Theory Exercises

Temperature

Definition of Temperature

Temperature is a measure of the average kinetic energy (Ek) of particles (atoms and molecules) in a substance. Important distinction:
  • Temperature: Measure of average molecular motion (scalar)
  • Heat: Energy transferred between objects due to temperature difference
  • Thermal energy: Total kinetic energy of all particles

Temperature vs. Heat

Key Differences

TemperatureHeat
Measure of molecular EkEnergy transfer
Scalar quantityEnergy (scalar)
Measured in °C, °F, KMeasured in Joules (J)
Property of matterProcess between objects
Same in all reference framesDirectional (hot to cold)
Temperature determines direction of heat flow:
  • Heat flows from higher temperature to lower temperature
  • At equilibrium: temperatures equal, heat flow stops

Effects of Temperature

1. Thermal Expansion

Most substances expand when heated and contract when cooled.

Linear Expansion

\[\Delta L = \alpha L_0 \Delta T\]
Where:
  • ΔL = change in length
  • α = linear expansion coefficient
  • L₀ = original length
  • ΔT = temperature change
Example: A 2-meter aluminum rod (α = 23 × 10⁻⁶ /°C) is heated from 10°C to 300°C. Calculate the change in length.
\[\Delta L = 23 \times 10^{-6} \times 2 \times (300 - 10) = 23 \times 10^{-6} \times 2 \times 290 = 0.01334 \text{ m} = 13.34 \text{ mm}\]

Volume Expansion

\[\Delta V = \beta V_0 \Delta T\]
Where:
  • ΔV = change in volume
  • β = volumetric expansion coefficient (≈ 3α for solids)
Examples:
  • Bridge expansion joints prevent cracking
  • Power lines sag in summer (thermal expansion)
  • Mercury thermometer works due to expansion
Example: A steel sphere of 10 cm radius is heated from 20°C to 200°C. Calculate the change in volume.
\[\Delta V = \beta V_0 \Delta T = 3 \times 23 \times 10^{-6} \times \frac{4}{3} \pi (0.1)^3 \times (200 - 20) = 3 \times 23 \times 10^{-6} \times \frac{4}{3} \pi (0.1)^3 \times 180 = 0.000778 \text{ m}^3 = 778 \text{ cm}^3\]

2. Changes in Physical Properties

As temperature increases:
PropertyEffectExample
DensityDecreasesIce floats on water
SolubilityUsually increasesMore salt dissolves in hot water
Electrical resistanceIncreases (metals)Light bulb filament resistance
ReactivityIncreasesChemical reactions faster

Temperature and Motion

Absolute Zero

Temperature at which all molecular motion theoretically stops
  • 0 K = -273.15°C = -459.67°F
  • Cannot be reached (laws of thermodynamics)
  • Reference point for absolute temperature scale

Types of molecular movement

  • Translation: Movement from one place to another
  • Rotation: Rotation around an axis
  • Vibration: Oscillation around an equilibrium position