As you are assisting in the investigation, you notice that Polly's apartment has maintained a cozy temperature even though her heat had been turned off and it's a cold winter's day. (Could this be another clue?) One explanation is that her apartment has nice double pane windows, consisting of two glass panes that are each 3-mm thick sandwiching a well- sealed air gap 6-mm thick. In "steady state", the rate that heat flows through a glass pane equals the rate that heat flows through the air gap in the double pane window (otherwise there would be a net heat flow into the air or window, changing its temperature -- whatever flows into one of these materials must flow out to maintain a given temperature).


Since the thermal conductivity of still air [0.025 W/(m°C)] is much smaller than the thermal conductivity of glass [0.80 W/(m°C)], the temperature difference across the double pane window is almost entirely over the air gap. (Again, in this steady state, the rate of heat flow through the glass and air are the same for the double pane window, so if the conductivity of air is much smaller than that of glass, the temperature difference across the air must be much larger than that across the glass for these windows.)


Required:

Considering this, what is the ratio of the rate of heat flow through a cheap window with a single pane of glass 5-mm thick compared to a nicer double pane window with an air gap of 5 mm if the temperature difference across them is the same (and they have the same areas)?