Thermal Physics
What this domain tests
Thermometry, heat capacity and latent heat, methods of heat transfer, the kinetic theory of gases, ideal gas behaviour and the first law of thermodynamics. Questions test careful accounting of energy in mixtures and correct use of kelvin temperatures in gas calculations.
Heat and temperature
- T(K) = θ(°C) + 273.15. Always use kelvin in pV = nRT and in kinetic theory.
- Q = mcΔθ for a temperature change; Q = mL for a change of state at constant temperature.
- In a mixture, heat lost = heat gained, provided the container is insulated and its heat capacity is either included or negligible.
- A thermometric property must change continuously and linearly with temperature; fixed points are the ice point and steam point.
- Heat transfer: conduction (lattice vibration and free electrons), convection (bulk fluid motion), radiation (infrared, no medium needed, surface-dependent).
Gases and thermodynamics
- Ideal gas law: pV = nRT, with R = 8.31 J mol⁻¹ K⁻¹.
- Kinetic theory: pV = ⅓Nm⟨c²⟩ and mean translational kinetic energy = (3/2)kT; therefore internal energy of an ideal gas depends only on T.
- First law: ΔU = Q − W, where W is work done by the gas. Isothermal: ΔU = 0. Adiabatic: Q = 0. Isobaric: W = pΔV. Isochoric: W = 0.
Worked example
0.25 kg of water at 80 °C is mixed with 0.50 kg of water at 15 °C in an insulated vessel. Find the final temperature (c = 4200 J kg⁻¹ K⁻¹).
Heat lost = 0.25 × 4200 × (80 − θ); heat gained = 0.50 × 4200 × (θ − 15). Cancelling 4200: 0.25(80 − θ) = 0.50(θ − 15) 20 − 0.25θ = 0.50θ − 7.5 → 27.5 = 0.75θ → θ = 36.7 °C.
Traps that cost marks
- Substituting Celsius values into pV = nRT - a classic lost mark.
- Confusing specific heat capacity c with specific latent heat L, or using L during a temperature change.
- Ignoring heat absorbed by the calorimeter (use mcccΔθ when the material and mass are given).
- Forgetting to convert grams to kilograms, or cm³ to m³.
- Sign errors in the first law - state whether W is work done by or on the gas.
- Claiming internal energy of an ideal gas depends on pressure or volume.