Thermometry and Thermal Expansion
Thermometric properties, Celsius and Kelvin temperature scales, constant-volume gas thermometer, linear, superficial, and cubical thermal expansion of solids and liquids, real vs apparent expansion, and anomalous expansion of water.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Construct and calibrate empirical temperature scales using measurable physical thermometric properties.
- Calculate linear (ΔL = L₀αΔT), superficial (ΔA = A₀βΔT), and cubical (ΔV = V₀γΔT) expansion of solids and liquids.
- Distinguish real and apparent cubical expansivity of liquids (γ_r = γ_a + γ_glass) and explain ecological consequences of water density maximum at 4 °C.
Core Theory & Concepts
Thermal physics begins with temperature—a macroscopic measure of average molecular translational kinetic energy. When thermal energy is added to matter, internal vibrational amplitudes increase, producing thermal expansion in solids and liquids.
Two-Point Linear Celsius Scale
For any property X varying linearly with temperature: θ = [(X_θ - X₀) / (X₁₀₀ - X₀)] × 100 °C.
Linear Expansion of Solids
Fractional change in length per unit temperature rise: ΔL = L₀ · α · ΔT.
Real vs Apparent Liquid Expansivity
Real volume expansion equals apparent liquid overflow plus vessel expansion: γ_real = γ_apparent + γ_glass = γ_apparent + 3α_glass.
Common Misconceptions
When a ring or hollow sphere is heated, the internal hole shrinks because material expands inward.
Syllabus Topic Outline
- 1Thermometric properties and scale calibration: θ = [(X_θ - X₀)/(X₁₀₀ - X₀)] × 100
- 2Absolute thermodynamic temperature scale and triple point of water (273.16 K)
- 3Coefficients of linear (α), superficial (β ≈ 2α), and cubical (γ ≈ 3α) expansion
- 4Real vs apparent expansion of liquids in dilatometer vessels
- 5Anomalous expansion of water between 0 °C and 4 °C