Heat Transfer Physics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A copper rod (k=385 W/(m\cdotpK)k = 385 \text{ W/(m·K)}) and an iron rod (k=80 W/(m\cdotpK)k = 80 \text{ W/(m·K)}) have the same length (0.5 m0.5 \text{ m}) and cross-sectional area (0.001 m20.001 \text{ m}^2). Both connect a 100°C100°\text{C} source to a 25°C25°\text{C} sink. What is the rate of heat conduction through each?

Solution

  1. 1
    Copper: Qt=kAΔTL=385×0.001×750.5=28.8750.5=57.75 W\frac{Q}{t} = \frac{kA\Delta T}{L} = \frac{385 \times 0.001 \times 75}{0.5} = \frac{28.875}{0.5} = 57.75 \text{ W}.
  2. 2
    Iron: Qt=80×0.001×750.5=60.5=12 W\frac{Q}{t} = \frac{80 \times 0.001 \times 75}{0.5} = \frac{6}{0.5} = 12 \text{ W}.
  3. 3
    Copper conducts heat 57.7512≈4.8\frac{57.75}{12} \approx 4.8 times faster than iron.

Answer

Copper: 57.75 W,Iron: 12 W\text{Copper: } 57.75 \text{ W}, \quad \text{Iron: } 12 \text{ W}
Thermal conductivity determines how rapidly heat flows through a material. Copper is an excellent thermal conductor, which is why it is used in cookware and heat exchangers.

About Heat Transfer

The spontaneous flow of thermal energy from a hotter object to a cooler one until they reach thermal equilibrium (the same temperature).

Learn more about Heat Transfer →

More Heat Transfer Examples

Example 1 easy

Identify the primary mode of heat transfer in each case: (a) a metal spoon in hot soup, (b) warmth f

Example 2 medium

A glass window ([formula], area [formula], thickness [formula]) has [formula] inside and [formula] o

Example 3 medium

A thermos flask uses a vacuum between its double walls. Explain why this reduces heat transfer, and

← All Heat Transfer Examples Heat Transfer Concept