Relate the temperature of a gas to the average kinetic energy of the particles; recall and use the equation T (in K) = θ (in °C) + 273

IGCSE Physics (0625) – Complete Revision Notes

1 Motion, Forces & Energy

Objective

Understand and apply the definitions, equations and graphical methods for motion, the effects of forces, and the concepts of work, energy and power.

Key quantities & definitions

• Distance (s) – total path covered (m).
• Displacement (Δx) – straight‑line change in position (m).
• Speed (v) – distance ÷ time (m s⁻¹). Scalar.
• Velocity (v) – displacement ÷ time (m s⁻¹). Vector.
• Acceleration (a) – change in velocity ÷ time (m s⁻²).
• Force (F) – interaction that changes motion (N).
• Weight (W) – force of gravity, W = mg (N).
• Momentum (p) – p = mv (kg m s⁻¹).
• Impulse (J) – J = FΔt = Δp (N s).
• Work (W) – W = F s cosθ (J).
• Power (P) – P = W/t = Fv (W).
• Energy (E) – capacity to do work (J).

Equations of motion (constant acceleration)

Graphical interpretation

• Distance‑time graph – gradient = speed (horizontal = rest).
• Velocity‑time graph – gradient = acceleration; area = displacement.
• Force‑displacement graph – area = work done.

Forces

• Resultant force = vector sum of all forces (ΣF).
• Newton’s First Law – an object remains at rest or in uniform motion unless acted on by a resultant force.
• Newton’s Second Law – ΣF = ma.
• Friction (static & kinetic) opposes motion; usually expressed as F_f = μN.

Worked example (motion)

A car accelerates uniformly from rest to 20 m s⁻¹ in 5 s. Find the acceleration and the distance travelled.

1. Acceleration: a = (v – u)/t = (20 – 0)/5 = 4 m s⁻².
2. Distance: s = ut + ½at² = 0 + ½(4)(5)² = ½·4·25 = 50 m.

Practical ideas

2 Thermal Physics

2.1 Particle Model of Matter (Syllabus 2.1.2)

Objective

Relate the temperature of a gas to the average kinetic energy of its particles and use the conversion between Celsius and Kelvin.

States of matter – qualitative description

• Solids – particles closely packed in a regular pattern; vibrate about fixed positions.
• Liquids – particles close together but free to move past one another; definite volume, no fixed shape.
• Gases – particles far apart, move rapidly in random directions; fill the container.

Key terminology

Temperature ↔ average kinetic energy

The average translational kinetic energy of one particle in an ideal gas is

\$E{\text{avg}} = \frac{3}{2}\,k{\mathrm{B}}\,T\$

• \$k_{\mathrm{B}} = 1.38\times10^{-23}\ \text{J K}^{-1}\$ (Boltzmann constant).
• For IGCSE it is enough to remember E₍avg₎ ∝ T.

Pressure from collisions

• Higher temperature → faster particles → more energetic collisions → higher pressure.
• More particles (higher density) → more frequent collisions → higher pressure.

Brownian motion – experimental evidence

Microscopic pollen grains in water jiggle randomly under a microscope. The motion is caused by invisible water molecules striking the grains, confirming that particles are always in motion.

Conversion between °C and K

\$T\;(\text{K}) = \theta\;(\text{°C}) + 273\;( \text{or } 273.15)\$

To convert back, subtract the same amount.

Worked example (kinetic energy)

Find \$E_{\text{avg}}\$ for a gas at \$25^\circ\text{C}\$.

1. Convert to kelvin: \$T = 25 + 273 = 298\ \text{K}\$.
2. \$E_{\text{avg}} = \frac{3}{2}(1.38\times10^{-23})(298) \approx 6.2\times10^{-21}\ \text{J}\$.

Practical ideas

2.2 Thermal Properties

Thermal expansion

• Linear: ΔL = α L₀ ΔT
• Area: ΔA = 2α A₀ ΔT
• Volume: ΔV = 3α V₀ ΔT (or use coefficient of volumetric expansion β ≈ 3α)

α – coefficient of linear expansion (K⁻¹).

Specific heat capacity

\$Q = mc\Delta T\$

• \$Q\$ – heat energy (J).
• \$m\$ – mass (kg).
• \$c\$ – specific heat capacity (J kg⁻¹ K⁻¹).
• \$\Delta T\$ – temperature change (K).

Latent heat (phase change)

\$Q = mL\$

• \$L\$ – latent heat of fusion (solid↔liquid) or vaporisation (liquid↔gas) (J kg⁻¹).

Worked example (specific heat)

How much energy is required to heat 250 g of water from 20 °C to 80 °C? (c₍water₎ = 4200 J kg⁻¹ K⁻¹)

1. Convert mass: \$m = 0.250\ \text{kg}\$.
2. ΔT = 80 – 20 = 60 K.
3. \$Q = (0.250)(4200)(60) = 6.3\times10^{4}\ \text{J}\$.

Practical ideas

Transfer of thermal energy

• Conduction – transfer through direct contact; rate ∝ area, temperature gradient, and material’s thermal conductivity.
• Convection – bulk movement of fluid; driven by density differences.
• Radiation – emission of electromagnetic waves; follows \$P = \varepsilon\sigma A T^{4}\$ (Stefan‑Boltzmann law, not required for IGCSE calculations).

3 Waves

Objective

Describe the properties of transverse and longitudinal waves, use the wave‑speed equation, and apply concepts of reflection, refraction, diffraction and the electromagnetic spectrum.

Basic definitions

• Wave – disturbance that transfers energy without permanent displacement of the medium.
• Transverse wave – particle motion ⟂ to direction of travel (e.g., light, water surface ripples).
• Longitudinal wave – particle motion ∥ to direction of travel (e.g., sound).
• Frequency (f) – number of oscillations per second (Hz).
• Period (T) – time for one oscillation; \$T = 1/f\$.
• Wavelength (λ) – distance between successive crests (or compressions) (m).
• Wave speed (v) – \$v = f\lambda\$.

Reflection & refraction

• Reflection: angle of incidence = angle of reflection.
• Refraction: wave changes speed when entering a medium with a different propagation speed; described by Snell’s law \$n1\sin\theta1 = n2\sin\theta2\$ (for light).

Diffraction & superposition

• Diffraction – bending of waves around obstacles or through openings comparable to λ.
• Superposition – when two waves meet, the resultant displacement is the algebraic sum of the individual displacements.

Sound

• Longitudinal wave in air (speed ≈ 340 m s⁻¹ at 20 °C).
• Echo – reflected sound; time delay \$t\$ gives distance \$d = vt/2\$.
• Doppler effect – observed frequency changes when source or observer moves.

Light

• Electromagnetic wave – does not require a medium.
• Reflection from mirrors, refraction through lenses, dispersion (prism).
• Key formulas for thin lenses: \$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\$ (sign convention as per IGCSE).

Worked example (wave speed)

A tuning fork of frequency 256 Hz produces a standing wave with five complete loops in a 1.00 m long tube closed at one end. Find the speed of sound in the tube.

1. For a tube closed at one end, the length \$L = \frac{(2n-1)\lambda}{4}\$ with \$n = 5\$ loops ⇒ \$L = \frac{9\lambda}{4}\$.
2. Thus \$\lambda = \frac{4L}{9} = \frac{4(1.00)}{9} = 0.444\ \text{m}\$.
3. Speed \$v = f\lambda = 256 \times 0.444 \approx 1.14\times10^{2}\ \text{m s}^{-1}\$.

Practical ideas

4 Electricity & Magnetism

4.1 Electric charge, current & potential

• Charge (Q) – measured in coulombs (C). 1 C = 6.25×10¹⁸ e⁻.
• Current (I) – flow of charge, \$I = \Delta Q/\Delta t\$ (A).
• Potential difference (V) – work done per unit charge, \$V = W/Q\$ (V).
• Resistance (R) – \$R = V/I\$ (Ω). Depends on material, length, cross‑section and temperature.

4.2 Power & energy in electrical circuits

\$P = VI = I^{2}R = \frac{V^{2}}{R}\$

Energy transferred: \$E = Pt\$ (J) or \$E = VIt\$ (also expressed in kWh for domestic use).

4.3 Series and parallel circuits

Worked example (total resistance)

Find the equivalent resistance of a 10 Ω resistor in series with a parallel combination of 20 Ω and 30 Ω.

1. Parallel part: \$1/R{p}=1/20+1/30= (3+2)/60 =5/60\$ → \$R{p}=60/5=12\ \Omega\$.
2. Series total: \$R_{eq}=10+12=22\ \Omega\$.

4.4 Magnetism

• Magnetic field lines emerge from the north pole and enter the south pole.
• Force on a current‑carrying conductor: \$F = BIl\sin\theta\$ (N). For a straight conductor perpendicular to the field, \$F = BIl\$.
• Electromagnet – coil of wire around an iron core; field strength increases with current and number of turns.
• Motor principle – a current‑carrying loop in a magnetic field experiences a torque, causing rotation.
• Generator principle – rotating a coil in a magnetic field induces an emf (Faraday’s law, qualitative for IGCSE).

Practical ideas

5 Nuclear Physics

Objective

Understand the structure of the atom, the nature of radioactivity, and the concepts of half‑life and nuclear energy.

Atomic structure

• Protons (+e) and neutrons (neutral) in the nucleus; electrons (‑e) in shells.
• Atomic number \$Z\$ = number of protons; mass number \$A\$ = protons + neutrons.
• Isotopes – same \$Z\$, different \$A\$.

Radioactive decay

• α‑decay – emission of a helium nucleus (2p + 2n); reduces \$A\$ by 4, \$Z\$ by 2.
• β‑decay – neutron → proton + electron; \$A\$ unchanged, \$Z\$ increases by 1.
• γ‑radiation – high‑energy photons; no change in \$A\$ or \$Z\$.

Half‑life

Number of undecayed nuclei after time \$t\$: \$N = N{0}\left(\frac{1}{2}\right)^{t/t{1/2}}\$.

Worked example (half‑life)

A sample contains \$8.0\times10^{6}\$ nuclei of a radionuclide with a half‑life of 3 h. How many nuclei remain after 9 h?

1. Number of half‑lives: \$9/3 = 3\$.
2. \$N = 8.0\times10^{6}\left(\frac{1}{2}\right)^{3}=8.0\times10^{6}\times\frac{1}{8}=1.0\times10^{6}\$.

Nuclear reactions

• Fission – heavy nucleus splits into lighter fragments, releasing energy (≈200 MeV per fission).
• Fusion – light nuclei combine (e.g., deuterium + tritium) to form a heavier nucleus, releasing energy (≈17 MeV per reaction).

Practical ideas

6 Space Physics

Objective

Explain the apparent motions of the Sun and Moon, the causes of seasons, and the basic concepts of gravity and orbital motion.

Earth’s rotation & revolution

• Rotation period ≈ 24 h → day/night.
• Revolution period ≈ 365.25 d → year; axis tilt ≈ 23.5° causes seasons.

Lunar phases & eclipses

• Phases result from the relative positions of Sun, Earth and Moon.
• Solar eclipse – Moon blocks Sun; lunar eclipse – Earth blocks Sun’s light from reaching Moon.

Gravity

Force between two masses:

\$F = G\frac{m{1}m{2}}{r^{2}}\$

• \$G = 6.67\times10^{-11}\ \text{N m}^{2}\text{kg}^{-2}\$.
• Weight \$W = mg\$ (where \$g = 9.8\ \text{m s}^{-2}\$ at Earth’s surface).

Orbital speed

For a circular orbit of radius \$r\$ around a planet of mass \$M\$:

\$v = \sqrt{\frac{GM}{r}}\$

Worked example (orbital speed)

Calculate the speed of a satellite in a circular low‑Earth orbit 300 km above the surface. (Earth radius \$R{E}=6.37\times10^{6}\,\$m, \$M{E}=5.97\times10^{24}\,\$kg.)

1. Orbital radius \$r = R_{E}+300\,000 = 6.67\times10^{6}\,\$m.
2. \$v = \sqrt{\dfrac{6.67\times10^{-11}\times5.97\times10^{24}}{6.67\times10^{6}}}\approx 7.73\times10^{3}\ \text{m s}^{-1}\$.

Practical ideas

Summary of Core Relationships

Key Constants (to 3 sf unless otherwise noted)

• \$k_{\!B} = 1.38\times10^{-23}\ \text{J K}^{-1}\$
• \$g = 9.8\ \text{m s}^{-2}\$ (Earth’s surface gravity)
• \$G = 6.67\times10^{-11}\ \text{N m}^{2}\text{kg}^{-2}\$
• \$c_{\text{water}} = 4200\ \text{J kg}^{-1}\text{K}^{-1}\$
• \$L_{\text{fusion (D–T)}} \approx 17\ \text{MeV per reaction}\$
• \$L_{\text{fission (U‑235)}} \approx 200\ \text{MeV per reaction}\$

Final Checklist for Exam Preparation

• Can you convert between °C and K and explain why kelvin is required for kinetic‑energy calculations?
• Are you able to sketch and interpret distance‑time and velocity‑time graphs?
• Do you know the three ways thermal energy is transferred and the relevant formulas for expansion, specific heat and latent heat?
• Can you use \$v = f\lambda\$ and the lens formula correctly?
• Are you comfortable with series/parallel circuit analysis and calculating power?
• Can you describe α, β, γ radiation and perform half‑life calculations?
• Do you understand why seasons occur and can you apply \$F = Gm1m2/r^2\$ to simple problems?

Suggested diagrams (to be drawn by the learner)

1. Particle spacing in solid, liquid and gas with arrows indicating motion.
2. Graph of a speed‑time line showing constant acceleration.
3. Wave diagram illustrating wavelength, amplitude and direction of propagation.
4. Simple circuit showing series and parallel branches with symbols.
5. Radioactive decay chain (α and β steps).
6. Earth‑Sun‑Moon geometry for seasons and lunar phases.