Last reviewed 16 Sept 2026 · 8 min read
Temperature and thermometry
- Temperature — measure of the degree of hotness; determines direction of heat flow (zeroth law).
- Heat — energy transferred due to temperature difference (J; 1 cal ≈ 4.186 J).
FormulaTemperature scales
- Water freezes at 0 °C = 32 °F = 273.15 K; boils (1 atm) at 100 °C = 212 °F = 373.15 K
- −40 °C = −40 °F
- Absolute zero = 0 K = −273.15 °C
Thermometers
| Type | Principle | Use |
|---|---|---|
| Liquid-in-glass (mercury, alcohol) | Thermal expansion of liquid | General use; alcohol for low temperatures |
| Constant volume gas thermometer | Pressure change of gas | Standard, accurate |
| Resistance thermometer (RTD, e.g. Pt-100) | Resistance change of metal | Industrial, accurate |
| Thermistor | Resistance of semiconductor (large change) | Electronic sensing |
| Thermocouple | Seebeck effect — EMF at junction of two metals | Wide range, concrete temperature monitoring, furnaces |
| Pyrometers (radiation/optical) | Radiation from hot bodies | Very high temperatures (kilns, molten metal) |
| Infrared thermometers/cameras | IR radiation | Non-contact — building envelope inspection |
| Bimetallic strip | Differential expansion | Thermostats |
Thermal expansion
FormulaExpansion relations
Linear: Superficial (area): , Volumetric: ,
Thermal stress (fully restrained bar):
(independent of length)
Typical coefficients of linear expansion (per °C, approx.)
| Material | α |
|---|---|
| Steel | ≈ 12 × 10⁻⁶ |
| Concrete | ≈ 10 × 10⁻⁶ (varies with aggregate, about 7–12 × 10⁻⁶) |
| Aluminium | ≈ 23 × 10⁻⁶ |
| Copper | ≈ 17 × 10⁻⁶ |
| Glass (ordinary) | ≈ 9 × 10⁻⁶ |
| Invar (Fe–Ni alloy) | ≈ 1 × 10⁻⁶ (very low) — surveying tapes, precision instruments |
- Steel and concrete have nearly equal coefficients — essential for reinforced concrete to act compositely without large thermal stresses.
Engineering applications
- Expansion joints in bridges (finger joints, strip seals), buildings (long blocks separated by joints), concrete pavements (expansion and contraction joints), pipelines (expansion loops, bellows).
- Gaps in railway tracks (or long welded rails with de-stressing at neutral temperature).
- Bridge bearings (roller/sliding/elastomeric) allow thermal movement.
- Temperature corrections in steel tape measurements (surveying).
- Hot riveting (contraction on cooling tightens joints); shrink fits.
- Thermal cracking of mass concrete and restrained slabs.
- Overhead lines sag more in summer.
Anomalous expansion of water
- Water contracts when heated from 0 °C to 4 °C and expands thereafter — maximum density at 4 °C.
- Consequences: lakes freeze from the top, preserving aquatic life; freezing water expands (~9%) → frost damage to concrete, rocks and pipes (freeze–thaw weathering).
Calorimetry
FormulaHeat relations
Sensible heat: ( = specific heat capacity) Heat capacity Latent heat: (no temperature change during phase change) Principle of calorimetry (mixtures): heat lost by hot bodies = heat gained by cold bodies (no losses)
| Property | Value (approx.) |
|---|---|
| Specific heat of water | 4186 J/kg·K (1 cal/g·°C) — high value moderates climate |
| Specific heat of concrete | ≈ 880–1000 J/kg·K |
| Specific heat of steel | ≈ 460–490 J/kg·K |
| Latent heat of fusion of ice | ≈ 334 kJ/kg |
| Latent heat of vaporisation of water (100 °C) | ≈ 2257 kJ/kg |
Thermal mass (high heat capacity materials such as concrete and brick) moderates indoor temperature swings.
Kinetic theory of gases
Ideal gas laws
- Boyle's law: = constant (constant T).
- Charles' law: = constant (constant p).
- Gay-Lussac's law: = constant (constant V).
- Ideal gas equation: , J/mol·K; , J/K.
- Avogadro's law — equal volumes of gases at the same T and p contain equal numbers of molecules; molar volume at STP ≈ 22.4 L.
- Dalton's law of partial pressures.
Molecular interpretation
FormulaKinetic theory
Pressure: Mean kinetic energy per molecule — temperature is a measure of average molecular KE RMS speed: Average speed ; most probable speed ()
Degrees of freedom and equipartition
- Each degree of freedom has average energy .
- Monatomic gas: 3 DOF → , .
- Diatomic gas (room temperature): 5 DOF → , (air).
- (Mayer's relation).
Real gases
- Deviations at high pressure and low temperature — van der Waals equation .