📚 IB CIE Science: Formula Summary Handbook | IB CIE 科学：公式汇总手册
This handbook brings together the most essential formulas from the IB and CIE science curricula, covering both physics and chemistry. Each formula is presented with clear notation, units, and a brief explanation of its use. Whether you are revising for Paper 2, tackling numerical problems, or preparing for practical assessments, this compact reference will help you recall and apply key equations accurately and efficiently.
本手册汇集了 IB 和 CIE 科学课程中最核心的公式，涵盖物理和化学两门学科。每个公式都配以清晰的符号、单位及用途简述。无论你是在为 Paper 2 复习、攻克计算题，还是准备实验评估，这本精简的参考手册都能帮助你准确、高效地回忆并运用关键方程。
1. Kinematics | 运动学
The equations of motion describe the relationship between displacement, velocity, acceleration, and time for uniformly accelerated linear motion.
运动学方程描述了匀加速直线运动中位移、速度、加速度和时间之间的关系。
v = u + at
Where v is final velocity, u is initial velocity, a is constant acceleration, and t is time.
其中 v 是末速度，u 是初速度，a 是恒定加速度，t 是时间。
s = ut + ½at²
This gives the displacement s after time t.
该式给出经过时间 t 后的位移 s。
v² = u² + 2as
Use this when time is not explicitly known.
当时间未知时使用该式。
2. Dynamics | 动力学
Newton’s laws form the foundation of dynamics, relating forces to the motion of objects.
牛顿定律构成了动力学的基础，将力与物体的运动联系起来。
F = ma
Net force F equals mass m times acceleration a.
净力 F 等于质量 m 乘以加速度 a。
W = mg
Weight W is the force due to gravity; g = 9.81 m s⁻² on Earth.
重量 W 是由重力产生的力；地球上 g = 9.81 m s⁻²。
p = mv
Linear momentum p is the product of mass and velocity.
线动量 p 是质量与速度的乘积。
F = Δp/Δt
The rate of change of momentum equals the net force (Newton’s second law in momentum form).
动量的变化率等于净力（动量形式的牛顿第二定律）。
3. Work, Energy and Power | 功、能量与功率
Energy is conserved and can be transferred via work or heat; power is the rate of energy transfer.
能量守恒，可通过做功或热传递进行转移；功率是能量转移的速率。
W = Fd cos θ
Work done W by a constant force F over displacement d, where θ is the angle between force and displacement.
恒力 F 在位移 d 上所做的功 W，θ 是力与位移之间的夹角。
Ek = ½mv²
Kinetic energy Ek of an object of mass m moving at speed v.
质量为 m、速度为 v 的物体的动能 Ek。
Ep = mgΔh
Change in gravitational potential energy near Earth’s surface.
地球表面附近重力势能的变化。
P = W/t = Fv
Power P as work per unit time or force times velocity (for constant force and velocity in the same direction).
功率 P，即单位时间做功或力乘以速度（适用于恒力且力与速度同向的情况）。
4. Thermal Physics | 热物理学
These formulas link heat, temperature change, and phase changes to the microscopic behaviour of particles.
这些公式将热量、温度变化和相变与粒子的微观行为联系起来。
Q = mcΔT
Heat energy Q required to change temperature of mass m with specific heat capacity c.
使质量为 m、比热容为 c 的物质温度变化所需的热量 Q。
Q = mL
Heat required for a phase change at constant temperature; L is specific latent heat (fusion or vaporisation).
恒温下相变所需的热量；L 是比潜热（熔化或汽化）。
pV = nRT
Ideal gas law: pressure p, volume V, amount n (mol), gas constant R = 8.31 J K⁻¹ mol⁻¹, temperature T in kelvin.
理想气体定律：压力 p、体积 V、物质的量 n（摩尔）、气体常数 R = 8.31 J K⁻¹ mol⁻¹、热力学温度 T（开尔文）。
Ek = (3/2)kBT
Average translational kinetic energy per particle in an ideal gas; kB = 1.38 × 10⁻²³ J K⁻¹.
理想气体中每个粒子的平均平动动能；kB = 1.38 × 10⁻²³ J K⁻¹。
5. Waves | 波动
Wave behaviour can be described by relationships between speed, frequency, wavelength, and refractive indices.
波动行为可通过速度、频率、波长和折射率之间的关系来描述。
v = f λ
Wave speed v equals frequency f times wavelength λ.
波速 v 等于频率 f 乘以波长 λ。
n = c/v
Refractive index n of a medium, where c is the speed of light in vacuum and v is the speed in the medium.
介质的折射率 n，其中 c 是真空中的光速，v 是介质中的光速。
n1 sin θ1 = n2 sin θ2
Snell’s law of refraction.
斯涅耳折射定律。
6. Electricity and Magnetism | 电学与磁学
Fundamental circuit rules and field equations are essential for analysing electrical systems.
基本电路规律和场方程是分析电气系统的基础。
V = IR
Ohm’s law: potential difference V equals current I times resistance R.
欧姆定律：电势差 V 等于电流 I 乘以电阻 R。
P = IV = I²R = V²/R
Electrical power P in terms of current, voltage, and resistance.
电功率 P 用电流、电压和电阻表示。
F = BIL sin θ
Force on a current-carrying conductor of length L in a magnetic field B, with angle θ between current and field.
长度为 L 的载流导体在磁场 B 中所受的力，θ 为电流与磁场间的夹角。
ΣIin = ΣIout and ΣV = 0
Kirchhoff’s current and voltage laws for circuit analysis.
用于电路分析的基尔霍夫电流定律和电压定律。
7. Atomic and Nuclear Physics | 原子与核物理
Equations describing radioactivity, nuclear reactions, and the dual nature of matter and radiation.
描述放射性、核反应以及物质与辐射波粒二象性的方程。
A = λN
Activity A of a radioactive sample: decay constant λ times number of undecayed nuclei N.
放射性样品的活度 A：衰变常数 λ 乘以未衰变原子核数 N。
N = N₀ e-λt
Exponential decay law.
指数衰变定律。
t½ = ln2/λ
Half-life t½ related to decay constant.
半衰期 t½ 与衰变常数的关系。
E = hf
Photon energy E equals Planck’s constant h × frequency f.
光子能量 E 等于普朗克常数 h × 频率 f。
8. Stoichiometry | 化学计量学
The mole concept and quantitative relationships in chemical reactions.
摩尔概念与化学反应中的定量关系。
n = m/M
Amount of substance n (mol) equals mass m divided by molar mass M.
物质的量 n（摩尔）等于质量 m 除以摩尔质量 M。
n = V/Vm
For gases at STP, molar volume Vm = 22.7 dm³ mol⁻¹ (or 22.4 dm³ at 0 °C and 1 atm).
对于标准状况下的气体，摩尔体积 Vm = 22.7 dm³ mol⁻¹（或 22.4 dm³ 在 0 °C 和 1 atm 下）。
n = cV
Amount from solution concentration c (mol dm⁻³) and volume V (dm³).
通过溶液浓度 c（mol dm⁻³）和体积 V（dm³）求物质的量。
% yield = (actual yield/theoretical yield) × 100%
Percentage yield calculation.
产率百分比计算。
9. Thermodynamics (Chemistry) | 热力学（化学）
Enthalpy changes, entropy, and Gibbs free energy determine the feasibility of reactions.
焓变、熵和吉布斯自由能决定了反应的自发性。
ΔH = ΣΔHf°(products) – ΣΔHf°(reactants)
Standard enthalpy change of reaction from enthalpies of formation.
由生成焓计算反应的标准焓变。
q = mcΔT
Heat energy transferred in calorimetry; same form as in thermal physics.
量热法中的热传递；与热物理学中的形式相同。
ΔG = ΔH – TΔS
Gibbs free energy change; a reaction is spontaneous when ΔG < 0 at constant temperature and pressure.
吉布斯自由能变；恒温恒压下，当 ΔG < 0 时反应自发进行。
10. Equilibrium | 平衡
The equilibrium constant expresses the ratio of products to reactants at equilibrium.
平衡常数表示平衡时产物与反应物的比值。
Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ
Equilibrium constant in terms of concentration for the reaction aA + bB ⇌ cC + dD.
对于反应 aA + bB ⇌ cC + dD，以浓度表示的平衡常数。
Kp = (p_C)ᶜ (p_D)ᵈ / (p_A)ᵃ (p_B)ᵇ
Equilibrium constant in terms of partial pressures for gaseous systems.
对于气体体系，以分压表示的平衡常数。
If the temperature changes, K changes; use Le Chatelier’s principle to predict shifts.
温度变化时，K 值改变；可运用勒夏特列原理预测平衡移动方向。
11. Acids and Bases | 酸与碱
pH, dissociation constants, and buffer calculations are central to acid-base chemistry.
pH、解离常数和缓冲溶液计算是酸碱化学的核心。
pH = –log₁₀[H⁺]
Definition of pH; [H⁺] in mol dm⁻³.
pH 的定义；[H⁺] 单位为 mol dm⁻³。
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 298 K
Ionic product of water.
水的离子积。
Ka = [H⁺][A⁻]/[HA]
Acid dissociation constant for a weak acid HA.
弱酸 HA 的酸解离常数。
pH = pKa + log₁₀([A⁻]/[HA])
Henderson–Hasselbalch equation for buffer solutions.
缓冲溶液的 Henderson–Hasselbalch 方程。
12. Electrochemistry | 电化学
Electrode potentials and Faraday’s laws connect electricity with chemical change.
电极电势和法拉第定律将电与化学变化联系起来。
E°cell = E°cathode – E°anode
Standard cell potential from standard electrode potentials.
由标准电极电势计算标准电池电动势。
ΔG° = –nFE°cell
Relationship between free energy change and cell potential; F = 96 500 C mol⁻¹.
自由能变与电池电动势的关系；F = 96 500 C mol⁻¹。
Q = It and n = Q/(zF)
Charge Q passed is current × time; amount of substance produced or consumed at an electrode, where z is the number of electrons transferred per ion.
通过的电量 Q = 电流 × 时间；电极上生成或消耗的物质的量，其中 z 为每个离子转移的电子数。
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