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

Question

Calculate the rate of heat conduction (in W) through a double-paned window that has a 2.50 m2 area and is made of two panes of 0.700 cm thick glass separated by a 1.00 cm air gap. The inside surface temperature is 25.0°C, while that on the outside is

19.0°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.)

  W

(b)

Calculate the rate of heat conduction (in W) through a 1.40 cm-thick window of the same area and with the same temperatures.

  W

Compare your answer with that for part (a).

=  

(Q/t)glass only / (Q/t)glass and air

Explanation / Answer

The rate of heat flow is same.through glass and air.

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

then 2x +y = 25 - (-19)= 44

As the rate of heat flow is same, so

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

so, kg x A x x/Lg = ka x A x y/La

so, kg x/Lg = ka y/La

(The thermal conductivity of glass is 36 times that of air)

so, 36x/0.7 = y

so, y=51.43 x

2 x +51.43 x = 44

so, x = 0.8235 C

y = 0.8235 x 51.43= 42.35 C

rate of heat flow = kg x A x x/Lg

=0.8 x 2.5 x 0.8235/0.007

= 235.28 W/s

b. The rate of heat flow through  a 1.40 cm-thick window of the same area and with the same temperatures

=0.8 x 2.5 x 44/0.014

= 6285.71 W/s

all the best in the course work

(Q/t)glass W/s (Q/t)glass and air= 235.28 W/s

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