A 1500 W portable heater is needed to replace the heat lost through a circular window 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 radius of the window?

Question

Quizplus · Accepted Answer

First, we need to calculate the rate of heat loss through the window using the formula:
Q/t = k*A*(T2-T1)/d
where Q/t is the rate of heat loss, k is the thermal conductivity, A is the area of the window, T2 is the outside temperature, T1 is the inside temperature, and d is the thickness of the glass.

Rearranging this equation to solve for the area A, we get:
A = (Q/t)*(d)/(k*(T2-T1))

Plugging in the given values, we get:
A = (1500 W)*(0.003 m)/(0.63 W/mK*(20+273 K - (-12+273 K)))
A = 0.0126 m^2

The area of a circle is given by the formula:
A = pi*r^2

Solving for r, we get:
r = sqrt(A/pi)
r = sqrt(0.0126/3.14)
r = 0.1123 m = 11.23 cm

Therefore, the radius of the window is approximately 27 cm.

A 1500 W Portable Heater Is Needed to Replace the Heat