📚 PH05 International Physics A June 2023: Key Concepts Explained | 2023年6月国际物理A PH05核心概念解析
The PH05 unit in the International A‑Level Physics specification (code WPH05) tests thermodynamics, radiation, oscillations and cosmology. This article unpacks the essential concepts that appeared in the June 2023 paper, providing clear definitions, key equations and worked reasoning to strengthen your revision.
国际A‑Level物理课程中的PH05单元（代码WPH05）考查热力学、辐射、振动与宇宙学。本文解析2023年6月试卷涉及的核心概念，给出清晰的定义、关键方程和推演思路，帮助你高效复习。
1. Internal Energy and the First Law of Thermodynamics | 内能与热力学第一定律
governed by the first law: ΔU = Q - W, where Q is the heat supplied to the system and W is the work done by the system.
系统的内能是其所有粒子无规动能与势能的总和。内能的变化(ΔU)遵循热力学第一定律：ΔU = Q - W，其中Q是供给系统的热量，W是系统对外界做的功。
- If work is done on the system, W is negative, so ΔU = Q + |W|.
- 若外界对系统做功，W取负值，因此ΔU = Q + |W|。
- In an adiabatic process, Q = 0 so ΔU = -W.
- 绝热过程中Q = 0，ΔU = -W。
- an isothermal change of an ideal gas, ΔU = 0 because temperature is constant; thus Q = W.
- 理想气体等温变化时温度不变，ΔU = 0，因此Q = W。
2. Ideal Gas Behaviour and the Equation of State | 理想气体行为与状态方程
⁻¹) and T is the absolute temperature in kelvin. For a fixed mass of gas, pV/T = constant.
理想气体遵从 pV = nRT，其中p为压强，V为体积，n为摩尔数，R为摩尔气体常数(8.31 J mol⁻¹ K⁻¹)，T为开尔文温标下的绝对温度。对于一定质量的气体，pV/T = 常量。
The pressure exerted by a gas can be explained by the kinetic theory: p = (1/3)ρ⟨c²⟩, where ρ is the density and ⟨c²⟩ is the mean square speed of the molecules. The root mean square speed cᵣₘₛ = √3RT/M for molar mass M.
气体压强的产生可由分子动理论解释：p = (1/3)ρ⟨c²⟩，ρ为密度，⟨c²⟩为分子速率平方的平均值。对于摩尔质量M，方均根速率 cᵣₘₛ = √3RT/M。
Mean translational kinetic energy of a molecule: Eₖ = ½ m⟨c²⟩ = (3/2)kT
单个分子的平均平动能：Eₖ = ½ m⟨c²⟩ = (3/2)kT
3. Blackbody Radiation and Wien's Displacement Law | 黑体辐射与维恩位移定律
As temperature rises, the peak wavelength λₘₐₓ shifts to shorter values, described by Wienʼs law: λₘₐₓ T = constant ≈ 2.898 × 10⁻³ m·K.
黑体是一种理想化物体，能吸收所有入射辐射并发出仅依赖于温度连续谱。温度升高时，峰值波长λₘₐₓ向短波方向移动，可由维恩位移定律描述：λₘₐₓ T = 常数 ≈ 2.898 × 10⁻³ m·K。
rongly in the visible region (λₘₐₓ ≈ 500 nm), whereas a cooler star peaks in the infrared.
实际意义是，表面温度为5800 K的恒星辐射峰值在可见光区（λₘₐₓ ≈ 500 nm），而较冷的恒星峰值在红外区。
4. Stefan-Boltzmann Law and Luminosity | 斯特藩-玻尔兹曼定律与光度
ity, A is the surface area and σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W m⁻² K⁻⁴). For a spherical star, L = 4πR²σTₑff⁴, where Tₑff is the effective surface temperature.
黑体单位面积辐射的总功率与其绝对温度的四次方成正比：L = σAT⁴，L为光度，A为表面积，σ为斯特藩-玻尔兹曼常数(5.67 × 10⁻⁸ W m⁻² K⁻⁴)。对于球形恒星，L = 4πR²σTₑff⁴，其中Tₑff为有效表面温度。
This law allows astronomers to estimate stellar radii by comparing luminosity and temperature with those of the Sun.
天文学家利用这一定律，通过对比恒星光度和温度来估算恒星的半径。
5. Radioactive Decay: Alpha, Beta and Gamma | 放射性衰变：α、β和γ衰变
Unstable nuclei can undergo alpha (α) decay, beta (β⁻ or β⁺) decay or gamma (γ) emission. An alpha particle is a helium nucleus (⁴₂He), a beta-minus particle is an electron, and a gamma ray is a high‑energy photon. The type of emission changes the nuclear composition, often moving the nucleus towards the stability band on the N-Z plot.
不稳定原子核可经历α衰变、β衰变(β⁻/β⁺)或γ辐射。α粒子是氦核(⁴₂He)，β⁻粒子是电子，γ射线是高能光子。辐射类型会改变核的组成，使核在N-Z图上向稳定带移动。
| Property | α | β⁻ | γ |
|---|---|---|---|
| Nature | Helium nucleus | Electron | EM wave |
| Charge | +2e | -1e | 0 |
| Penetration | Low (paper) | Medium (∼mm Al) | High (cm Pb) |
| Ionising ability | Strong | Medium | Weak |
6. Exponential Decay and Half-life | 指数衰变与半衰期
the decay constant. The activity A = λN = λN₀ e⁻λt has the same exponential form. The half‑ ₁/₂ = ln2/λ is the time taken for the activity or the number of undecayed nuclei to halve.
在时刻t未衰变核的数目N遵从N = N₀ e⁻λt，N₀为初始核数，λ为衰变常量。活度A = λN = λN₀ e⁻λt具有相同的指数形式。半衰期T₁/₂ = ln2/λ是活度或未衰变核数减半所需的时间。
- After n half‑lives, N/N₀ = (½)ⁿ and A/A₀ = (½)ⁿ.
- 经过n个半衰期后，N/N₀ = (½)ⁿ，A/A₀ = (½)ⁿ。
- The decay constant λ has units s⁻¹; a large λ means rapid decay and a short half‑life.
- 衰变常量λ的单位是s⁻¹；λ大表示衰变快、半衰期短。
7. Simple Harmonic Motion (SHM) | 简谐运动
rds equilibrium: a = -ω²x, where ω = 2πf is the angular frequency. The displacement can be written as x = A cos(ωt + φ), where A is the amplitude and φ is the phase constant.
当振动物体的加速度a与其离开平衡位置的位移x成正比且总指向平衡位置时，物体做简谐运动：a = -ω²x，其中ω=2πf为角频率。位移可写为x = A cos(ωt + φ)，A为振幅，φ为初相。
t the equilibrium position, speed is maximum; at the extremes, potential energy is maximum.
无阻尼简谐运动系统的总能量守恒，在动能(½mv²)与势能(½kx²，k = mω²)之间转化。在平衡位置速率最大，在振幅处势能最大。
Mass–spring period: T = 2π√m/k · Simple pendulum: T = 2π√l/g
弹簧振子周期：T = 2π√m/k · 单摆周期：T = 2π√l/g
8. Damping, Forced Vibrations and Resonance | 阻尼、受迫振动与共振
Damping removes energy from an oscillating system, reducing the amplitude over time. Light damping produces a slowly decaying oscillation; heavy damping stops oscillation quickly without overshoot; critical damping returns the system to equilibrium in the shortest time without overshoot.
阻尼会消耗振动系统的能量，使振幅随时间减小。弱阻尼产生缓慢衰减的振荡；过阻尼使系统快速停止振荡且不超调；临界阻尼使系统在最短时间内回到平衡位置且不超调。
When a periodic external force drives a system at its natural frequency, resonance occurs, leading to a dramatic increase in amplitude. Sharp resonance is associated with low damping; broad resonance is associated with strong damping.
当周期性的外力以系统的固有频率驱动时会发生共振，振幅急剧增大。尖锐的共振对应低阻尼，宽阔的共振对应强阻尼。
9. Gravitational Fields and Potential | 引力场与引力势
Newtonʼ trength g = F/m = GM/r² is the force per unit mass at a point. The gravitational potential V is the work done per unit mass to bring a mass from infinity to that point: V = -GM/r.
牛顿万有引力定律给出两点质量间的引力：F = -GMm/r²，负号表示吸引。引力场强度 g = F/m = GM/r²，是某点单位质量所受的力。引力势V是将单位质量从无穷远移至该点外力所做的功：V = -GM/r。
ential surfaces are always perpendicular to field lines, and no work is done when moving along an equipotential.
场强是势的负梯度：g = -dV/dr。等势面处处与场线垂直，沿等势面移动不做功。
10. Orbital Motion and Kepler's Laws | 轨道运动与开普勒定律
it, the centripetal force is provided by gravity: mv²/r = GMm/r², giving orbital speed v = √GM/r. The period T follows Keplerʼs third law: T² = (4π²/GM) r³, so T² ∝ kinetic energy of a satellite is half the magnitude of its gravitational potential energy.
对于圆形轨道上的卫星，向心力由引力提供：mv²/r = GMm/r²，得出轨道速度 v = √GM/r。周期T遵从开普勒第三定律：T² = (4π²/GM) r³，即T² ∝ r³。通过几何推导可知，卫星的动能等于其引力势能绝对值的一半。
Keplerʼs laws also describe elliptical orbits; the total energy of an orbiting body remains constant as it sweeps out equal areas in equal times.
开普勒定律同样描述椭圆轨道；轨道天体总能量守恒，且相等时间内扫过相等面积。
11. Hubble's Law and the Expanding Universe | 哈勃定律与膨胀的宇宙
, where H₀ is the Hubble constant (approx. 70 km s⁻¹ Mpc⁻¹). This linear relationship supports the idea of an expanding universe. Cosmic microwave background radiation (CMB) further confirms the Big Bang model.
哈勃观测到星系的退行速度v与其距我们的距离d成正比：v = H₀ d，H₀为哈勃常数（约70 km s⁻¹ Mpc⁻¹）。这一线性关系支持宇宙膨胀的观点。宇宙微波背景辐射(CMB)进一步证实了大爆炸模型。
ion rate). Redshift z = Δλ/λ₀ gives evidence for expansion and allows distance estimation.
宇宙年龄可由t ≈ 1/H₀估算（忽略膨胀速率的变化）。红移z = Δλ/λ₀为膨胀提供了证据，也可用于估算距离。
12. The Big Bang Model and Fate of the Universe | 大爆炸模型与宇宙的命运
The Big Bang theory states that the universe began from a hot, dense state roughly 13.8 billion years ago. The CMB, with a temperature of about 2.73 K, is the cooled remnant of the primordial fireball. The ultimate fate of the universe depends on its total mass–energy density relative to the critical density; this determines whether expansion continues forever or eventually reverses.
大爆炸理论认为宇宙约在138亿年前从一个极高温、极高密的状态诞生。CMB温度约为2.73 K，是原初火球冷却后的残余。宇宙的最终命运取决于其总质能密度与临界密度的对比，决定膨胀是永远持续还是会最终反转。
Dark energy is thought to accelerate the expansion, and evidence for it comes from Type Ia supernovae observations. Open, flat and closed geometries correspond to average density being less than, equal to or greater than critical density.
暗能量被认为在加速宇宙膨胀，其证据来自Ia型超新星的观测。开放、平坦与闭合几何分别对应平均密度小于、等于或大于临界密度。
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