Heat & Thermodynamics
Heat Transfer: Conduction, Convection, Radiation, U-Values & Stefan's Law
5th Year · 6th Year (Leaving Cert)
- ✓By the end of this lesson students will be able to define and explain the three modes of heat transfer: conduction, convection, and radiation.
- ✓By the end of this lesson students will be able to describe factors affecting the rate of heat transfer by conduction, convection, and radiation.
- ✓By the end of this lesson students will be able to define U-value, explain its significance in insulation, and solve problems involving heat loss through building materials.
- ✓By the end of this lesson students will be able to state and apply Stefan's Law to calculate the power radiated by a black body (Higher Level).
- ✓By the end of this lesson students will be able to identify good and poor conductors, absorbers, and emitters of heat.
Key concepts
Conduction is the transfer of heat energy through direct contact between particles, without any net movement of the material itself. It is most significant in solids, where vibrating particles pass energy to adjacent particles. In metals, free electrons also play a crucial role in rapidly transferring energy.
Convection is the transfer of heat energy in fluids (liquids and gases) by the actual movement of the fluid particles. When a fluid is heated, it becomes less dense and rises. Cooler, denser fluid then sinks to take its place, creating a continuous circulation called a convection current.
Radiation is the transfer of heat energy by electromagnetic waves, primarily infrared radiation. Unlike conduction and convection, radiation does not require a medium for transfer and can travel through a vacuum. All objects above absolute zero emit thermal radiation.
The U-value (or thermal transmittance) is a measure of the rate of heat loss through a material or structure per unit area per unit temperature difference. A low U-value indicates good insulation, meaning less heat is lost through the material. It is measured in watts per square metre per kelvin (W m⁻² K⁻¹) or watts per square metre per degree Celsius (W m⁻² °C⁻¹).
Stefan's Law states that the total power (energy per unit time) radiated per unit surface area of a black body is directly proportional to the fourth power of its absolute temperature. A black body is an idealised object that absorbs all incident electromagnetic radiation and emits thermal radiation perfectly. For real objects, an emissivity (ε) factor is included.
Key facts to remember
- 1Conduction is the primary mode of heat transfer in solids, especially metals due to free electrons.
- 2Convection involves the movement of fluid particles and is the main mode of heat transfer in liquids and gases.
- 3Radiation is the transfer of heat by electromagnetic waves and does not require a medium.
- 4Dark, dull surfaces are good absorbers and emitters of thermal radiation, while light, shiny surfaces are poor absorbers/emitters and good reflectors.
- 5A low U-value indicates a material is a good insulator, reducing heat loss.
- 6Stefan's Law (HL) states that radiated power is proportional to the fourth power of the absolute temperature (P ∝ T⁴).
- 7The Stefan-Boltzmann constant (σ) is a fundamental constant used in Stefan's Law.
- 8Temperature in Stefan's Law calculations must always be expressed in Kelvin.
Worked examples
Example 1
A wall in a house has an area of 25 m² and a U-value of 0.28 W m⁻² K⁻¹. If the inside temperature is 21 °C and the outside temperature is 4 °C, calculate the rate of heat loss through the wall.
Answer
The rate of heat loss through the wall is 119 W.
A lower U-value indicates better insulation, leading to less heat loss.
Example 2
A filament of a light bulb has a surface area of 1.0 × 10⁻⁵ m² and operates at a temperature of 2800 K. Assuming it behaves as a black body, calculate the total power radiated by the filament. (Stefan-Boltzmann constant σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴).
Answer
The total power radiated by the filament is approximately 3.49 W.
Temperature must always be in Kelvin for Stefan's Law calculations.
Common mistakes
- ✗Confusing the mechanisms of heat transfer (e.g., describing convection as conduction).
- ✗Failing to convert Celsius temperatures to Kelvin when using Stefan's Law (HL).
- ✗Incorrectly stating the units for U-value (W m⁻² K⁻¹ or W m⁻² °C⁻¹).
- ✗Assuming all objects are perfect black bodies when applying Stefan's Law without considering emissivity (HL).
- ✗Not calculating the surface area (A) correctly for objects in Stefan's Law problems.
Exam tips
- ★Clearly define each mode of heat transfer and provide a relevant example for each.
- ★Remember the formula P = UAΔT for U-value calculations and ensure correct units.
- ★For Stefan's Law (HL), always convert Celsius to Kelvin (T_K = T_C + 273.15) before calculation.
- ★Pay close attention to whether a question asks for heat loss per unit area or total heat loss, especially in U-value problems.
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