Thermal Physics and Kinetic Theory
Thermal Physics and Kinetic Theory tests the distinction between heat and temperature, calorimetry, expansion, the gas laws, the kinetic model of matter, heat transfer and the first law of thermodynamics. Quantitative calorimetry and gas-law items recur, as do explanations of pressure in terms of molecular bombardment.
Core rules
- Temperature is a measure of average kinetic energy of particles; heat is energy transferred because of a temperature difference. Kelvin = °C + 273.
- Sensible heat Q = mcΔθ; latent heat Q = mL, absorbed or released at constant temperature during a change of state.
- Linear expansion ΔL = αLΔθ; area expansivity is about 2α and volume expansivity about 3α.
- Boyle's law pV = constant at fixed temperature; Charles's law V/T constant at fixed pressure; pressure law p/T constant at fixed volume. Combined: p₁V₁/T₁ = p₂V₂/T₂, with T in kelvin.
- Ideal gas equation pV = nRT with R = 8.31 J mol⁻¹ K⁻¹.
- Kinetic theory assumptions: a very large number of identical molecules, random motion, negligible molecular volume compared with the container, no intermolecular forces except during collisions, perfectly elastic collisions, and negligible collision duration.
- Kinetic result: p = ⅓ρc̄², and mean translational kinetic energy per molecule = (3/2)kT.
- Heat transfers by conduction (lattice vibration and free electrons), convection (bulk fluid movement) and radiation (infrared, needs no medium).
- First law: ΔU = Q − W, where W is work done by the gas.
Worked example
0.20 kg of water at 90 °C is mixed with 0.30 kg of water at 20 °C in an insulated container. Find the final temperature, neglecting losses. Heat lost = heat gained: 0.20 × c × (90 − T) = 0.30 × c × (T − 20). The specific heat capacity cancels: 18 − 0.2T = 0.3T − 6, so 24 = 0.5T and T = 48 °C. The answer lies closer to 20 °C because the cooler mass is larger - a quick sanity check worth doing.
Traps that cost marks
- Substituting Celsius temperatures into a gas-law ratio instead of kelvin.
- Using mcΔθ during melting or boiling, where the temperature does not change.
- Forgetting to convert grams to kilograms in calorimetry.
- Treating heat and temperature as synonyms in explanation items.
- Assuming real gases obey pV = nRT at high pressure or near liquefaction.
- Ignoring heat lost to the container and surroundings when the question says losses are not negligible.