📚 Changing Temperature | 改变温度
Temperature is a fundamental concept in thermal physics that governs how energy is transferred between objects and how substances change their physical state. In A-Level Physics, understanding how temperature changes relate to heat, internal energy, and phase transitions is essential for solving calorimetry problems and explaining everyday phenomena.
温度是热物理学中一个基本概念，它决定了能量如何在物体之间传递以及物质如何改变其物理状态。在 A-Level 物理中，理解温度变化与热量、内能和相变之间的关系，对于解决量热学问题和解释日常现象至关重要。
1. What is Temperature? | 什么是温度？
Temperature is a scalar physical quantity that indicates how hot or cold an object is. Microscopically, it is proportional to the average random kinetic energy of the particles (atoms or molecules) making up the substance. The higher the temperature, the more vigorously the particles move.
温度是一个标量物理量，表示物体的冷热程度。从微观上看，温度与构成物质的粒子（原子或分子）的平均无规则动能成正比。温度越高，粒子运动越剧烈。
It is crucial to distinguish temperature from thermal energy (heat). A large iceberg has a much lower temperature than a cup of boiling water, yet it contains far more internal energy because of its enormous mass. Temperature tells us the direction of spontaneous heat flow: energy flows from a region of higher temperature to one of lower temperature until thermal equilibrium is reached.
区分温度和热能（热量）至关重要。巨大的冰山虽然温度远低于一杯沸水，但由于其质量极大，它所包含的内能要多得多。温度告诉我们自发传热的方向：能量从高温区域流向低温区域，直至达到热平衡。
2. Thermal Energy and Heat | 热能与热量
Thermal energy refers to the total kinetic and potential energy of all particles in a system. Heat, however, is the transfer of thermal energy from one body to another due to a temperature difference. It is not a property of a body; we do not say an object contains 'heat'.
热能指的是系统内所有粒子的动能和势能的总和。然而，热量是由于温差而从一个物体传递到另一个物体的热能。热量不是物体自身的属性；我们不说一个物体“含有”热量。
When a substance is heated and its temperature rises, the heat transferred increases the random kinetic energy of its particles. If a phase change occurs at constant temperature, the heat breaks or weakens inter-particle bonds without increasing kinetic energy.
当物质受热且温度升高时，传递的热量增加了其粒子的无规则动能。如果在恒定温度下发生相变，热量则用于破坏或削弱粒子间的键能，而不增加动能。
3. Temperature Scales: Celsius and Kelvin | 温标：摄氏与开尔文
The Celsius scale defines 0 °C as the freezing point of water and 100 °C as the boiling point of water at standard atmospheric pressure. However, the thermodynamic (Kelvin) scale is central to A-Level physics. The kelvin is the SI base unit of temperature, defined by the triple point of water and the Boltzmann constant.
摄氏温标将标准大气压下水的冰点定义为 0 °C，沸点定义为 100 °C。然而，在 A-Level 物理中，热力学温标（开尔文）居于核心地位。开尔文是温度的国际基本单位，由水的三相点和玻尔兹曼常数定义。
K, is the temperature at which particles have the minimum possible energy; it is equal to – 1 °C. The conversion is T (K) = θ (°C) + 273.15, often simplified to +273 in calculations.
绝对零度 0 K 是粒子具有最低可能能量时的温度，相当于 –273.15 °C。两个温标的温度间隔相同：1 K 的变化等于 1 °C 的变化。换算关系为 T (K) = θ (°C) + 273.15，在计算中通常简化为 +273。
4. Internal Energy | 内能
The internal energy of a system is the sum of the randomly distributed kinetic energies and the potential energies of its constituent particles. The kinetic part depends on temperature; the potential part depends on the forces between particles and the relative separations.
系统的内能是其组成粒子的无规则分布的动能与势能之和。动能部分取决于温度；势能部分取决于粒子间的作用力及其相对间距。
When heating a solid, liquid or gas without a phase change, the temperature rises, so the internal energy increases solely because of the increase in particle kinetic energy. During a phase change, temperature remains constant, but internal energy still increases due to the gain in potential energy as bonds are broken or stretched.
加热固体、液体或气体而不发生相变时，温度升高，因此内能仅因粒子动能增加而增加。在相变过程中，温度保持不变，但内能仍会由于键的断裂或拉伸而导致势能增加而增加。
5. Heating and Temperature Change: Specific Heat Capacity | 加热与温度变化：比热容
The specific heat capacity c of a material is the energy required to raise the temperature of 1 kg of the substance by 1 K (or 1 °C) without any change of state. It is a property characteristic of the material. The unit is J kg⁻¹ K⁻¹.
物质的比热容 c 是指使 1 kg 该物质的温度升高 1 K（或 1 °C）且不发生状态变化所需的能量。它是材料的特性参数，单位为 J kg⁻¹ K⁻¹。
The energy transferred ΔE (often represented by Q) when a mass m of a substance undergoes a temperature change Δθ is given by:
当质量为 m 的物质发生温度变化 Δθ 时，传递的能量 ΔE（常用 Q 表示）由下式给出：
ΔE = m c Δθ
This equation assumes no heat losses and no phase change. Different materials have different specific heat capacities; water has a very high value (4180 J kg⁻¹ K⁻¹), which makes it an excellent coolant and a thermal buffer in climates.
该方程假设没有热量损失且不发生相变。不同材料具有不同的比热容；水的比热容非常高（4180 J kg⁻¹ K⁻¹），这使其成为极佳的冷却剂和气候中的热缓冲物质。
6. Heat Capacity | 热容量
1 K. It is related to specific heat capacity by C = m c. The unit of heat capacity is J K⁻¹.
热容量 C 是使某一特定物体或样品的温度升高 1 K 所需的能量。它与比热容的关系为 C = m c。热容量的单位是 J K⁻¹。
Heat capacity is an extensive property; it depends on the mass and the material, whereas specific heat capacity is intensive. A large body of water has an enormous heat capacity, which explains why an ocean takes a long time to warm up or cool down.
因此，对于给定的物体，ΔE = C Δθ。热容量是一个广延量，取决于质量和材料，而比热容则是强度量。巨大的水体具有极大的热容量，这就解释了为什么海洋升温或降温非常缓慢。
7. Determining Specific Heat Capacity Experimentally | 实验测定比热容
A standard school laboratory method uses an electric heater to supply energy to a metal block of known mass. The block is surrounded by thermal insulation to minimise heat losses. A thermometer and a stopwatch are used to record the temperature rise and the heating time.
标准的学校实验室方法是使用电加热器向已知质量的金属块提供能量。金属块用绝热材料包裹以尽量减少热损失。使用温度计和秒表记录温升和加热时间。
suming that all this energy increases the internal energy of the block, we equate V I t = m c Δθ, and thus c = V I t / (m Δθ).
提供的电能由 ΔE = V I t 计算，其中 V 是加热器两端的电压，I 是电流，t 是时间。假设所有能量都用于增加金属块的内能，则有 V I t = m c Δθ，从而 c = V I t / (m Δθ)。
In practice, this method overestimates the specific heat capacity if heat losses are significant. Adding a layer of insulation, using a polished block to reduce radiation, and applying a cooling correction can improve accuracy. A continuous-flow calorimeter is a more sophisticated technique, but the electrical method remains the most common in practical assessments.
实际上，如果热量损失显著，该方法会高估比热容。增加隔热层、使用抛光金属块以减少辐射，以及进行冷却修正都可以改善精度。连续流动量热计是一种更精密的技术，但电热法在实验考试中仍最为常见。
8. Phase Changes and Latent Heat | 相变与潜热
When a substance changes state—melting, freezing, boiling, condensing—its temperature remains constant even though heat is being supplied. This energy is called latent heat because it is 'hidden': it does not produce a temperature change but instead provides the energy required to overcome intermolecular forces.
当物质发生状态变化时——熔化、凝固、沸腾、凝结——即使持续供热，其温度也保持不变。这部分能量被称为潜热，因为它是“潜伏的”：它不会引起温度变化，而是提供克服分子间作用力所需的能量。
The specific latent heat L of a substance is the energy required to change the state of 1 kg of the substance at constant temperature. The energy E needed for a mass m is simply:
物质的比潜热 L 是指使 1 kg 物质在恒温下改变状态所需的能量。使质量 m 的物质发生相变所需的能量 E 为：
E = m L
Latent heat has the unit J kg⁻¹. During fusion (melting), it is called specific latent heat of fusion Lf; during vaporisation (boiling), it is specific latent heat of vaporisation Lv.
比潜热的单位是 J kg⁻¹。在熔化过程中，称为熔化比潜热 Lf；在汽化过程中，称为汽化比潜热 Lv。
9. Specific Latent Heat of Fusion and Vaporisation | 熔化比潜热与汽化比潜热
The latent heat of fusion is associated with the solid–liquid transition. For ice, Lf ≈ 3.34 × 10⁵ J kg⁻¹. The latent heat of vaporisation is much larger because it involves completely overcoming attractive forces rather than merely weakening them. For water, Lv ≈ 2.26 × 10⁶ J kg⁻¹.
熔化潜热与固–液相变相关。对于冰，Lf ≈ 3.34 × 10⁵ J kg⁻¹。汽化潜热要大得多，因为它需要完全克服吸引力，而不仅仅是减弱它们。对于水，Lv ≈ 2.26 × 10⁶ J kg⁻¹。
This large difference explains why steam at 100 °C causes much more severe burns than boiling water at the same temperature. Steam first condenses, releasing a huge amount of latent heat, and then the condensed water cools, releasing further thermal energy.
这一巨大差异解释了为什么 100 °C 的蒸汽造成的烫伤比同温度的沸水严重得多。蒸汽首先凝结，释放大量潜热，然后凝结后的水冷却时还会释放更多的热能。
The heating curve of water illustrates both specific and latent heat: temperature rises linearly with energy during warming of ice, then stays constant at 0 °C while ice melts, then rises again as water warms, stays constant at 100 °C during boiling, and rises again for steam.
水的加热曲线同时体现了比热和潜热：在冰升温期间，温度随能量线性升高；在冰融化时温度恒定于 0 °C；随后水升温时温度再次升高；在沸腾时温度恒定于 100 °C；之后蒸汽温度继续升高。
10. Measuring Specific Latent Heat | 实验测定比潜热
To determine the specific latent heat of fusion of ice, a mixture method is often used. A known mass of ice is added to a known mass of warm water in a calorimeter. The temperature drop of the water is recorded. The energy lost by the water and the calorimeter equals the energy gained by the ice to melt and then to warm up to the final temperature.
为测定冰的熔化比潜热，常采用混合法。将已知质量的冰加入热量计内已知质量的温水中，记录水的温度下降量。水和热量计失去的能量等于冰熔化并升温至终温所获得的能量。
er the water has reached a steady boiling condition, the mass of water vaporised in a measured time t is collected and weighed. Then, assuming no energy loss, V I t = m Lv, allowing Lv to be calculated.
对于汽化比潜热，采用电学法较为方便。将电加热器完全浸入水中，提供的功率为 P = V I。水达到稳定沸腾状态后，收集并称量在测量时间 t 内汽化的水的质量。假设无能量损失，则有 V I t = m Lv，从而可计算出 Lv。
In either experiment, heat losses to the surroundings represent the main source of uncertainty. Effective lagging, a low initial temperature difference, and stirring for uniform temperature help improve accuracy.
在两种实验中，向环境的热量损失都是误差的主要来源。有效的绝热包扎、较小的初始温差以及搅拌使温度均匀都有助于提高准确性。
11. Heat Transfer and Temperature Change | 热传递与温度变化
Heat can be transferred by conduction, convection and radiation. In solids, conduction is the primary mechanism—vibrating atoms and free electrons transfer kinetic energy through the material. Metals are good conductors because they have many free electrons.
热量可以通过传导、对流和辐射传递。在固体中，传导是主要机制——振动的原子和自由电子将动能传递通过材料。金属是良导体，因为它们含有大量自由电子。
Convection occurs in fluids (liquids and gases) where heated, less dense fluid rises and cooler, denser fluid sinks, setting up a convection current. Radiation is the transfer of energy by electromagnetic waves, mainly infrared, and does not require a medium. All bodies above absolute zero emit thermal radiation.
对流发生在流体（液体和气体）中，受热后密度较小的流体上升，而较冷、密度较大的流体下沉，形成对流循环。辐射是通过电磁波（主要是红外线）传递能量，不需要介质。任何高于绝对零度的物体都会发出热辐射。
The rate of heat transfer affects how quickly the temperature of an object changes. A large temperature gradient speeds up conduction and convection; a dark, matt surface emits and absorbs radiation more effectively than a shiny, white surface, which has implications for practical apparatus design.
热量传递的速率影响物体温度变化的快慢。大的温度梯度会加速传导和对流；深色、粗糙表面比光亮、白色的表面更有效地发射和吸收辐射，这对实验装置的设计有启示意义。
12. Summary of Key Equations | 关键公式总结
The relationships governing temperature changes and phase transitions can be reviewed in one place. The table below presents the essential formulae used in A-Level CIE thermal physics to calculate energies associated with changing temperature and changing state.
与温度变化和相变相关的公式可汇总于一处。下表列出了 A-Level CIE 热学中用于计算与改变温度和改变状态有关能量的基本公式。
| Equation | Meaning 意义 |
|---|---|
| ΔE = m c Δθ | Energy for temperature change (no phase change) 改变温度所需的能量（无相变） |
| ΔE = C Δθ | Energy using heat capacity 使用热容量时的能量 |
| E = m L | Energy for phase change at constant temperature 恒温相变所需的能量 |
| E = V I t | Electrical energy supplied by a heater 电加热器提供的电能 |
| C = m c | Relationship between heat capacity and specific heat capacity 热容量与比热容的关系 |
These equations, together with an understanding of internal energy and temperature scales, form the backbone of calorimetry and a large part of the thermodynamics topics in the CIE A-Level syllabus.
这些方程连同对内能和温标的理触，构成了量热学的核心，也是 CIE A-Level 教学大纲中热力学部分的重要内容。
Published by TutorHao | Physics Revision Series | aleveler.com
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