Theory Exercises

Temperature

Definition of Temperature

Temperature is a measure of the average kinetic energy 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 Scales

1. Celsius (°C)

Most common scale worldwide
  • 0°C: Freezing point of water
  • 100°C: Boiling point of water (at sea level)
  • -273.15°C: Absolute zero (theoretical lowest temperature)

2. Fahrenheit (°F)

Used primarily in United States
  • 32°F: Freezing point of water
  • 212°F: Boiling point of water
  • Lower values: Colder temperatures
Conversion from Celsius:
\[T_F = \frac{9}{5}T_C + 32\]

\[T_C = \frac{5}{9}(T_F - 32)\]

3. Kelvin (K)

Absolute temperature scale, SI unit
  • 0 K: Absolute zero (no molecular motion)
  • 273.15 K: Freezing point of water
  • 373.15 K: Boiling point of water
Conversion from Celsius:
\[T_K = T_C + 273.15\]

\[T_C = T_K - 273.15\]

> [Ejemplo: Room temperature 20°C: > - Fahrenheit: T_F = (9/5)(20) + 32 = 36 + 32 = 68°F > - Kelvin: T_K = 20 + 273.15 = 293.15 K]

Temperature vs. Heat

Key Differences

TemperatureHeat
Measure of molecular KEEnergy 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 on Matter

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

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

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

3. Phase Changes

Temperature causes transitions between solid, liquid, and gas:

Phase ChangeExampleTemperature (H₂O)
MeltingSolid → Liquid0°C (273 K)
FreezingLiquid → Solid0°C (273 K)
Boiling/VaporizationLiquid → Gas100°C (373 K)
CondensationGas → Liquid100°C (373 K)
SublimationSolid → GasDry ice (-78.5°C)
DepositionGas → SolidFrost formation

Thermal Properties of Matter

Specific Heat Capacity

Specific heat (c) is energy required to raise temperature of 1 kg by 1°C.

\[Q = m c \Delta T\]

Where:
  • Q = heat energy (Joules, J)
  • m = mass (kg)
  • c = specific heat capacity (J/kg·°C)
  • ΔT = temperature change (°C)
Specific heat values:
Materialc (J/kg·°C)
Water4,200
Ice2,100
Aluminum900
Iron450
Lead130
Water has highest specific heat - why oceans moderate climate!

> [Ejemplo: Heating 2 kg of water by 10°C: > - Q = 2 × 4,200 × 10 = 84,000 J]

Heat Capacity

Heat capacity (C) is energy to raise temperature of entire object by 1°C.

\[C = m c\]

\[Q = C \Delta T\]

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

Kinetic Theory Connection

Temperature is directly related to average molecular kinetic energy:

\[KE_{\text{avg}} = \frac{3}{2}k_B T\]

Where:
  • k_B = Boltzmann's constant
  • T = absolute temperature (Kelvin)

Higher temperature = faster particle motion

Real-World Applications

Material Engineering

  • Thermal stress: Temperature changes create stress in materials
  • Bimetallic strips: Different expansion rates in thermostats
  • Shape memory alloys: Return to shape when heated

Environmental Effects

  • Thermal pollution: Heated water affects aquatic ecosystems
  • Climate change: Global temperature increase affects weather patterns
  • Urban heat island: Cities warmer than surrounding areas

Comfort and Safety

  • Human body: 37°C (98.6°F) optimal temperature
  • Hypothermia: Body below 35°C (95°F)
  • Fever: Body above 38°C (100.4°F)

Industrial Processes

  • Tempering steel: Heating and cooling controls hardness
  • Annealing glass: Slow cooling prevents stress
  • Refrigeration: Removing heat from food

Measuring Temperature

Thermometer Types

Liquid-in-glass:
  • Mercury or alcohol
  • Expands/contracts with temperature
  • Simple, reliable
Digital:
  • Electrical resistance or thermistor
  • Quick response
  • Electronic display
Infrared:
  • Measures radiant heat
  • Non-contact
  • Used for remote sensing
Thermocouple:
  • Two dissimilar metals
  • Generates voltage based on temperature
  • Industrial applications

Key Takeaways

  1. Temperature: Measure of average molecular kinetic energy
  2. Scales: Celsius (water reference), Fahrenheit (US), Kelvin (absolute)
  3. Heat: Energy transfer from hot to cold objects
  4. Thermal expansion: Most substances expand when heated
  5. Specific heat: Energy per unit mass per degree change (Q = mcΔT)
  6. Phase changes: Occur at fixed temperatures
  7. Absolute zero: 0 K = -273.15°C (theoretical limit)
  8. Applications: Material engineering, climate, industrial processes