Thermal Properties of Matter
Heat and temperature govern the behavior of matter. Bridges expand in summer, food cooks when thermal energy transfers, and water has a remarkably high specific heat.
Start with the simplest version: this lesson is about Thermal Properties of Matter. If you can explain the core idea to a friend using everyday language, examples, and one clear reason why it matters, you have moved from memorising to understanding.
Heat and temperature govern the behaviour of matter. A frozen nail is brittle; when heated, it becomes malleable. Bridges expand in summer and contract in winter. Food cooks when thermal energy transfers to it. This chapter explores how matter responds to temperature changes, how heat flows, and the physical foundations of thermal phenomena.
Temperature versus Heat
Temperature measures the average kinetic energy of particles — a property of a state. Heat is energy in transit between systems due to a temperature difference; it is a process, not a quantity stored in a body. SI unit of temperature is the kelvin (K); 0 K is absolute zero. Conversions: T(K) = T(°C) + 273.15; T(°F) = (9/5) T(°C) + 32.
Ideal Gas Law and Absolute Temperature
For an ideal gas, PV = nRT, with R = 8.314 J/(mol·K). At constant V, P ∝ T (Charles's/Gay-Lussac's law); at constant P, V ∝ T. Linear extrapolation of these proportionalities defines the absolute (Kelvin) scale.
Thermal Expansion
Linear expansion: ΔL = α L₀ ΔT. Area expansion: ΔA = β A₀ ΔT with β ≈ 2α. Volume expansion: ΔV = γ V₀ ΔT with γ ≈ 3α for isotropic solids. Water is anomalous: between 0 °C and 4 °C it contracts on heating (maximum density at 4 °C), which is why ice floats and lakes freeze from the top.
Specific Heat Capacity
Q = m c ΔT; SI unit of c is J/(kg·K). Water has c ≈ 4186 J/(kg·K), unusually high — making it a good coolant and stabiliser of climate. Molar heat capacity C = M·c. For an ideal gas: C_p − C_v = R (Mayer's relation); ratio γ = C_p/C_v.
Calorimetry
For an isolated system, heat lost by the hot body = heat gained by the cold body: m₁c₁(T₁ − T_f) = m₂c₂(T_f − T₂). The calorimeter constant accounts for heat absorbed by the container.
Change of State and Latent Heat
During a phase change, temperature stays constant while heat is supplied. Energy needed: Q = m L, where L is the latent heat. For water: L_f ≈ 3.34 × 10⁵ J/kg (fusion), L_v ≈ 2.26 × 10⁶ J/kg (vaporisation). The very high L_v is why sweating is so cooling.
Heat Transfer
Conduction in a steady state through a slab: H = dQ/dt = k A (T_H − T_C)/L, where k is thermal conductivity. Convection involves bulk flow (e.g. land–sea breezes). Radiation: every body emits electromagnetic radiation; the Stefan–Boltzmann law gives radiated power per unit area σ T⁴ for a blackbody (σ = 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴).
Newton's Law of Cooling
For small temperature differences with the surroundings, the rate of cooling is proportional to the excess temperature: dT/dt = −k(T − T_s).
Socratic Questions
- Why does pouring boiling water into a thick glass tumbler shatter it, while a thin glass survives?
- Why do coastal regions have milder temperatures than inland regions at the same latitude?
- Why does ice float on water, and what would happen to lakes in winter if water did not have its density anomaly?
- Why is sweating an effective way to cool the body, even when the air is warmer than the skin?
- Why does a hot cup of tea cool faster on a windy day than on a still day, even at the same air temperature?