Paper 3 Thermal Physics B Answers

Q1 Kinetic theory derivation logic

1. Molecules are point-like/negligible volume; random motion; elastic collisions; no intermolecular forces except during collisions; collision duration negligible. Any three. [3]
2. Molecules rebound from walls, changing momentum. The wall exerts force on molecules, and molecules exert equal opposite force on wall. Many impacts per unit time produce pressure. [3]
3. $pV=\frac{1}{3}Nm⟨c^2⟩$. The factor $1/3$ comes from equal mean square velocity components in three perpendicular directions for random motion. [2]
4. Equating with $pV=NkT$ gives $\frac{1}{3}m⟨c^2⟩=kT$, so $\frac{1}{2}m⟨c^2⟩=\frac{3}{2}kT$. [3]

Q2 Thermodynamic process reasoning

1. Isothermal compression. [1]
2. $\Delta U=0$ for an ideal gas at constant temperature. [1]
3. Work done on the gas would tend to increase internal energy, but temperature is held constant. Therefore equal energy is transferred out by heating, so $Q=-W_{on}$ with the $\Delta U=Q+W_{on}$ convention. [3]
4. A rectangular-hyperbola-like curve with pressure increasing as volume decreases. [2]