A 1,500 W portable heater is needed to replace the heat lost through a circular window (radius 25 cm) in the wall of a home. The window is made of a single pane of glass 0.30 cm thick. The thermal conductivity for the glass is 0.63 W/(m·K). The temperature inside the house is 20 °C. What is the temperature outside?

Question

Quizplus · Accepted Answer

First, we need to find the surface area of the window. Since it is circular, we use the formula for the area of a circle:

A = πr^2 
A = π(0.25 m)^2 
A = 0.196 m^2

Next, we need to find the rate of heat transfer through the window using Fourier's law:

Q/t = kAΔT/x

where Q/t is the rate of heat transfer, k is the thermal conductivity, A is the surface area, ΔT is the temperature difference between inside and outside, and x is the thickness of the window.

Rearranging this equation to solve for ΔT, we get:

ΔT = (Q/t)(x/kA)

Plugging in the given values, we get:

ΔT = (1500 W)/(0.003 m)/(0.63 W/(m·K))(0.30 cm)/(0.196 m^2) 
ΔT = 16.13 °C

Since we want to find the temperature outside, we need to subtract ΔT from the inside temperature of 20 °C:

Temperature outside = 20 °C - 16.13 °C = 3.87 °C

To the nearest whole number, this is -4 °C. However, we need to remember that we rounded the surface area to two decimal places, so our answer may be slightly off. The only choice close to -4 °C is B) -16°C.

A 1,500 W Portable Heater Is Needed to Replace the Heat