WPH15 Thermodynamics, Radiation, Oscillations and Cosmology

Lessons in WPH15

1. Specific heat capacity and specific latent heat
   ΔE = mcΔθ for temperature change; ΔE = LΔm for change of state at constant temperature.
2. Core practical 12: calibrating a thermistor as a thermostat
   Thermistor plus fixed resistor as a potential divider; stir and heat slowly; plot V_out against temperature; read temperatures off the curve.
3. Core practical 13: specific latent heat
   L = Pt / Δm; a control funnel removes melting caused by the room; two powers cancel heat losses in vaporisation.
4. Internal energy and absolute zero
   Internal energy = sum of random molecular E_k and E_p. 0 K = -273 °C; mean E_k is proportional to T in kelvin.
5. The ideal gas equation
   pV = NkT with T in kelvin; for a fixed mass pV/T is constant.
6. Core practical 14: pressure and volume of a gas
   Fixed mass, constant temperature: p is proportional to 1/V; plot p against 1/V for a straight line through the origin; wait for the temperature to settle.
7. Kinetic theory of gases
   pV = (1/3)Nm<c²>; (1/2)m<c²> = (3/2)kT; mean molecular E_k depends only on T.
8. Mass deficit and nuclear binding energy
   Mass deficit = mass of nucleons - mass of nucleus; binding energy = c²Δm; 1 u = 1.66 x 10^-27 kg; higher BE per nucleon = more stable.
9. Fission, fusion and the binding energy curve
   Moving towards iron-56 on the BE per nucleon curve releases energy. Fusion needs high temperature (to overcome repulsion) and high density (for enough collision
10. Alpha, beta and gamma radiation, and nuclear equations
    Subtract background. α: He nucleus, A - 4, Z - 2, stopped by paper. β-: electron, Z + 1, stopped by aluminium. γ: EM wave, no change, reduced by lead.
11. Core practical 15: absorption of gamma radiation by lead
    Subtract background; fixed distance; ln C against x has gradient -μ; half-thickness = ln 2 / μ; tongs, distance, short exposure.
12. Random decay, activity and half-life
    Decay is spontaneous and random. A = λN; dN/dt = -λN; λ = ln 2/t_1/2; after n half-lives (1/2)ⁿ remains.
13. Exponential decay equations and log graphs
    N = N_0e^-λt, A = A_0e^-λt; ln A against t has gradient -λ; t = ln(1/f)/λ.
14. Simple harmonic motion
    SHM: a = -ω^2x (acceleration proportional to displacement, towards equilibrium). x = A cos ωt; v_max = Aω; a_max = Aω²; ω = 2πf.
15. Mass-spring systems and simple pendulums
    T = 2π sqrt(m/k); T = 2π sqrt(l/g) for small angles; neither depends on amplitude.
16. SHM graphs and energy in oscillations
    Gradient of x-t = v; gradient of v-t = a; a is in antiphase with x. Undamped: total energy constant, E_k and E_p swap. Damped: energy decreases.
17. Free and forced oscillations, resonance and damping
    Free: natural frequency. Forced: driving frequency. Resonance: maximum amplitude when driving frequency ≈ natural frequency. Damping lowers and broadens the pea
18. Core practical 16: finding a mass from resonant frequencies
    1/f² against m (or T² against m) is a straight line with gradient 4π²/k; read the unknown mass from the graph.
19. Gravitational fields and Newton's law of gravitation
    g = F/m; F = Gm_1m_2/r² (always attractive); g = GM/r²; like electric fields, inverse square, but mass not charge.
20. Gravitational potential and orbits
    V_grav = -GM/r (zero at infinity); ΔW = mΔV; g = -ΔV/Δr; orbits: GMm/r² = mv²/r, so v = sqrt(GM/r) and T² = 4π^2r3/GM.
21. Black body radiation, Stefan-Boltzmann and Wien
    Black body: absorbs all, emits most. λ_max T = 2.898 x 10^-3 m K. L = σAT⁴ with A = 4πr².
22. Intensity, parallax and standard candles
    I = L/4πd²; parallax: d = 1 AU / p, d (pc) = 1/p (arcsec), nearby stars only; standard candles: known L, measure I, d = sqrt(L/4πI).
23. The Hertzsprung-Russell diagram and stellar evolution
    HR diagram: luminosity up, temperature decreasing to the right. Main sequence (hydrogen fusion), giants top right, white dwarfs bottom left. Mass decides the li
24. Redshift, Hubble's law and the fate of the universe
    Redshift z = Δλ/λ ≈ v/c means recession; v = H_0d; age ≈ 1/H_0; fate depends on density, which is uncertain because of dark matter.

Next exams for WPH15

• January 2027: Thu 21 Jan 2027, afternoon, 1h 45m
• Summer 2027: Thu 3 Jun 2027, morning, 1h 45m

From Pearson's final timetables. All exam dates. Always confirm your entries with your exams officer.