Question

Compare the rate of heat conduction through a 13.0-cm-thick wall that has an area of 10.0m² and a thermal conductivity twice that of glass wool with the rate of heat conduction through a 0.750-cm-thick window that has an area of 2.00m², assuming the same temperature difference across each.

(a) Wall
(b) Window
(c) Equal
(d) Cannot be determined

Answer 1

The rate of heat conduction will be higher through the window because it has a thinner barrier for heat transfer despite a smaller area as compared to the wall. The wall has twice the thermal conductivity, but its thicker structure makes heat conduction less efficient.

Step-by-step explanation:

Heat Conduction Comparison

To compare the rate of heat conduction through the wall and the window, we use the equation for heat transfer given by Fourier’s law of thermal conduction:

Q/t = k × A × (ΔT/L)

Where:

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For the wall, assuming the thermal conductivity of glass wool to be k and the wall having twice that conductivity, it would be:

Q/t (wall) = 2k × 10.0 m² × (ΔT/0.13 m)

For the window:

Q/t (window) = k × 2.00 m² × (ΔT/0.0075 m)

Given that the wall is thicker and has a lower area compared to the area and thickness of the window, the rate of heat conduction will be higher through the window as it has a thinner barrier despite a smaller area than the wall with twice the thermal conductivity of the window's material.