Heat and Heat Transfer Notes

Heat & Temperature Scales

• Temperature and heat are distinct concepts.
• Temperature determines the direction of heat flow when objects are in thermal contact; heat flows from high to low temperature.

Temperature Scales

• SI Scale: Kelvin (K)
• Common Scale: Celsius (°C), widely used, including in clinical settings.
• Celsius Scale:
  • 0°C: Freezing point of water at Standard Temperature and Pressure (STP)
  • 100°C: Boiling point of water at STP
• Conversions:
  • Celsius to Kelvin: $K = °C + 273.15$
  • Celsius to Fahrenheit: $°F = (°C \times \frac{9}{5}) + 32$
  • Fahrenheit to Celsius: $°C = (°F - 32) \times \frac{5}{9}$

Fahrenheit Scale Usage

• Used in:
  • U.S.
  • Marshall Islands
  • Liberia
  • Jamaica
  • Belize

Absolute Zero

• Charles’ Law: Volume of an ideal gas is directly proportional to absolute temperature at constant pressure.
• Extrapolation to -273.15°C on a volume vs. temperature graph.
• Absolute Zero: -273.15°C, the starting point of the Kelvin scale.

Temperature Measurement

Thermometers

• Used to measure temperature.
• Calibrated to a reference material via its thermometric property.
  • Example: Mercury thermometer uses thermal expansion of mercury.
  • Change in mercury column height indicates temperature change.

Calorimeters

• Used to measure heat.

Thermometric Property

• Physical property of a substance that changes uniformly (not necessarily linearly) and predictably with temperature.
• Examples:
  • Volume
  • Color
  • Electrical resistance or voltage
  • Pressure

Types of Thermometers

• Mercury/Alcohol thermometer
• Thermocouple: Measures resistance of two different metals
• Gas-filled bulb thermometer
• Liquid crystal thermometer: Measures color change of crystals

Thermometer Function

• Mercury or alcohol expands when heated.
• Expansion is linear within a specific temperature range.
• After calibration, the thermometer can accurately measure temperature.

Human Body Temperature

• Core body temperature: Approximately 37°C (98.6°F).
• Temperature varies at extremities.

Body Temperature Variation

• Oral cavity: 0.4°C lower than core temperature.
• Rectum: 0.3°C higher than core temperature.
• Armpit (axilla): 0.9°C lower than core temperature.

Factors Affecting Body Temperature

• Hard exercise
• Hard work
• Emotion
• Age
• Time of day
• Smoking
• Hot/cold drinks
• Hormones
• Menstrual cycle: Used in the Rhythm Method of birth control
  • Reliability: ~75%

Changes in Temperature

• Heat energy must be added or removed to change an object's temperature.
• The rise in temperature ($\Delta T$) depends on:
  • Quantity of heat added (Q)
  • Mass (m)
  • Specific heat capacity (c)

Specific Heat Capacity (SHC)

• Amount of heat energy required to raise the temperature of 1 kg of a substance by 1 Kelvin.
• Units: J kg⁻¹ K⁻¹
• Formula: $Q = mc\Delta T$

Water's High SHC

• Water has a very high SHC value.
• The human body has a high water content, resulting in high thermal inertia (resistance to temperature change).
• Example Specific Heat Capacity:
  • Steel: 0.45

Example Calculation

• Problem: How much heat energy is required to raise the temperature of 3L of water from 20 to 80°C? (SHC of water = 4200 J/kg.K)
• Solution:
  • m = 3 kg (1L of water = 1 kg)
  • $\Delta T = 80 - 20 = 60°C$
  • $Q = 3 \times 4200 \times 60 = 7.56 \times 10^5 J$

Heat Transfer

• Heat flows from one object to another via three methods:
  • Radiation: Does not require a medium
  • Convection: Occurs in liquids and gases
  • Conduction: Occurs in solids

Conduction

• Heat transfer by direct contact.
• Formula: $H_{cd} = \frac{kA\Delta T}{L}$
  • $H_{cd}$: Rate of heat transfer by conduction
  • $k$: Thermal conductivity of the material (W/m.K)
  • $A$: Cross-sectional area (m²)
  • $\Delta T$: Temperature difference (K)
  • $L$: Length of the material (m)

Thermal Conductivity Examples

• Air vs. Water:
  • Air feels colder than water at 0°C due to differences in thermal conductivity.
  • $k_{air} = 0.023 J s^{-1} m^{-1} K^{-1}$
  • $k_{water} = 0.56 J s^{-1} m^{-1} K^{-1}$
  • Water is 24 times better at conducting heat than air.
  • Air is a good insulator.

Insulation Examples

• Arctic Fox: Winter coat has a larger volume for better insulation.
• Reindeer (Caribou): Hair follicles are hollow, trapping insulating air.
• String Vests: Air in the holes provides insulation; air is a better insulator than cotton.

Convection

• Heat transfer in fluids (liquids or gases).
• Heated fluid becomes less dense and rises.
• Cooler, denser fluid sinks to replace it, creating convection cells.

Convection Examples

• Solar Surface: Convection cells are visible.
• Tectonic Plates: Geo-thermal convection drives their movement.

Rate of Convective Heat Flow

• Formula: $q = hA\Delta T$
  • $q$: Rate of convective heat flow
  • $h$: Convective heat transfer constant (depends on shape, orientation, surface; for humans, approximately 7.1 W m⁻² K⁻¹)
  • $A$: Surface area
  • $\Delta T$: Temperature difference

Wind-Chill

• Convection causes wind-chill: moving cold air cools you down.

Fan Oven Effect

• Moving hot air will cause the food/substance/person to heat up more quickly.
• If T > 37°C, and there is no air conditioning, fans can cause fatalities in heatwaves by increasing convection.

Radiation

• Heat transfer that does not require a medium.
• Relies on photons, so it can occur across a vacuum.
• Formula: $P = e\sigma A(T^4 - T_0^4)$
  • $P$: Net radiated power
  • $e$: Emissivity (0 = bad, 1 = perfect)
  • $\sigma$: Stefan’s constant = 5.7 x 10⁻⁸ W m⁻² K⁻⁴
  • $A$: Surface area
  • $T$: Temperature of the object in Kelvin
  • $T_0$: Temperature of the surroundings in Kelvin