Heat and Gases
Heat and Gases tests your understanding of temperature, internal energy, heat transfer, and the macroscopic and molecular behaviour of gases. HKDSE questions commonly combine specific heat capacity, latent heat, and gas-law calculations, or ask you to explain pressure and temperature using kinetic theory.
Core rules and concepts
- Temperature measures average kinetic energy of particles; internal energy includes both kinetic and potential energy of the particles.
- Heating without a state change: Q = mcΔT. Heating during a state change: Q = ml, and temperature stays constant.
- Energy is conserved in mixing and heat-transfer problems if losses are negligible.
- For an ideal gas, pV = nRT, where T must be in kelvin. Boyle’s, Charles’s, and pressure laws are special cases with one variable fixed; for a fixed mass, pV/T is constant.
- Kinetic theory explains gas pressure as collisions of molecules with the container walls. Higher temperature means greater mean molecular speed and greater pressure if volume is fixed.
Worked example
0.50 kg of water at 20 °C is mixed with 0.30 kg of water at 80 °C in an insulated container. Find the final temperature.
Let the final temperature be T. Heat lost by hot water equals heat gained by cold water: 0.30 × 4200 × (80 − T) = 0.50 × 4200 × (T − 20). The specific heat capacity cancels: 0.30(80 − T) = 0.50(T − 20) 24 − 0.30T = 0.50T − 10 34 = 0.80T T = 42.5 °C. The answer is between the two starting temperatures, as expected, and closer to the colder water because it has the larger mass.
Traps that cost marks
- Substituting Celsius temperatures into pV = nRT; convert to kelvin first.
- Using Q = mcΔT during melting or boiling, where temperature does not change.
- Forgetting that the mixture’s final temperature must lie between the initial temperatures.
- Ignoring heat capacity of the container when the question says it is not negligible.
- Confusing specific heat capacity with latent heat; their units and meanings differ.