Thermodynamics and Kinetic Theory
Thermodynamics and Kinetic Theory
This domain covers temperature and heat, specific and latent heat, the first and second laws, ideal gases, kinetic theory, and heat engines. The exam emphasizes sign conventions and the distinction between state functions and path-dependent quantities.
Core rules and concepts
- Heat is energy transferred because of a temperature difference; temperature measures average molecular kinetic energy.
- Q = mcΔT for temperature changes; Q = mL for phase changes at constant temperature.
- First law: ΔU = Q - W for work done by the system. Sign conventions vary, so identify the convention stated in the item.
- Ideal gas law: PV = nRT; temperature must be in kelvin. Kinetic theory links average kinetic energy to absolute temperature.
- Second law: entropy of an isolated system increases; no heat engine can exceed Carnot efficiency e = 1 - Tc/Th, with temperatures in kelvin.
Worked example
How much heat is needed to warm 0.20 kg of water from 20°C to 80°C? c = 4186 J/(kg·°C). Q = (0.20)(4186)(60) = 50,232 J ≈ 5.0 × 10⁴ J. If the water then boiled, the temperature would stay at 100°C while latent heat is added.
Traps that cost marks
Using Celsius in gas-law calculations; forgetting that temperature is constant during a phase change; reversing the sign of work; and using Carnot efficiency as the actual efficiency of a real engine. In kinetic theory, molecular speed distributions shift with temperature, but average kinetic energy depends only on T.