IB Physics: Thermodynamics Laws and Processes Master Summary | IB物理：热力学定律与过程要点总结

📚 IB Physics: Thermodynamics Laws and Processes Master Summary | IB物理：热力学定律与过程要点总结

Thermodynamics is the study of energy transformations involving heat, work, and internal energy. In IB Physics, a clear grasp of the laws of thermodynamics and the behavior of ideal gases is essential for solving both multiple-choice and extended-response questions.

热力学是研究涉及热量、功和内能的能量转换的科学。在IB物理中，清晰掌握热力学定律以及理想气体的行为，对于解答选择题和拓展回答题都至关重要。

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1. System, Surroundings, and State Variables | 系统、外界与状态变量

A thermodynamic system is the object or region under investigation; everything outside it is called the surroundings. Systems can be open (exchanging both energy and matter), closed (exchanging energy but not matter), or isolated (exchanging neither).

热力学系统是被研究的对象或区域；它之外的一切称为外界。系统可以是开放的（交换能量和物质）、封闭的（交换能量但不交换物质）或孤立的（两者都不交换）。

State variables such as pressure P, volume V, temperature T, and internal energy U describe the equilibrium state of a system. These variables depend only on the current state, not on the path taken to reach it.

状态变量如压强P、体积V、温度T和内能U描述系统的平衡状态。这些变量只取决于当前状态，而与达到该状态所经历的路径无关。

• Open system: energy and matter can be exchanged with the surroundings.

  开放系统：与外界交换能量和物质。

• Closed system: energy can be exchanged, but matter cannot.

  封闭系统：可以交换能量，但不能交换物质。

• Isolated system: no exchange of energy or matter.

  孤立系统：既不交换能量也不交换物质。

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2. Heat, Work, and Internal Energy | 热量、功与内能

Heat Q is energy transferred between systems due to a temperature difference. Work W is energy transferred when a force moves an object, such as a gas expanding against a piston. Internal energy U is the total kinetic and potential energy of all particles within the system.

热量Q是由于温度差而在系统之间传递的能量。功W是力推动物体移动时传递的能量，例如气体推动活塞膨胀。内能U是系统内所有粒子的总动能与势能之和。

In IB Physics, the first law of thermodynamics is often written with the convention that Q is positive when heat is added to the system, and W is positive when the gas does work on its surroundings.

在IB物理中，热力学第一定律常采用如下约定：Q为正值表示系统吸收热量，W为正值表示气体对外界做功。

For an ideal gas, internal energy depends only on temperature. This is a key simplification because the potential energy between particles is neglected.

对于理想气体，内能仅取决于温度。这是一个重要的简化，因为忽略了粒子间的势能。

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3. The First Law of Thermodynamics | 热力学第一定律

The first law is a statement of energy conservation. It connects the change in internal energy ΔU to the heat added to the system Q and the work done by the system W.

第一定律是能量守恒的表述。它将内能的变化ΔU与系统吸收的热量Q及系统对外做的功W联系起来。

ΔU = Q − W

If heat is added, Q is positive and ΔU increases. If the gas expands and does work, W is positive and ΔU decreases. In a compression, W is negative, so ΔU increases.

如果系统吸收热量，Q为正值，ΔU增大。如果气体膨胀对外做功，W为正值，ΔU减小。在压缩过程中，W为负值，因此ΔU增大。

When applying this equation, always define positive directions clearly before solving a problem.

应用该方程时，解题前一定要先明确正方向的定义。

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4. The Four Thermodynamic Processes | 四种热力学过程

The four idealised processes are distinguished by which quantity remains constant. They form the basis of many IB exam problems.

四种理想化过程的区别在于哪一个物理量保持不变。它们是IB考试中许多题目的基础。

Process | 过程	Constant | 不变	Key Relation | 关键关系
Isovolumetric / Isochoric | 等容过程	Volume V | 体积V	W = 0, ΔU = Q
Isobaric | 等压过程	Pressure P | 压强P	W = PΔV, ΔU = Q − PΔV
Isothermal | 等温过程	Temperature T | 温度T	ΔU = 0, Q = W
Adiabatic | 绝热过程	No heat exchange Q = 0 | 无热量交换Q = 0	ΔU = −W

In an isothermal process, the temperature stays constant, so for an ideal gas the internal energy does not change. In an adiabatic process, no heat enters or leaves the system, so any work done changes the internal energy and hence the temperature.

在等温过程中，温度保持不变，因此对于理想气体，内能不变。在绝热过程中，系统没有热量进出，因此任何做功都会改变内能和温度。

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5. Work Done by a Gas and p–V Diagrams | 气体做功与p–V图

On a pressure–volume diagram, the work done by a gas during a process is equal to the area under the curve between the initial and final volumes.

在压强–体积图上，气体在某一过程中对外做的功等于过程曲线与横轴（体积轴）之间、从初态到末态所围成的面积。

W = ∫ P dV

For an expansion, V increases, so W is positive. For a compression, V decreases, so W is negative. In a cyclic process, the net work done per cycle equals the area enclosed by the loop on the p–V diagram.

对于膨胀过程，体积V增大，W为正；对于压缩过程，体积V减小，W为负。在循环过程中，每循环的净功等于p–V图上循环曲线所包围的面积。

Remember: the shape of the curve matters. Adiabatic curves are steeper than isothermal curves because temperature changes during an adiabatic process.

注意：曲线的形状很重要。绝热曲线比等温曲线更陡，因为绝热过程中温度会变化。

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6. The Second Law of Thermodynamics | 热力学第二定律

The second law of thermodynamics states that heat cannot spontaneously flow from a colder body to a hotter body. It also implies that no heat engine can convert all input heat into useful work without rejecting some heat to a cold reservoir.

热力学第二定律指出，热量不能自发地从低温物体传递到高温物体。它还意味着任何热机都不可能在不向低温热源排放热量的情况下，将输入的热量全部转化为有用功。

In terms of entropy, the second law can be stated as: the total entropy of an isolated system always increases for an irreversible process and remains constant for a reversible process.

从熵的角度，第二定律可以表述为：孤立系统的总熵在不可逆过程中总是增加，在可逆过程中保持不变。

ΔS = Q_rev / T

Here ΔS is the change in entropy, Q_rev is the heat transferred reversibly, and T is the absolute temperature in kelvin.

其中ΔS是熵的变化，Q_rev是可逆过程中传递的热量，T是以开尔文为单位的绝对温度。

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7. Entropy and Probability | 熵与概率

Entropy can be understood as a measure of the number of microstates corresponding to a given macrostate. A system naturally evolves toward the macrostate with the largest number of microstates, which is the most probable arrangement.

熵可以理解为给定宏观态所对应的微观状态数的量度。系统会自发地朝向具有最多微观状态数的宏观态演化，也就是最可能的排列方式。

For example, when a gas expands freely into a vacuum, it becomes more spread out. This new distribution is more probable because there are far more ways to arrange the particles throughout the larger volume.

例如，当气体自由膨胀到真空中时，它会变得更分散。这种新的分布更可能发生，因为在更大的体积内排列粒子的方式要多得多。

The second law therefore reflects the natural tendency of energy and matter to become more disordered, as long as no external work is done to reverse the process.

因此，第二定律反映了能量和物质在没有外部做功逆转过程时，自然趋向于更加无序的趋势。

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8. Heat Engines and Efficiency | 热机与效率

A heat engine absorbs heat Q_h from a hot reservoir, converts part of it into work W, and reject the remaining heat Q_c to a cold reservoir.

热机从高温热源吸收热量Q_h，将其中一部分转化为功W，并将剩余的热量Q_c排放到低温热源。

The efficiency η of a heat engine is defined as the ratio of useful work output to heat input.

热机的效率η定义为有用功输出与输入热量之比。

η = W / Q_h = (Q_h − Q_c) / Q_h = 1 − Q_c / Q_h

For a Carnot engine, the maximum possible efficiency depends only on the absolute temperatures of the hot and cold reservoirs.

对于卡诺热机，最大可能效率仅取决于高温和低温热源的绝对温度。

η_Carnot = 1 − T_c / T_h

All temperatures must be in kelvin. This is a common error in IB exams: using Celsius values in the Carnot efficiency formula.

所有温度必须使用开尔文单位。这是IB考试中常见的错误：在卡诺效率公式中使用摄氏温度。

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9. Refrigerators and Heat Pumps | 制冷机与热泵

A refrigerator or heat pump is a heat engine operating in reverse. Work W is done on the system, causing heat Q_c to be removed from the cold reservoir and heat Q_h to be delivered to the hot reservoir.

制冷机或热泵是反向运行的热机。外界对系统做功W，使热量Q_c从低温热源吸走，并将热量Q_h释放到高温热源。

The coefficient of performance (COP) of a refrigerator is the ratio of heat extracted from the cold reservoir to the work input.

制冷机的性能系数（COP）是从低温热源提取的热量与输入功之比。

COP_refrigerator = Q_c / W

For an ideal Carnot refrigerator, this becomes:

对于理想卡诺制冷机，该比值变为：

COP_refrigerator = T_c / (T_h − T_c)

In IB physics, this demonstrates that work must be supplied to move heat against its natural direction.

在IB物理中，这说明了要使热量逆着自然方向流动，必须提供功。

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10. Cyclic Processes and Net Work | 循环过程与净功

In a cyclic process, the system returns to its initial state, so the total change in internal energy is zero: ΔU_cycle = 0. Therefore, the net heat absorbed equals the net work done per cycle.

在循环过程中，系统回到初始状态，因此内能的总变化为零：ΔU_循环 = 0。所以，每循环吸收的净热量等于对外做的净功。

Q_net = W_net

On a p–V diagram, a clockwise loop corresponds to a heat engine producing net positive work. An anticlockwise loop corresponds to a refrigerator or heat pump requiring net work input.

在p–V图上，顺时针循环对应热机对外做正功；逆时针循环对应制冷机或热泵，需要输入净功。

When calculating net work, always take the area inside the loop. Do not simply sum the areas under each curve, as they may partially cancel.

计算净功时，一定要取循环曲线内部包围的面积。不要简单将每条曲线下的面积相加，因为部分面积会相互抵消。

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11. Common Exam Tips and Misconceptions | 常见考点提示与误区

• Always convert temperatures to kelvin for entropy and Carnot efficiency calculations.

  在计算熵和卡诺效率时，务必把温度转换为开尔文。

• Use a consistent sign convention for Q and W. State whether W represents work done by the system or work done on the system.

  对Q和W使用一致的符号约定。明确W表示系统对外做的功，还是外界对系统做的功。

• Do not assume an adiabatic process is isothermal. In adiabatic processes, temperature changes unless the gas is ideal and no work is done.

  不要认为绝热过程就是等温过程。在绝热过程中，温度会变化，除非理想气体不做功。

• Remember that the area under a p–V curve represents work, but only the closed loop area gives net work for a cycle.

  记住p–V曲线下的面积表示功，但只有闭合回路的面积才表示一个循环的净功。

• Entropy is not a measure of “order” alone; it is fundamentally about probability and the number of microstates.

  熵不仅仅是“有序程度”的量度；从根本上说，它涉及概率和微观状态数。

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12. Conclusion | 总结

The laws of thermodynamics govern the conversion of heat into work and the direction of natural energy flow. Mastery of the first law, the four idealised processes, p–V diagrams, entropy, and engine efficiency will allow you to solve a wide range of IB Physics problems confidently.

热力学定律支配着热量转化为功的过程以及自然界能量流动的方向。熟练掌握第一定律、四种理想化过程、p–V图、熵和热机效率，将帮助你自信地解决各种IB物理问题。

Focus on understanding the physical meaning behind each equation, and practise drawing and interpreting p–V diagrams before your exam.

在考试前，要着重理解每个方程背后的物理含义，并多加练习绘制和解读p–V图。

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