Question 2: In Montana the temperature outside can get down to -10°C during the

Question

Question 2: In Montana the temperature outside can get down to -10°C during the winter months. However, for humans to be comfortable we would like the tenperature to be around 23 , which requires heating units in ide of homes. Suppose you own a house (don't laugh out loud too hard at this) and one of your exterior walls is 3 m by 2m. The wall is made, roughly, from 2 half inch panes of drywall with six inches of insulation between. The insulation as a thermal conductivity of 0.024 and the drywall has a thermal conductivity of 0.043 a) Assuming you keep your house heated at room temperature, calculate how much power is lost trough this wall due to heat transfer trough the wall b) Suppose you want to have a view of the mountains from your couch. So, you decide to put a single pane window, 1 cm in thickness, into this exterior wall. After this window is installed, you notice that your heater in this room has to work 105 times as hard to keep the room heated to room temperature. Find the area of the window you put in

Explanation / Answer

A)

0.5 in = 1.25 cm = 0.0125m
6 in = 15cm = 0.15m

A = 3x2 = 6m^2

Thermal resistance = L/kA
Total thermal resistance = 0.0125 / (0.043 x 6) + 0.0125/(0.043 x 6) + 0.15/(0.024 x 6) = 1.14

Now

P = Q/t = (T2-T1)/R = (23+10) / 1.14 = 33/1.14 = 28.95 W .... heat loss before the wall

b)

As it is said the work increases 105 times, heat loss would have increased 105 times
P = 28.95 x 105
That means R has decreased by 105 times

Rp = 1.14/105

R1 , the initial resistance will now change. As the net area of wall has decreased (6-A). Some area is taken by the window. Let this area be A
So, R1 = 1.14 x 6/(6-A) = 6.84 / (6-A)
R2 = resistance of the glass pane window = L/kA = 0.01 / 0.8A = 0.0125/A

...k for glass googled to get 0.8 as it wasn't given in the question

Using parallel combination

1/Rp = 1/R1 + 1/R2

105/1.14 = (6-A)/6.84 + A/0.0125

solving for A in calci

A = 1.14 m^2 .... Area of the glass window pane installed.

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