A 1500 W portable heater is needed to replace the heat lost through a circular window (radius 25 cm) in the wall of a home. The thermal conductivity for the glass is 0.63 W/mK. The temperature inside the house is 20 °C and outside is −12°C. What is the thickness of the window?

Question

Quizplus · Accepted Answer

The heat lost through the window can be calculated using the formula:

Q = (kAΔT)/d

where Q is the heat lost per unit time (in Watts), k is thermal conductivity (in W/mK), A is the area of the window (in m^2), ΔT is the temperature difference between inside and outside (in K), and d is the thickness of the window (in m).

We are given Q = 1500 W, k = 0.63 W/mK, A = πr^2 where r = 0.25 m, ΔT = (20 - (-12))/2 = 16 °C = 16 K (since we need to use absolute temperature difference), and we need to find d.

Plugging in the values, we get:

1500 = (0.63 x π x 0.25^2 x 16)/d

Solving for d, we get:

d = (0.63 x π x 0.25^2 x 16)/1500

d ≈ 0.0026 m or 2.6 mm

Therefore, the thickness of the window is 2.6 mm. The correct answer is (C).

A 1500 W Portable Heater Is Needed to Replace the Heat