📚 Changing Temperature | 温度变化
When a solid, liquid or gas is heated, its temperature often rises, but the amount of temperature change depends on mass, material and the rate of energy supply. In CIE A-Level Physics, this topic links the macroscopic measurements of temperature and heat to the microscopic kinetic particle model.
当固体、液体或气体被加热时，其温度通常会升高，但温度变化的大小取决于质量、材料以及能量供应速率。在 CIE A-Level 物理中，本主题将宏观的温度与热量测量和微观的分子动理论模型联系起来。
1. Heat, Temperature and Thermal Energy | 热量、温度与内能
Temperature measures how hot or cold an object is and determines the direction of thermal energy transfer. Heat is the transfer of thermal energy from a hotter body to a colder body as a result of a temperature difference.
温度衡量物体的冷热程度，并决定热传递的方向。热量是由于温差而从较热物体向较冷物体传递的热能。
Internal energy is the sum of the random kinetic energy and potential energy of all particles in a substance. When a substance is heated, its internal energy increases, but this does not always cause a temperature rise.
内能是物质中所有粒子的随机动能和势能的总和。当物质被加热时，其内能增加，但这并不总是导致温度升高。
2. The Kinetic Particle Model | 分子动理论模型
In the kinetic particle model, gas particles move randomly, and their average kinetic energy is proportional to the absolute temperature in kelvin. For an ideal gas, the average translational kinetic energy per particle is (3/2)kT, where k is the Boltzmann constant.
在分子动理论模型中，气体粒子随机运动，其平均动能与开尔文绝对温度成正比。对于理想气体，每个粒子的平均平动动能为 (3/2)kT，其中 k 为玻尔兹曼常数。
For solids and liquids, particles vibrate or move around fixed positions. Raising the temperature increases their average kinetic energy, so particles vibrate more vigorously or move faster.
对于固体和液体，粒子在固定位置附近振动或移动。升高温度会增加其平均动能，因此粒子振动更剧烈或移动更快。
3. Internal Energy During Heating | 加热过程中的内能变化
When a solid is heated at temperatures below its melting point, most of the supplied energy increases the vibrational kinetic energy of particles, so the temperature rises. At the melting point, added energy is used to break inter-particle bonds and increase potential energy, so the temperature remains constant.
当固体在其熔点以下被加热时，大部分供给的能量增加了粒子的振动动能，因此温度升高。在熔点时，增加的能量用于破坏粒子间的键并增加势能，因此温度保持不变。
This explains why internal energy can increase without a change in temperature: potential energy changes while kinetic energy stays constant during a phase change.
这解释了为什么内能可以在温度不变的情况下增加：在相变期间，势能变化而动能保持不变。
4. 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 kelvin (or 1 °C) without a change of state. Its unit is J kg⁻¹ K⁻¹.
比热容 c 是使 1 kg 物质的温度升高 1 开尔文（或 1 °C）而不发生物态变化所需的能量。其单位为 J kg⁻¹ K⁻¹。
Q = mcΔT
where Q is the thermal energy transferred, m is mass, c is specific heat capacity and ΔT is the temperature change in K or °C.
其中 Q 为传递的热能，m 为质量，c 为比热容，ΔT 为温度变化，单位为 K 或 °C。
Water has a high specific heat capacity of about 4200 J kg⁻¹ K⁻¹, which is why it is used as a coolant and why coastal climates are moderate.
水的比热容较高，约为 4200 J kg⁻¹ K⁻¹，因此常用作冷却剂，也是沿海气候温和的原因。
5. Heat Capacity of an Object | 物体的热容量
Heat capacity C is the energy required to raise the temperature of an entire object by 1 kelvin. It is given by C = mc, so Q = CΔT. Its unit is J K⁻¹.
热容量 C 是使整个物体温度升高 1 开尔文所需的能量。其公式为 C = mc，因此 Q = CΔT。单位为 J K⁻¹。
Unlike specific heat capacity, heat capacity depends on both the material and the mass. A larger mass of the same substance has a larger heat capacity and responds more slowly to the same heating power.
与比热容不同，热容量取决于材料和物体的质量。同种物质质量越大，热容量越大，在相同加热功率下温度变化越慢。
6. Measuring Specific Heat Capacity | 比热容的测量
A common CIE experiment to measure c uses an electric heater inserted into a metal block or immersed in a liquid. Measure the mass m, initial temperature, switch on the heater and record electrical energy E = VIt and final temperature after a known time.
CIE 常考的测量比热容实验使用插入金属块或浸入液体中的电加热器。测量质量 m、初始温度，打开加热器并记录电能 E = VIt 以及已知时间后的最终温度。
If no heat is lost to the surroundings, c = E / (mΔT). In practice, insulation and a small starting temperature difference reduce heat loss. If losses are ignored, the calculated value is usually too high because not all recorded energy is absorbed by the substance.
如果没有热量损失到环境中，c = E / (mΔT)。实际中，使用隔热材料和较小的起始温差可减少热损失。如果忽略损失，计算值通常偏高，因为记录的电能并非全部被物质吸收。
7. Latent Heat and Phase Change | 潜热与相变
Specific latent heat L is the energy required to change the state of 1 kg of a substance at constant temperature. The latent heat of fusion is for melting or freezing, and the latent heat of vaporisation is for boiling or condensing.
比潜热 L 是使 1 kg 物质在恒定温度下发生物态变化所需的能量。熔化潜热用于熔化或凝固，汽化潜热用于沸腾或冷凝。
Q = mL
During a phase change, the temperature does not rise even though energy is being supplied, because the energy is used to separate particles rather than increase their kinetic energy.
在相变过程中，即使持续供给能量，温度也不会升高，因为能量用于分离粒子，而不是增加其动能。
8. Heating and Cooling Curves | 加热与冷却曲线
A heating curve plots temperature against time while energy is supplied at a constant rate. Its slope depends on specific heat capacity and mass; a smaller slope indicates a larger heat capacity or a lower heating power.
加热曲线是在恒定功率供能时温度随时间变化的图线。其斜率取决于比热容和质量；斜率越小，表示热容量越大或加热功率越低。
Flat sections appear during melting and boiling. During these plateaus, the substance absorbs latent heat while the temperature remains constant.
在熔化和沸腾期间出现水平段。在这些平台期，物质吸收潜热，温度保持不变。
A cooling curve is the reverse: plateaus show freezing and condensation, where latent heat is released without a temperature drop.
冷却曲线则相反：平台表示凝固和冷凝，此时释放潜热而温度不下降。
9. Power and Rate of Temperature Change | 功率与温度变化速率
If a heater supplies power P, the energy transferred in time t is Q = Pt. If there is no phase change and no loss, the rate of temperature rise is ΔT/t = P / (mc).
如果加热器功率为 P，在时间 t 内传递的能量为 Q = Pt。如果没有相变且无损失，升温速率为 ΔT/t = P / (mc)。
This relationship explains why doubling the power doubles the temperature rise rate, and why an object with larger mass or higher specific heat capacity heats more slowly for the same power.
这一关系式解释了为什么功率加倍会使温升速率加倍，以及为什么在相同功率下，质量更大或比热容更高的物体加热更慢。
10. Thermal Equilibrium and Energy Conservation | 热平衡与能量守恒
When a hot object and a cold object are placed in contact in an insulated container, thermal energy is transferred from the hot object to the cold object until they reach the same final temperature.
当热物体和冷物体在绝热容器中接触时，热能从热物体传递到冷物体，直到两者达到相同的最终温度。
m₁c₁(T₁ − Tf) = m₂c₂(Tf − T₂)
assuming no energy is lost to the surroundings. This principle, called thermal equilibrium, is often used in CIE calculation problems to find the final temperature or specific heat capacity.
假设没有能量散失到环境中。这一称为热平衡的原理常用于 CIE 计算题，以求出最终温度或比热容。
11. Worked Example: Two Common Calculations | 典型例题计算
Worked example 1: Calculate the energy needed to heat 2.0 kg of water from 20 °C to 80 °C. Using Q = mcΔT, Q = 2.0 × 4200 × (80 − 20) = 504 000 J.
例题 1：计算将 2.0 kg 水从 20 °C 加热到 80 °C 所需的能量。由 Q = mcΔT，Q = 2.0 × 4200 × (80 − 20) = 504 000 J。
Worked example 2: A 0.50 kg aluminium block at 100 °C is placed in 0.40 kg water at 20 °C. Find the final temperature if c_al = 900 J kg⁻¹ K⁻¹ and no heat is lost. Use heat lost = heat gained and solve for Tf.
例题 2：将 0.50 kg、100 °C 的铝块放入 0.40 kg、20 °C 的水中。若 c_al = 900 J kg⁻¹ K⁻¹ 且无热量损失，求最终温度。利用放热 = 吸热并解出 Tf。
0.50 × 900 × (100 − Tf) = 0.40 × 4200 × (Tf − 20). This gives 450(100 − Tf) = 1680(Tf − 20), so Tf ≈ 36.9 °C.
0.50 × 900 × (100 − Tf) = 0.40 × 4200 × (Tf − 20)。解得 450(100 − Tf) = 1680(Tf − 20)，因此 Tf ≈ 36.9 °C。
12. Exam Tips for CIE Physics | CIE物理考试技巧
In CIE exams, always state the unit of c or L when defining them, and use kelvin or Celsius consistently for temperature change. Remember that a temperature difference of 1 °C is equal to 1 K.
在 CIE 考试中，定义 c 或 L 时务必写出单位，并且温度变化要一致使用开尔文或摄氏度。请记住 1 °C 的温差等于 1 K。
- English: Convert all temperatures to kelvin only when using gas laws or kinetic theory equations; for Q = mcΔT, either K or °C works for ΔT.
中文： 仅在使用气体定律或分子动理论方程时才需要将温度转换为开尔文；对于 Q = mcΔT，ΔT 用 K 或 °C 均可。 - English: Include latent heat only during a change of state, and do not use Q = mcΔT while a substance is melting or boiling.
中文： 只有在物态变化期间才考虑潜热，物质熔化或沸腾时不要使用 Q = mcΔT。
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