Thermal Physics for AQA International A-level | AQA 国际版 A-level 热物理学

📚 Thermal Physics for AQA International A-level | AQA 国际版 A-level 热物理学

Thermal physics connects everyday observations like melting ice and boiling water to the microscopic behaviour of particles. In AQA International A-level Physics, this topic covers temperature scales, heat transfer, internal energy, ideal gases and the kinetic theory model, giving you both macroscopic laws and molecular explanations.

热物理学将冰融化和水沸腾等日常现象与粒子的微观行为联系起来。在 AQA 国际版 A-level 物理中，本主题涵盖温标、传热、内能、理想气体和分子动理论模型，既给出宏观定律，也提供分子层面的解释。

1. Temperature and Thermal Equilibrium | 温度与热平衡

Temperature is a measure of how hot or cold an object is, but in thermodynamics it is defined as a property that determines the direction of thermal energy transfer between two objects in contact. Thermal energy flows from a region of higher temperature to a region of lower temperature until thermal equilibrium is reached, when both regions have the same temperature and there is no net energy transfer.

温度是物体冷热程度的量度，但在热力学中它被定义为决定两个接触物体之间热能传递方向的性质。热能从高温区域流向低温区域，直到达到热平衡，此时两个区域温度相同，没有净能量传递。

The Kelvin scale is the absolute temperature scale used in thermal physics. A change of 1 K is exactly the same as a change of 1 °C, but 0 K is absolute zero, the lowest possible temperature, which corresponds to −273.15 °C.

开尔文温标是热物理学中使用的绝对温标。1 K 的变化与 1 °C 的变化完全相同，但 0 K 是绝对零度，即可能达到的最低温度，对应 −273.15 °C。

T(K) = θ(°C) + 273.15

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2. Heat and Internal Energy | 热量与内能

Internal energy is the sum of the randomly distributed kinetic energy and potential energy of all the particles in a substance. For an ideal gas, internal energy is purely kinetic because there are no intermolecular forces, so potential energy is zero.

内能是物质中所有粒子随机分布的动能和势能的总和。对于理想气体，内能纯粹是动能，因为分子间没有作用力，所以势能为零。

Heat is the transfer of internal energy from a hotter body to a cooler body as a result of a temperature difference. It is not the same as internal energy: an object does not contain heat, but it does have internal energy.

热量是由于温度差而从较热物体向较冷物体传递的内能。热量与内能不同：物体不含有热量，但它具有内能。

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3. 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 K without a change of state. The equation is:

比热容 c 是使 1 kg 物质在状态不变的情况下温度升高 1 K 所需的能量。公式为：

Q = mcΔθ

In this equation, Q is the thermal energy supplied in joules, m is the mass in kilograms, c is the specific heat capacity in J kg⁻¹ K⁻¹, and Δθ is the temperature change in kelvin or degrees Celsius. When a substance cools, the same equation gives the energy released as the temperature falls.

式中 Q 为供给的热能（焦耳），m 为质量（千克），c 为比热容（J kg⁻¹ K⁻¹），Δθ 为温度变化（开尔文或摄氏度）。当物质冷却时，同一公式给出温度降低时释放的能量。

Substance | 物质	Specific heat capacity / J kg⁻¹ K⁻¹ | 比热容
Water | 水	4200
Copper | 铜	385
Aluminium | 铝	900

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4. Specific Latent Heat | 比潜热

Specific latent heat L is the energy required to change the state of 1 kg of a substance at constant temperature. The equation is:

比潜热 L 是使 1 kg 物质在恒定温度下改变状态所需的能量。公式为：

Q = mL

Specific latent heat of fusion involves melting or freezing, while specific latent heat of vaporisation involves boiling or condensing. During a change of state, the temperature remains constant even though energy is being supplied. The energy is used to break intermolecular bonds rather than to increase particle kinetic energy.

熔化或凝固涉及比熔化潜热，沸腾或凝结涉及比汽化潜热。在状态变化过程中，即使不断供给能量，温度也保持不变。这些能量用于破坏分子间键，而不是增加粒子的动能。

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5. The Mole and Avogadro Constant | 摩尔与阿伏伽德罗常数

gadro constant Nₐ. This number applies to atoms, molecules, ions or any specified elementary entity.

摩尔是物质的量的 SI 单位。1 摩尔恰好包含 6.02 × 10²³ 个粒子，即阿伏伽德罗常数 Nₐ。这个数目适用于原子、分子、离子或任何指定的基本单元。

The molar mass M of a substance is the mass of one mole, measured in kilograms per mole (kg mol⁻¹). For a sample of mass m, the number of moles n is:

物质的摩尔质量 M 是 1 摩尔物质的质量，单位为千克每摩尔（kg mol⁻¹）。对于质量为 m 的样品，摩尔数 n 为：

n = m ÷ M

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6. Ideal Gases and the Gas Laws | 理想气体与气体定律

sures, volumes and temperatures. Its particles have negligible volume, move in random motion, collide elastically and exert no intermolecular forces except during collisions.

理想气体是在所有压强、体积和温度下都遵守 pV = nRT 方程的理论气体。其粒子体积可忽略，做随机运动，发生弹性碰撞，除碰撞瞬间外不施加分子间作用力。

Boyle' constant temperature, pressure is inversely proportional to volume: pV = constant. Charles' onstant volume, pressure is directly proportional to absolute temperature: p/T = constant.

玻意耳定律指出，一定质量气体在温度不变时，压强与体积成反比：pV = 常数。查理定律指出，在压强不变时，体积与绝对温度成正比：V/T = 常数。压强定律指出，在体积不变时，压强与绝对温度成正比：p/T = 常数。

Law | 定律	Condition | 条件	Relationship | 关系
Boyle's law | 玻意耳定律	Constant T | 温度不变	p ∝ 1/V
Charles's law | 查理定律	Constant p | 压强不变	V ∝ T
Pressure law | 压强定律	Constant V | 体积不变	p ∝ T

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7. The Ideal Gas Equation | 理想气体状态方程

Combining the three gas laws gives the ideal gas equation:

综合三条气体定律得到理想气体状态方程：

pV = nRT

Here p is pressure in pascals, V is volume in cubic metres, n is the number of moles, R is the molar gas constant 8.31 J K⁻¹ mol⁻¹, and T is absolute temperature in kelvin.

其中 p 是压强（帕斯卡），V 是体积（立方米），n 是摩尔数，R 是摩尔气体常数 8.31 J K⁻¹ mol⁻¹，T 是绝对温度（开尔文）。

Often it is useful to write the equation in terms of the number of molecules N = nNₐ:

有时用分子数 N = nNₐ 表示更方便：

pV = NkT

Here k is the Boltzmann constant, 1.38 × 10⁻²³ J K⁻¹, and k = R/Nₐ.

其中 k 是玻尔兹曼常数，1.38 × 10⁻²³ J K⁻¹，且 k = R/Nₐ。

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8. Kinetic Theory of Gases | 气体分子动理论

The kinetic theory model explains gas pressure as the force per unit area produced by many molecules colliding with the walls of the container. The pressure depends on the number density of molecules, their mass and their mean square speed.

分子动理论模型把气体压强解释为大量分子与容器壁碰撞产生的单位面积作用力。压强取决于分子数密度、分子质量和方均速率。

The key equation derived from kinetic theory is:

由分子动理论导出的关键方程为：

pV = ⅓ N m ⟨c²⟩

Here N is the total number of molecules, m is the mass of one molecule, and ⟨c²⟩ is the mean square speed of the molecules.

其中 N 是分子总数，m 是单个分子的质量，⟨c²⟩ 是分子的方均速率。

Combining pV = NkT with pV = ⅓ N m ⟨c²⟩ gives:

将 pV = NkT 与 pV = ⅓ N m ⟨c²⟩ 结合可得：

½ m ⟨c²⟩ = ³⁄₂ kT

This shows that the average translational kinetic energy of a gas molecule is directly proportional to the absolute temperature.

这表明气体分子的平均平动动能与绝对温度成正比。

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9. Molecular Kinetic Energy and Temperature | 分子平均动能与温度

For an ideal gas, the average kinetic energy of a molecule is given by:

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