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 needs a reproducible calibrated relationship with temperature over the working range; it need not be linear. Ice and steam points are traditional calibration examples, with pressure and other conditions specified.
- Heat transfer: conduction (lattice vibration and free electrons), convection (bulk fluid motion), thermal radiation (electromagnetic emission over a temperature-dependent spectrum, requiring no material medium and depending on surface properties).
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; for a fixed amount of an ideal gas, internal energy depends on temperature rather than pressure and volume independently.
- 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.