📚 B.4 Thermodynamics | B.4 热力学
Thermodynamics is the branch of physics that deals with heat, work, and energy, and the macroscopic properties of systems in equilibrium. It provides fundamental laws that govern energy conversion, the direction of processes, and the ultimate limits of efficiency for engines and refrigerators. In IB Physics Topic B.4, you will explore the first and second laws, thermodynamic processes, heat engines, and the powerful concept of entropy.
热力学是物理学中研究热、功、能量以及平衡系统宏观性质的分支。它提供了支配能量转换、过程方向以及热机和制冷机效率极限的基本定律。在 IB 物理 B.4 主题中，你将探索热力学第一和第二定律、热力学过程、热机以及熵这个强大的概念。
1. Thermodynamic Systems and State Variables | 热力学系统与状态变量
described by macroscopic state variables such as pressure (P), volume (V), temperature (T), and amount of substance (n). An equation of state, like the ideal gas law PV = nRT, relates these variables at equilibrium.
热力学系统是为研究而选定的特定物质或空间区域。系统可分为开放系统（与外界交换物质和能量）、封闭系统（交换能量但不交换物质）和孤立系统（既不交换物质也不交换能量）。系统的状态由宏观状态变量描述，如压强(P)、体积(V)、温度(T)和物质的量(n)。状态方程，如理想气体定律 PV = nRT，将这些平衡状态下的变量联系起来。
2. Internal Energy and the Microscopic Picture | 内能与微观图像
n the temperature rises, the average kinetic energy of particles increases, which is why temperature is a measure of the average random kinetic energy per particle. In real substances, intermolecular potential energies also contribute to U, leading to phase changes without temperature change.
系统的内能 U 是其所有组成粒子无规动能和势能的总和。对于理想单原子气体，内能仅取决于温度：U = (3/2)nRT。温度升高时，粒子的平均动能增加，这正是温度成为每个粒子平均无规动能度量的原因。在真实物质中，分子间势能也会对内能做出贡献，从而导致没有温度变化的相变。
3. The First Law of Thermodynamics | 热力学第一定律
The first law is a statement of energy conservation: the change in internal energy ΔU of a system equals the net heat Q added to the system minus the net work W done by the system. It is written as:
热力学第一定律是能量守恒的表述：系统内能的变化 ΔU 等于系统吸收的净热量 Q 减去系统对外做的净功 W。写作：
ΔU = Q - W
one on the system. It is essential to be clear about which convention you are using. The first law accounts for all energy transfers and explains why the internal energy of an isolated system remains constant.
在这种符号约定中，当热量进入系统时 Q 为正，当系统膨胀并对环境做功时 W 为正。有些教材使用 ΔU = Q + W，其中 W 是外界对系统做的功。明确使用哪一种约定至关重要。第一定律解释了所有能量传递，并说明了为什么孤立系统的内能保持不变。
4. Thermodynamic Processes and Their p-V Diagrams | 热力学过程及其 p-V 图
Thermodynamic processes can be represented on pressure–volume (p-V) diagrams. The most important reversible processes are:
热力学过程可以用压强-体积(p-V)图表示。最重要的可逆过程有：
- Isochoric (constant volume): at transfer changes only internal energy, ΔU = Q. On a p-V diagram, it is a vertical line.
- 等容过程： 体积恒定，故 W = 0。任何热量传递只改变内能，ΔU = Q。在 p-V 图上是一条竖直线。
- Isobaric (constant pressure): . The work done is W = PΔV. The heat added goes into both internal energy change and work.
- 等压过程： 压强恒定。做功为 W = PΔV。加入的热量同时用于内能变化和做功。
- Isothermal (constant temperature): equilibrium with a reservoir. On a p-V diagram, it appears as a hyperbola (PV = constant).
- 等温过程： 对于理想气体，ΔU = 0，因此 Q = W。该过程足够慢，使系统与热源保持热平衡。在 p-V 图上呈现为双曲线（PV = 常数）。
- Adiabatic (no heat exchange): es as the gas expands or compresses without heat transfer. The curve on a p-V diagram is steeper than an isotherm.
- 绝热过程： Q = 0，因此 ΔU = -W。气体在无热传递的情况下膨胀或压缩时温度发生变化。p-V 图上的曲线比等温线更陡。
5. Work Done in Thermodynamic Processes | 热力学过程中的做功
The work done by a gas during an expansion or compression is given by the area under the p-V curve. Mathematically,
气体在膨胀或压缩过程中所做的功由 p-V 曲线下的面积给出。数学上，
W = ∫ P dV
n a cyclic process, the net work done per cycle equals the area enclosed by the cycle on the p-V diagram. This is particularly useful when analyzing heat engines.
对于等压过程，这简化为 W = P(V₂ − V₁)。对于理想气体的等温膨胀，功可表示为 W = nRT ln(V₂/V₁)。在循环过程中，每个循环所做的净功等于 p-V 图上循环所围的面积。这在分析热机时特别有用。
6. Heat Engines and Thermal Efficiency | 热机与热效率
W + Qc. The thermal efficiency e of the engine is defined as the ratio of useful work output to the heat input:
热机是一种通过循环将热能转化为机械能的装置。它从高温热源吸收热量 Qh，将其中一部分转化为有用功 W，并将余热 Qc 排放到低温热源。能量守恒给出 Qh = W + Qc。热机的热效率 e 定义为有用功输出与输入热量之比：
e = W / Qh = (Qh - Qc) / Qh = 1 - (Qc / Qh)
No heat engine can be 100% efficient because some heat must always be rejected to a cold reservoir. The maximum possible efficiency between two temperatures is given by a reversible engine, such as the Carnot engine.
没有热机能够达到 100% 的效率，因为总有部分热量必须被排放到低温热源。在两个温度之间可能达到的最大效率由可逆热机给出，例如卡诺热机。
7. The Second Law of Thermodynamics | 热力学第二定律
The second law places constraints on the direction of energy transfer. Two classic formulations are:
第二定律对能量传递的方向施加了限制。两个经典表述是：
- Clausius statement: It is impossible for a self-acting machine, working in a cycle, to transfer heat from a colder body to a hotter body without an external work input.
- 克劳修斯表述： 不可能使热量由低温物体传到高温物体而不引起其他变化（即不需要外界做功）。
- Kelvin-Planck statement: It is impossible to construct a heat engine that operates in a cycle and converts all the heat absorbed from a single reservoir into useful work.
- 开尔文-普朗克表述： 不可能制成一种循环动作的热机，只从一个热源吸取热量，使之完全变为有用功而不产生其他影响。
These statements are equivalent and imply that a perpetual motion machine of the second kind is impossible. The second law introduces the concept of entropy and the irreversible nature of natural processes.
这些表述是等价的，都意味着第二类永动机是不可能制成的。第二定律引入了熵的概念以及自然过程的不可逆性质。
8. The Carnot Cycle and Carnot’s Theorem | 卡诺循环与卡诺定理
The Carnot cycle is an idealized thermodynamic cycle consisting of four reversible stages: isothermal expansion at high temperature Tₕ, adiabatic expansion (temperature falls to Tₖ), isothermal compression at low temperature Tₖ, and adiabatic compression back to Tₕ. The cycle is perfectly reversible and sets the upper limit for the efficiency of any heat engine operating between two reservoirs:
卡诺循环是一个理想化的热力学循环，由四个可逆阶段组成：高温 Tₕ 下的等温膨胀、绝热膨胀（温度降至 Tₖ）、低温 Tₖ 下的等温压缩，以及绝热压缩回到 Tₕ。该循环是完全可逆的，并设定了任何在两个热源之间运行的热机的效率上限：
eCarnot = 1 - (Tₖ / Tₕ)
Here, temperatures must be expressed in kelvin. Carnot’s theorem states that no real engine operating between the same two reservoirs can exceed this efficiency, and all reversible engines have the same efficiency regardless of the working substance. This result is fundamental to understanding the limits of energy conversion technology.
这里温度必须用开尔文表示。卡诺定理指出，在相同两个热源之间工作的任何实际热机都不可能超过这一效率，而且所有可逆热机无论工质如何都具有相同的效率。这一结果对理解能量转换技术的极限至关重要。
9. Entropy: The Arrow of Time | 熵：时间之箭
be arranged. For a reversible isothermal process, the change in entropy is given by ΔS = Qrev / T. The second law can be expressed in terms of entropy: in any spontaneous process, the total entropy of an isolated system always increases or, in the limiting case of a reversible process, remains constant. This provides a thermodynamic arrow of time, explaining why processes like mixing, heat conduction, and burning happen naturally in one direction but never spontaneously reverse.
熵 S 是一个态函数，用于衡量系统的无序程度或微观排列方式的数量。对于可逆等温过程，熵的变化由 ΔS = Qrev / T 给出。第二定律可以用熵来表述：在任何自发过程中，孤立系统的总熵总是增加，或在可逆过程的极限情况下保持不变。这提供了一个热力学的时间之箭，解释了为什么混合、热传导和燃烧等过程会自然地朝一个方向发生，而绝不会自发逆转。
10. Thermodynamic Temperature Scale and Absolute Zero | 热力学温标与绝对零度
is identical to the ideal gas temperature scale and its zero point, absolute zero (0 K or – odynamics states that it is impossible to reach absolute zero in a finite number of steps.
热力学温标独立于任何物质的性质，基于卡诺热机的效率来定义。两个温度 Tₕ 和 Tₖ 的比值由传递的热量比决定：Tₕ / Tₖ = Qh / Qc。这一温标与理想气体温标一致，其零点——绝对零度（0 K 或 –273.15 °C）——是卡诺热机效率将达到 1 的温度（尽管这是无法达到的）。热力学第三定律指出，不可能通过任何有限步骤达到绝对零度。
11. Real-World Applications: Refrigerators and Heat Pumps | 实际应用：冰箱与热泵
p, COP_HP = Qh / W. The Carnot cycle also provides the maximum possible COP values: COP_R,max = Tₖ / (Tₕ - Tₖ) and COP_HP,max = Tₕ / (Tₕ - Tₖ). These principles underpin modern heating and cooling technologies.
冰箱和热泵是反向运行的热机。它们从低温空间提取热量 Qc，并依靠输入功 W，将热量 Qh = Qc + W 排放到高温环境。其性能由性能系数(COP)衡量：对于冰箱，COP_R = Qc / W；对于热泵，COP_HP = Qh / W。卡诺循环同样给出了可能的最大 COP 值：COP_R,max = Tₖ / (Tₕ - Tₖ) 和 COP_HP,max = Tₕ / (Tₕ - Tₖ)。这些原理是现代供暖和制冷技术的基础。
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