📚 Thermal Physics | 热物理
Thermal physics is the study of how energy is transferred as heat and how the microscopic motion of particles gives rise to macroscopic observable quantities such as temperature and pressure. This topic links three core ideas: internal energy, the equilibrium behaviour of gases, and the kinetic model of an ideal gas.
热物理学研究能量以热量形式转移的规律，以及粒子微观运动如何决定温度、压强等宏观可观测量。本专题将三个核心概念联系起来：内能、气体的平衡态行为，以及理想气体的分子动理论模型。
1. Internal Energy and Thermal Equilibrium | 内能与热平衡
The internal energy of a system is the sum of the total random kinetic energy and the total intermolecular potential energy of all the particles within it. In a real gas, the potential energy term accounts for the weak forces between molecules; in an ideal gas this term is taken to be zero because intermolecular forces are neglected.
系统的内能等于其内部所有粒子无规则热运动的总动能与分子间总势能之和。对实际气体而言，势能项来源于分子间微弱的作用力；在理想气体模型中，由于忽略分子间作用力，该势能项被视为零。
Thermal equilibrium is reached when two objects in thermal contact stop exchanging net energy. At this point they share the same temperature. Temperature therefore determines the direction of net energy flow: heat flows spontaneously from a hotter body to a colder one until equilibrium is established.
当两个相互接触的物体之间不再有净能量交换时，便达到热平衡，此时二者具有相同的温度。因此，温度决定了净能量传递的方向：热量自发地从高温物体传向低温物体，直至达到热平衡。
For a monatomic ideal gas, the internal energy is simply the total translational kinetic energy of its molecules, and this is directly proportional to the absolute temperature in kelvin.
对于单原子理想气体，内能就是分子总平动动能，它与以开尔文为单位的绝对温度成正比。
2. Specific Heat Capacity | 比热容
The specific heat capacity c of a substance is defined as the energy required to raise the temperature of 1 kg of the substance by 1 K, which is equal to 1 °C. It is measured in J kg⁻¹ K⁻¹.
物质的比热容 c 定义为使 1 kg 该物质温度升高 1 K（与升高 1 °C 相同）所需吸收的能量，单位是 J kg⁻¹ K⁻¹。
ΔQ = mcΔθ
where ΔQ is the thermal energy supplied, m is the mass and Δθ is the temperature rise. When using this equation you must be careful with the sign convention: a temperature rise requires energy input, whereas a fall releases energy.
其中 ΔQ 为供给的热能，m 为质量，Δθ 为升高的温度。使用此式时须注意符号约定：温度升高需要吸收能量，温度降低则释放能量。
Different materials have different specific heat capacities because of their different internal structures and bonding. Water, with c = 4200 J kg⁻¹ K⁻¹, has a particularly high value, which is why oceans moderate coastal climates.
不同材料因内部结构和键合方式不同而具有不同的比热容。水的比热容高达 4200 J kg⁻¹ K⁻¹，正因如此，海洋对沿海气候起到重要的调节作用。
3. Latent Heat and Phase Changes | 潜热与相变
During a phase change, such as melting or boiling, the temperature of a substance remains constant even though energy is still being supplied. The energy absorbed or released is called latent heat, and it is used to change the intermolecular potential energy rather than the kinetic energy of the molecules.
在熔化或沸腾等相变过程中，尽管系统持续吸热，温度却保持不变。此时吸收或释放的能量称为潜热，它用于改变分子间的势能，而不是分子的动能。
The specific latent heat l is defined as the energy required to change the phase of 1 kg of a substance without a change in temperature. It has units of J kg⁻¹.
比潜热 l 定义为使 1 kg 物质在温度不变的情况下发生相变所需的能量，单位是 J kg⁻¹。
Q = ml
Typical exam questions distinguish between the specific latent heat of fusion (melting or freezing, lf) and the specific latent heat of vaporisation (boiling or condensing, lv). The value of lv is generally much larger than lf because turning a liquid into a gas requires breaking almost all intermolecular bonds, whereas melting only partially disrupts them.
考试中常需区分熔化（凝固）比潜热 lf 和汽化（液化）比潜热 lv。通常 lv 远大于 lf，因为将液体变为气体需要破坏几乎全部分子间键，而熔化只需部分破坏这些键。
4. The Ideal Gas Laws | 理想气体定律
Three empirical laws describe the behaviour of a fixed mass of gas. Boyle’s law states that at constant temperature, pressure p is inversely proportional to volume V: p ∝ 1/V, so pV = constant.
三条实验定律描述了固定质量气体的行为。玻意耳定律指出：在温度恒定时，压强 p 与体积 V 成反比，即 p ∝ 1/V，故 pV = 常量。
Charles’s law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature T: V ∝ T, so V/T = constant.
查理定律指出：在压强恒定时，气体的体积与绝对温度 T 成正比，即 V ∝ T，故 V/T = 常量。
The pressure law (Gay-Lussac’s law) states that at constant volume, the pressure of a gas is directly proportional to its absolute temperature: p ∝ T, so p/T = constant.
压强定律（盖-吕萨克定律）指出：在体积恒定时，气体的压强与绝对温度 T 成正比，即 p ∝ T，故 p/T = 常量。
Notice that all three laws require temperature measured in kelvin. The kelvin scale is an absolute thermodynamic scale whose zero point, 0 K, corresponds to the temperature at which the kinetic energy of gas molecules would be zero.
请注意，三条定律都要求使用开尔文温标。开尔文温标是绝对热力学温标，其零点 0 K 对应气体分子动能为零时的温度。
5. The Ideal Gas Equation | 理想气体方程
Combining the three gas laws gives the ideal gas equation, which relates pressure, volume, temperature and the amount of gas for any ideal gas:
将三条气体定律合并即得理想气体方程，它联系了任意理想气体的压强、体积、温度与物质的量：
pV = nRT
Here p is measured in pascals, V in m³, T in kelvin, n is the number of moles and R = 8.31 J mol⁻¹ K⁻¹ is the molar gas constant. A gas that obeys this equation exactly is called an ideal gas; real gases approximate ideal behaviour at low pressure and high temperature, where intermolecular forces and molecular volume become negligible.
式中 p 以帕斯卡为单位，
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