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 that is made of a single pane of glass 0.30 cm thick.Thermal conductivity for the glass is 0.63 W/mK.The temperature inside the house is 20$^{\circ}$C and outside is -12$^{\circ}$C.What is the thickness of the window?

Question

Quizplus · Accepted Answer

The formula to calculate the heat loss through a flat circular window is:

Q = (π * k * A * ΔT) / d

Where:
Q = heat loss
π = 3.14
k = thermal conductivity (0.63 W/mK)
A = area of the window (πr^2 = 3.14 * 0.25^2 = 0.196 m^2)
ΔT = temperature difference between inside and outside (20 + 12 = 32 °C)
d = thickness of the window

We need to find the thickness of the window, so we rearrange the formula:

d = (π * k * A * ΔT) / Q

Plugging in the values:

d = (3.14 * 0.63 * 0.196 * 32) / 1500
d = 0.0266 m = 2.66 cm = 26.6 mm

Therefore, the thickness of the window is approximately 2.6 mm, which corresponds to choice C.

A 1500 W Portable Heater Is Needed to Replace the Heat