Thermodynamics and Kinetic Theory
Thermodynamics and Kinetic Theory on ORT Physics checks whether you can separate heat from temperature, apply energy conservation to thermal changes, and connect macroscopic gas laws to the microscopic particle model.
Core rules
- Temperature measures the average random kinetic energy of particles. Internal energy is the total kinetic plus potential energy of all particles, so it can change while temperature stays constant during a phase change.
- Heating a single phase: Q = mcΔT. At a phase change: Q = mL, where L is the specific latent heat.
- Ideal gas law: pV = nRT or pV = NkT. Temperature must be in kelvin, and V in m³ if using SI units.
- Kinetic theory assumptions: particles in random motion, negligible volume, no intermolecular forces except during collisions, elastic collisions, and negligible collision duration.
- First law: ΔU = Q − W, with W the work done by the gas. State your sign convention before substituting.
- Heat-engine efficiency: η = useful work output ÷ heat input; the Carnot limit depends on the absolute temperatures of the hot and cold reservoirs.
Worked example
A 0.50 kg aluminium block at 200 °C is dropped into 1.0 kg of water at 20 °C. Take c_Al = 900 J kg⁻¹ K⁻¹ and c_water = 4200 J kg⁻¹ K⁻¹, and assume no heat loss. Heat lost by aluminium equals heat gained by water: 0.50 × 900 × (200 − T) = 1.0 × 4200 × (T − 20). This gives 450(200 − T) = 4200(T − 20), so 90 000 − 450T = 4200T − 84 000, hence 174 000 = 4650T and T = 37.4 °C. The result is plausible because water has the larger heat capacity and the larger mass.
Traps
- Substituting Celsius temperatures into pV = nRT.
- Using mcΔT across a phase change instead of mL.
- Mixing up the sign of work in the first law.
- Assuming temperature rises while ice is melting at 0 °C.
- Ignoring heat losses to the surroundings in calorimetry.