Flashcards · YPH11 · Topic 5

Thermodynamics, Radiation, Oscillations and Cosmology flashcards

41 cards on Topic 5, subtopics 5.3 to 5.6. Pick a subtopic or study them all.

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5.3 Thermodynamics

Internal energy: The sum of the randomly distributed kinetic and potential energies of the molecules in a system.
Why does the temperature stay constant while a substance melts or boils?: The energy supplied increases the potential energy of the molecules (their separation), not their kinetic energy, so the temperature does not change.
Specific heat capacity and specific latent heat equations: ΔE = mcΔθ: energy to raise 1 kg by 1 K is c. ΔE = LΔm: energy to change the state of 1 kg with no temperature change is L.
Energy to turn 0.50 kg of water at 100 °C into steam? (L = 2.26 × 10⁶ J/kg): E = 2.26 × 10⁶ × 0.50 = 1.13 × 10⁶ J
Absolute zero and the kelvin scale: T(K) = θ(°C) + 273. At absolute zero the molecules have minimum internal energy, not zero energy.
Ideal gas equations: pV = nRT (R = 8.31 J mol⁻¹ K⁻¹) pV = NkT (k = 1.38 × 10⁻²³ J K⁻¹) T in kelvin.
Kinetic theory: pressure, and mean molecular kinetic energy: pV = ⅓Nm⟨c²⟩ ½m⟨c²⟩ = (3/2)kT: mean molecular kinetic energy depends only on absolute temperature.
Assumptions of the kinetic model of an ideal gas: Many molecules in random motion; molecular volume negligible; no forces between molecules except in collisions; collisions elastic; collision time negligible compared with time between collisions.
Why is the internal energy of an ideal gas only kinetic?: There are no intermolecular forces, so there is no molecular potential energy. The internal energy depends only on temperature.
Core Practicals 12, 13 and 14: 12: calibrate a thermistor in a potential divider as a thermostat. 13: determine a specific latent heat. 14: pressure and volume of a fixed mass of gas at constant temperature.

5.4 Nuclear Decay

Alpha radiation: A helium nucleus, charge +2. Stopped by paper. Strongly ionising.
Beta-minus radiation: An electron, charge −1. Stopped by about 3 mm of aluminium. Moderately ionising.
Gamma radiation: An electromagnetic photon, no charge. Reduced by thick lead. Weakly ionising.
Why is alpha the least penetrating radiation?: It is the most strongly ionising, so it loses its energy quickly and travels only a short distance.
Mass deficit and binding energy: Mass deficit: the mass of the separated nucleons minus the mass of the nucleus. The binding energy is ΔE = c²Δm. 1 u = 1.66 × 10⁻²⁷ kg.
Why do both fission and fusion release energy?: Binding energy per nucleon peaks around iron. Fusing light nuclei and splitting heavy nuclei both move towards higher binding energy per nucleon.
Beta-minus and beta-plus decay in terms of nucleons: β⁻: n → p + e⁻ + antineutrino (A same, Z + 1). β⁺: p → n + e⁺ + neutrino (A same, Z − 1).
Activity and the decay constant: A = λN (Bq). λ is the probability per unit time that a nucleus decays. N = N₀e^(−λt), and t½ = ln 2 / λ.
How do you find λ from activity measurements?: Subtract background, then plot ln A against t: a straight line of gradient −λ.
Core Practical 15: Investigate the absorption of gamma radiation by lead (count rate against absorber thickness, background subtracted).

5.5 Oscillations

Definition of simple harmonic motion: Acceleration is proportional to the displacement from the equilibrium position and always directed towards it: a = −ω²x. The restoring force F = −kx.
Maximum speed and maximum acceleration in SHM: v_max = ωA, at the equilibrium position. a_max = ω²A, at maximum displacement. ω = 2πf = 2π/T.
Periods of a simple pendulum and of a mass on a spring: Pendulum: T = 2π√(l/g) (small angles only). Mass–spring: T = 2π√(m/k). Neither depends on the amplitude.
A 0.60 kg mass oscillates on a spring of k = 15 N/m. Period?: T = 2π√(0.60/15) = 2π × 0.20 = 1.26 s
Phase of velocity relative to displacement in SHM: Velocity leads displacement by 90°: it is maximum at zero displacement and zero at maximum displacement.
Phase of acceleration relative to displacement in SHM: Acceleration is 180° out of phase with displacement: maximum and opposite at the extremes, zero at the centre.
Light damping: The amplitude decays gradually over many oscillations.
Critical damping: The fastest return to equilibrium without overshooting (used in car suspension). Heavy damping returns more slowly, also without oscillating.
Free vs forced oscillation, and resonance: Free: at the natural frequency with no driving force. Forced: driven by an external periodic force. Resonance: driving frequency = natural frequency, giving maximum amplitude.
Effect of more damping on a resonance curve: Lower peak amplitude, a broader curve, and the peak shifts slightly to a lower frequency.

5.6 Astrophysics and Cosmology

Newton’s law of gravitation, and the field of a point mass: F = Gm₁m₂/r² g = F/m = Gm/r²
Gravitational potential of a point mass: V = −Gm/r. Always negative, rising to zero at infinity (unlike electric potential, which can be positive).
Luminosity vs radiant flux: Luminosity L: total power emitted by a star. Radiant flux F: power received per unit area, F = L / (4πd²).
Standard candle, with an example: An object of known luminosity, so measuring its flux gives its distance. Type Ia supernovae have a consistent peak luminosity.
Trigonometric parallax: The apparent shift of a nearby star against distant background stars as the Earth orbits the Sun, used to find its distance.
Wien’s law and the Stefan–Boltzmann law: λmax T = 2.898 × 10⁻³ m K L = 4πr²σT⁴ Use Wien for temperature first, then Stefan for radius.
A star has surface temperature 5800 K. Peak wavelength?: λmax = 2.898 × 10⁻³ ÷ 5800 = 5.00 × 10⁻⁷ m (500 nm)
Hertzsprung–Russell diagram: axes and regions: Luminosity (up) against temperature (increasing to the left). Main sequence: diagonal band. Red giants: top right (cool, luminous, so large). White dwarfs: bottom left (hot, dim, so small).
Evolution of a Sun-like star and of a massive star: Sun-like: main sequence → red giant → planetary nebula → white dwarf. Massive: main sequence → red supergiant → supernova → neutron star or black hole.
Doppler red-shift equation, and the age of the universe: z = Δλ/λ ≈ v/c. Hubble’s law v = H₀d gives an age of about 1/H₀.
Why is there controversy about the age and fate of the universe?: The value of the Hubble constant is uncertain, and the possible existence of dark matter (from galactic rotation curves) and dark energy affects how the expansion changes.