroscopic behaviour of matter in terms of temperature, heat, energy transfer and the kinetic theory of gases. This article provides a structured revision guide to the essential ideas and formulas you need for your exams.
热学是IB物理的核心板块之一，它从温度、热量、能量传递和气体动理论等角度，研究物质的宏观热行为。本文将以清晰的知识框架，帮助你系统梳理考试中必须掌握的核心概念与公式。
1. Temperature and Thermal Equilibrium | 温度与热平衡
Temperature is a measure of the average random kinetic energy of particles in a substance. It determines the direction of net thermal energy transfer between two objects in contact.
温度是物体内部分子平均随机动能的量度。它决定了两个相互接触的物体之间净热传递的方向。
Thermal equilibrium occurs when two objects reach the same temperature and there is no net heat flow between them.
热平衡是指两个物体达到相同温度，彼此之间不再发生净热流。
The Kelvin scale is an absolute temperature scale based on the triple point of water (273.16 K). Absolute zero (0 K) is the theoretical minimum temperature where particles have minimum kinetic energy.
开尔文温标是以水的三相点（273.16 K）为基准的绝对温标。绝对零度（0 K）是粒子动能为最小值的理论最低温度。
To convert between Celsius and Kelvin: T(K) = θ(°C) + 273.15.
摄氏温度与开尔文温度的换算：T(K) = θ(°C) + 273.15。
T(K) = θ(°C) + 273.15
2. Thermal Energy Transfer | 热能的传递方式
Thermal energy can be transferred by three mechanisms: conduction, convection, and radiation. In IB Physics, you must be able to describe each mechanism in terms of particle behaviour.
热能可通过三种方式传递：传导、对流和辐射。在IB物理中，你需要能够从微观粒子行为的角度描述每种机制。
Conduction is the transfer of energy through a substance without bulk movement of the substance. It is most effective in solids, especially metals, due to free electrons.
传导是能量在物质内部传递而不伴随物质整体移动的过程。在固体中效果最好，尤其是金属，因为存在自由电子。
Convection involves the bulk movement of fluid due to density differences caused by temperature gradients. It is responsible for ocean currents and atmospheric circulation.
对流是流体因温度梯度导致密度差异而产生的整体运动。它是洋流和大气环流的原因。
Radiation is the transfer of energy by electromagnetic waves and requires no medium. All objects emit and absorb infrared radiation, with hotter objects emitting more.
辐射是通过电磁波传递能量，不需要介质。所有物体都发射和吸收红外辐射，温度越高辐射越强。
3. Specific Heat Capacity | 比热容
The specific heat capacity c of a substance is the energy required to raise the temperature of 1 kg of the substance by 1 K. It is a measure of a material's thermal inertia.
物质的比热容 c 是指使1 kg该物质温度升高1 K所需要的能量，它反映了材料的热惯性。
When a substance of mass m undergoes a temperature change ΔT, the thermal energy transferred is:
当质量为 m 的物质发生温度变化 ΔT 时，传递的热能为：
Q = mcΔT
ity (4.18 × 10³ J kg⁻¹ K⁻¹), which is why large bodies of water moderate coastal climates.
水的比热容很高（4.18 × 10³ J kg⁻¹ K⁻¹），因此大水体能够调节沿海气候。
cific heat capacity can be determined from c = IVt/(mΔT), taking heat losses into account.
在实验中，用电加热时：Q = IVt，因此比热容可由 c = IVt/(mΔT) 求得，需考虑热损失。
4. Phase Changes and Latent Heat | 相变与潜热
During a phase change, temperature remains constant while thermal energy is absorbed or released to break or form intermolecular bonds. Latent heat is the energy per unit mass involved in a phase change.
在相变过程中，温度保持不变，但热能会被吸收或释放，以破坏或形成分子间作用力。潜热是相变过程中单位质量吸收或释放的能量。
Q = mL
Specific latent heat of fusion Lf applies to melting/freezing; for water, Lf = 3.34 × 10⁵ J kg⁻¹.
熔化潜热 Lf 适用于熔化/凝固过程；水的熔化潜热为 Lf = 3.34 × 10⁵ J kg⁻¹。
Specific latent heat of vaporisation Lv applies to boiling/condensing; for water, Lv = 2.26 × 10⁶ J kg⁻¹, significantly larger than Lf because intermolecular bonds are completely separated.
汽化潜热 Lv 适用于沸腾/凝结过程；水的汽化潜热为 Lv = 2.26 × 10⁶ J kg⁻¹，远大于熔化潜热，因为汽化时分子间作用力被完全打破。
Heating and cooling curves show plateaus during phase changes, where the energy is used as latent heat rather than changing temperature.
加热和冷却曲线在相变阶段出现平台，此时能量作为潜热被吸收或释放，温度不再变化。
5. Kinetic Theory of Gases | 气体动理论
The kinetic theory models an ideal gas as a large number of point particles in constant random motion, colliding elastically with each other and with container walls.
气体动理论将理想气体视为大量做无规则运动的质点，粒子之间以及粒子与容器壁之间发生完全弹性碰撞。
Pressure arises from the force exerted by gas particles during collisions with the walls.
气体压强来源于粒子与容器壁碰撞时所产生的力。
The absolute temperature of an ideal gas is directly proportional to the average translational kinetic energy of its particles:
理想气体的绝对温度与其粒子的平均平动动能成正比：
⟨Ek⟩ = (3/2)kT
Here k is the Boltzmann constant (1.38 × 10⁻²³ J K⁻¹), and T is in kelvin.
其中 k 为玻尔兹曼常数（1.38 × 10⁻²³ J K⁻¹），T 为开尔文温度。
Root-mean-square speed of a gas molecule is given by vrms = √3RT/M, where M is molar mass.
气体分子的方均根速率定义为 vrms = √3RT/M，其中 M 为摩尔质量。
6. Ideal Gas Law | 理想气体定律
The ideal gas law combines Boyle's law, Charles's law, and Avogadro's principle into a single equation of state.
理想气体定律将玻意耳定律、查理定律和阿伏伽德罗原理统一为一个状态方程。
PV = nRT
P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (8.31 J mol⁻¹ K⁻¹), and T is thermodynamic temperature.
其中 P 为压强，V 为体积，n 为物质的量，R 为理想气体常数（8.31 J mol⁻¹ K⁻¹），T 为热力学温度。
Equivalently, in terms of the number of molecules N: PV = NkT.
若用分子数 N 表示，则可写为：PV = NkT。
: V₁/T₁ = V₂/T₂ (isobaric process). At constant volume: P₁/T₁ = P₂/T₂ (isochoric process).
温度恒定：P₁V₁ = P₂V₂（等温过程）。压强恒定：V₁/T₁ = V₂/T₂（等压过程）。体积恒定：P₁/T₁ = P₂/T₂（等容过程）。
7. Internal Energy | 内能
Internal energy U is the sum of the total kinetic energy of the particles and the potential energy associated with intermolecular forces. For an ideal gas, the intermolecular potential energy is assumed to be zero, so U depends only on temperature.
内能 U 是物体内部所有粒子的总动能与分子间作用力对应的势能之和。对于理想气体，分子间势能假设为零，因此内能只取决于温度。
For a monatomic ideal gas containing N particles: U = (3/2)NkT = (3/2)nRT.
对于单原子理想气体，若含有 N 个粒子：U = (3/2)NkT = (3/2)nRT。
In a real gas, potential energy contributes to internal energy, so changes in volume at constant temperature also change U.
对于真实气体，势能也对内能有贡献，因此在恒定温度下改变体积也会改变内能。
8. First Law of Thermodynamics | 热力学第一定律
The first law of thermodynamics is a statement of energy conservation for a thermodynamic system.
热力学第一定律是能量守恒定律在热力学系统中的表述。
ΔU = Q + W
Here, ΔU is the change in internal energy, Q is the thermal energy supplied to the system, and W is the work done on the system.
其中 ΔU 为内能变化，Q 为系统吸收的热量，W 为外界对系统做的功。
IB convention: Q is positive when heat is added to the system; W is positive when work is done on the system by its surroundings.
IB规定：系统吸收热量时 Q 为正；外界对系统做功时 W 为正。
In adiabatic processes (Q = 0), ΔU = W; in isochoric processes (W = 0), ΔU = Q.
绝热过程中（Q = 0），ΔU = W；等容过程中（W = 0），ΔU = Q。
9. Second Law and Entropy | 第二定律与熵
The second law of thermodynamics states that the total entropy of an isolated system never decreases; it either stays constant for reversible processes or increases for irreversible processes.
热力学第二定律指出：孤立系统的总熵永远不会减少；可逆过程熵不变，不可逆过程熵增加。
a measure of the disorder or the number of microstates available to a system: S = k ln Ω.
熵 S 是系统无序度或微观状态数的量度：S = k ln Ω。
Heat flows spontaneously from a hotter body to a colder body, not the reverse, because this leads to an increase in total entropy.
热自发地从高温物体流向低温物体，而不可能自发反向流动，因为正向流动导致总熵增加。
The Second Law can also be expressed as: for a reversible process, ΔS = Qrev/T; for an irreversible process, ΔS > Q/T.
第二定律也可表述为：可逆过程满足 ΔS = Qrev/T；不可逆过程满足 ΔS > Q/T。
10. Heat Engines and p-V Diagrams | 热机与p-V图
A heat engine absorbs thermal energy from a hot reservoir, converts some of it into work, and rejects the rest to a cold reservoir. Its efficiency is defined as the ratio of work output to heat input.
热机从高温热源吸收热量，将其中一部分转化为功，其余热量释放给低温热源。热机效率定义为输出功与输入热量之比。
η = Wout / Qh = 1 - Qc / Qh
On a p-V diagram, the work done by a gas during a thermodynamic cycle equals the area enclosed by the cycle on the diagram.
在p-V图上，气体在一个热力学循环中对外做的功等于循环曲线所围成的面积。
A cyclic process returns the system to its initial state, so ΔU = 0; therefore Qnet = Wnet.
循环过程结束时系统回到初态，因此 ΔU = 0，所以 Qnet = Wnet。
ngine is an ideal reversible engine with the maximum possible efficiency: η_carnot = 1 - Tc/Th, where temperatures are in kelvin.
卡诺热机是一种理想可逆热机，具有最高可能效率：η_carnot = 1 - Tc/Th，其中温度为开尔文温度。
11. Key Calculations and Exam Tips | 关键计算与考试贴士
Thoroughly understanding units and sign conventions is essential for solving thermal physics problems in IB exams.
在IB考试中解决热学问题，必须充分理解单位制和符号约定。
temperatures to kelvin when using gas laws or thermodynamic equations such as ΔU = Q + W.
在使用气体定律或热力学第一定律等方程时，务必先将温度换算为开尔文。
lost by hot object = energy gained by cold object, assuming no heat loss to surroundings.
当不同温度的物质混合时，列能量平衡方程：高温物体放出的热量 = 低温物体吸收的热量，假设没有热量散失到周围环境。
Know the difference between heat (energy transfer due to temperature difference) and temperature (average kinetic energy indicator) — a common source of conceptual errors.
理解热量（因温差引起的能量转移）与温度（平均动能的标志）的区别——这是常见概念错误来源。
Practice interpreting p-V diagrams: identify isothermal, isobaric, isochoric, and adiabatic segments, and calculate work from the area under/inside the curve.
练习解读p-V图：识别等温、等压、等容和绝热过程，并通过曲线面积计算功。
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