1. a.)Calculate the rate of heat conduction (in W) through a double-paned window

Question

1. a.)Calculate the rate of heat conduction (in W) through a double-paned window that has a 3.50 m2 area and is made of two panes of 0.600 cm thick glass separated by a 1.00 cm air gap. The inside surface temperature is 22.0°C, while that on the outside is 11.0°C. (Hint: There are identical temperature drops across the two glass panes. First find these and then the temperature drop across the air gap. This problem ignores the increased heat transfer in the air gap due to convection.)

b.) Calculate the rate of heat conduction (in W) through a 1.20 cm-thick window of the same area and with the same temperatures.

c.) Compare your answer with that of (a).

Explanation / Answer

If x = temperature drop across the glass and y= temperature drop across the air

then 2x + y = (22 - (-11))=33

Rate of heat flow through the glass = rate of heat flow through the air

then kgAx/Lg = kaAy/La (where k= thermal conductivity, A= area L= thickness)

As kg = 36 ka

so, 36 x /0.6 = y/1

so, 60 x=y

so, 2x +y=33

So, 62x =33

so, x =33/62 = 0.5322 C

y = 31.93 C

the heat transfer rate = 0.8 x 3.5 x 0.5322/0.006 = 248.36 W

b. The rate of heat conduction (in W) through a 1.2 cm - thick window of the same area and with the same temperature = 0.8 x 3.5 x 33/0.012 = 7700 W

c. Rate of heat transfer with air = 248.36 W

rate of heat transfer without air = 7700 W

all the best in the course work

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