Learning Objectives
- Understand temperature scales and their interconversion
- Learn about thermal expansion of solids, liquids, and gases
- Understand specific heat capacity and calorimetry
- Study the mechanisms of heat transfer: conduction, convection, radiation
- Learn about change of state and latent heat
Key Concepts
Temperature and Its Measurement
Temperature is a measure of the average kinetic energy of molecules.
Conversion formulas:
°F = (9/5)°C + 32; K = °C + 273.15
Absolute zero: 0 K = -273.15 °C (lowest possible temperature).
Thermal Expansion
Linear expansion: ΔL = αLΔT, so L' = L(1 + αΔT), where α is the coefficient of linear expansion.
Area expansion: ΔA = βAΔT, β ≈ 2α
Volume expansion: ΔV = γVΔT, γ ≈ 3α
Relation: α : β : γ = 1 : 2 : 3
Anomalous expansion of water: Water contracts from 0°C to 4°C and then expands. Maximum density at 4°C. This allows aquatic life to survive in frozen lakes.
Specific Heat Capacity
Heat absorbed/released: Q = mcΔT, where c is specific heat capacity (J/kg·K).
Molar specific heat: C = Mc (heat capacity per mole).
Water has a very high specific heat (4186 J/kg·K), making it useful as a coolant and for temperature regulation.
Calorimetry (principle of mixtures): Heat lost by hot body = Heat gained by cold body (in an insulated system).
Change of State and Latent Heat
During a phase change, temperature remains constant while heat is absorbed/released.
Latent heat of fusion (L_f): Heat to convert unit mass from solid to liquid. For ice: L_f = 3.33 × 10⁵ J/kg.
Latent heat of vaporisation (L_v): Heat to convert unit mass from liquid to gas. For water: L_v = 22.6 × 10⁵ J/kg.
Q = mL (heat for phase change).
Effect of pressure: Increase in pressure raises boiling point and lowers melting point (for water/ice).
Regelation: Melting of ice under pressure and refreezing when pressure is removed.
Heat Transfer
Conduction: Transfer through molecular collisions in solids. Rate: Q/t = KA(T₁ - T₂)/L (Fourier's law), K = thermal conductivity.
Convection: Transfer by bulk movement of fluid. Natural convection (due to density differences) and forced convection (by fans, pumps).
Radiation: Transfer through electromagnetic waves. No medium required.
Stefan-Boltzmann Law: E = σAT⁴ (power radiated by a black body). σ = 5.67 × 10⁻⁸ W/m²K⁴.
Wien's Displacement Law: λ_max × T = b = 2.898 × 10⁻³ m·K. Hotter bodies radiate at shorter wavelengths.
Newton's Law of Cooling: dT/dt = -k(T - T₀). Rate of cooling is proportional to temperature difference with surroundings.
Summary
Temperature is measured in Celsius, Fahrenheit, or Kelvin. Thermal expansion occurs in solids, liquids, and gases with coefficients α, β, γ. Specific heat capacity governs temperature change, while latent heat governs phase changes. Heat is transferred by conduction (solids), convection (fluids), and radiation (no medium needed). Stefan's law, Wien's law, and Newton's law of cooling describe radiative heat transfer.
Important Terms
- Thermal Equilibrium: State where no net heat flows between objects at same temperature
- Coefficient of Linear Expansion (α): Fractional increase in length per degree rise in temperature
- Specific Heat Capacity: Heat required to raise temperature of unit mass by 1°C
- Latent Heat: Heat absorbed/released during change of state without temperature change
- Black Body: Ideal body that absorbs and emits all radiation
- Thermal Conductivity: Measure of a material's ability to conduct heat
Quick Revision
- K = °C + 273.15; α : β : γ = 1 : 2 : 3
- Q = mcΔT (temperature change); Q = mL (phase change)
- Water: max density at 4°C (anomalous expansion)
- Conduction: Q/t = KA(T₁-T₂)/L; Stefan's law: E = σAT⁴
- Wien's law: λ_max T = constant
- Newton's law of cooling: rate ∝ (T - T₀)