Thermal Physics: Heat, Temperature and Gas Laws
Scope of the domain
This domain covers temperature and thermal equilibrium, specific heat capacity and latent heat, heat transfer, and ideal-gas behaviour. The exam asks you to calculate energy in heating and state changes, apply the gas laws with absolute temperature, and explain pressure using kinetic theory.
Core rules
- T(K) = θ(°C) + 273.15. Absolute zero is 0 K; Kelvin must be used in gas-law ratios.
- Heating without a state change: Q = mcΔT. A change of state at constant temperature: Q = mL.
- In a mixture, heat lost by hot bodies equals heat gained by cold bodies, provided no heat is lost to the surroundings.
- Conduction requires a temperature gradient in a solid; convection involves bulk movement in a fluid; radiation is electromagnetic and needs no medium.
- Ideal gas: pV = nRT, with R = 8.31 J mol⁻¹ K⁻¹. Combined law: p₁V₁/T₁ = p₂V₂/T₂.
- Kinetic theory: gas pressure arises from particle collisions with the container walls; average kinetic energy is proportional to thermodynamic temperature.
- Internal energy is the sum of the random kinetic and potential energies of the particles; temperature measures average random kinetic energy.
Worked example
0.20 kg of water at 90 °C is mixed with 0.30 kg of water at 20 °C. Taking c = 4200 J kg⁻¹ K⁻¹ and ignoring losses, find the final temperature. Heat lost = heat gained: 0.20 × 4200 × (90 − T) = 0.30 × 4200 × (T − 20). Dividing by 4200: 0.20(90 − T) = 0.30(T − 20), so 18 − 0.20T = 0.30T − 6. Hence 24 = 0.50T and T = 48 °C. The value lies between the two starting temperatures, as it must.
Traps that cost marks
- Substituting Celsius temperatures into pV = nRT or into gas-law ratios.
- Expecting temperature to rise during melting or boiling; the energy changes potential energy instead.
- Using the specific heat capacity while a substance is changing state.
- Forgetting the container's heat capacity when the question states it is significant.
- Confusing heat with temperature: a large mass at low temperature can transfer more energy.
- Mixing up conduction, convection and radiation explanations.