Thermodynamics and Properties of Matter
Domain 3: Thermodynamics and Properties of Matter
This domain tests heat versus temperature, calorimetry, the first and second laws, ideal-gas behavior, kinetic theory, thermal expansion, and phase changes. Items often combine a graph, such as a heating curve or PV diagram, with a calculation.
Core rules
- Q = mcΔT for temperature changes; Q = mL at a phase change, where temperature stays constant.
- First law: ΔU = Q − W, with W the work done by the gas; for a monatomic ideal gas U = (3/2)nRT.
- Ideal gas law: PV = nRT; temperature must be in kelvin. Average translational KE per molecule = (3/2)kBT, so vrms = √(3kBT/m).
- Thermal expansion: ΔL = αLΔT; area and volume use 2α and 3α.
- Second law: the entropy of an isolated system increases; heat flows spontaneously from hot to cold. Conduction rate depends on area, temperature gradient, and conductivity.
Worked example
0.20 kg of aluminum (c = 900 J/kg·K) at 150°C is dropped into 0.50 kg of water (c = 4186 J/kg·K) at 20°C. Heat lost equals heat gained: 0.20(900)(150 − T) = 0.50(4186)(T − 20). Thus 180(150 − T) = 2093(T − 20), giving 27,000 − 180T = 2093T − 41,860, so T ≈ 30°C. The aluminum's much larger temperature drop offsets its smaller mass and specific heat.
Traps
- Using Celsius in PV = nRT or in gas-law ratios.
- Forgetting the flat plateaus on a heating curve where latent heat is added.
- Sign errors in ΔU = Q − W; work done on the gas is negative by this convention.
- Assuming equal final temperatures imply equal heat capacities or equal heat flows.
- Treating rms speed as proportional to T rather than to √T.