Thermal Physics
Heat, temperature and specific heat capacity
Temperature measures the average kinetic energy of particles; internal energy includes both kinetic and potential energy of particles. Heating changes temperature according to Q = mcΔT, where c is specific heat capacity. A change of state occurs at constant temperature once the substance reaches its melting or boiling point.
Latent heat, gases and the first law
Latent heat Q = mL, where L is specific latent heat. For an ideal gas, pV = nRT, with temperature in kelvin. Kinetic theory assumes particles are in random motion, collisions are elastic, and intermolecular forces are negligible. The first law of thermodynamics: ΔU = Q − W, where W is work done by the gas. Heat transfers by conduction, convection and radiation.
Worked example
0.50 kg of water at 20°C is mixed with 0.30 kg of water at 80°C. Taking c = 4200 J kg⁻¹ K⁻¹ and assuming no heat loss, heat gained by cold water equals heat lost by hot water. 0.50(θ − 20) = 0.30(80 − θ). Expanding: 0.50θ − 10 = 24 − 0.30θ, so 0.80θ = 34 and θ = 42.5°C. The result lies between the two starting temperatures, as expected.
Traps
Using degrees Celsius in pV = nRT instead of kelvin; forgetting the latent-heat term during a phase change; assuming all supplied heat raises temperature; ignoring heat loss to the surroundings; confusing internal energy with temperature alone.