Thermal Conductivity: Understanding Heat Transfer in A-Level Science
What Is Thermal Conductivity?
Thermal conductivity (kkk) measures a material’s ability to conduct heat. It is a critical property in understanding heat transfer.
Key Equation for Heat Transfer
Fourier’s Law of Heat Conduction
The rate of heat transfer (QQQ) through a material:
Q=kAΔTdQ = \frac{kA\Delta T}{d}Q=dkAΔT
Where:
- QQQ: Heat transfer rate (WWW).
- kkk: Thermal conductivity (W/m⋅KW/m·KW/m⋅K).
- AAA: Cross-sectional area (m2m^2m2).
- ΔT\Delta TΔT: Temperature difference (KKK).
- ddd: Thickness of the material (mmm).
Thermal Resistance (RtR_tRt)
Thermal resistance opposes heat flow:
Rt=dkAR_t = \frac{d}{kA}Rt=kAd
Example: Insulation materials have high thermal resistance to reduce heat loss.
Applications of Thermal Conductivity
Building Insulation
Thermal conductivity determines the efficiency of insulation materials.
Electronics
Efficient heat dissipation in circuits and processors.
Cooking Equipment
Pans with high thermal conductivity cook food evenly.
Example Problem
A metal plate (k=200 W/m⋅Kk = 200 \, W/m·Kk=200W/m⋅K) is 0.01 m0.01 \, \text{m}0.01m thick with a cross-sectional area of 0.5 m20.5 \, \text{m}^20.5m2. If the temperature difference is 100 K100 \, \text{K}100K, calculate the heat transfer rate.
- Formula:
Q=kAΔTdQ = \frac{kA\Delta T}{d}Q=dkAΔT
- Substitute Values:
Q=200⋅0.5⋅1000.01=1,000,000 WQ = \frac{200 \cdot 0.5 \cdot 100}{0.01} = 1,000,000 \, \text{W}Q=0.01200⋅0.5⋅100=1,000,000W
Common Mistakes in Thermal Conductivity Calculations
- Forgetting to convert units for area and thickness.
- Neglecting temperature differences in Kelvin.
- Ignoring thermal resistance in systems with multiple layers.
Practice Questions
- A wall (d=0.05 md = 0.05 \, \text{m}d=0.05m, A=2 m2A = 2 \, \text{m}^2A=2m2) has k=0.03 W/m⋅Kk = 0.03 \, W/m·Kk=0.03W/m⋅K with a temperature difference of 20 K20 \, \text{K}20K. Calculate the heat transfer rate.
- Explain how thermal resistance affects building insulation.
- Describe one application of thermal conductivity in electronics.
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