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 4.00 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 22.0°C, while that on the outside is 14.0°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

a )

given

A = 4.00 m2 = area

glass thickness tglass = 0.7 cm

tgap = 1 cm

T1 = 22.0°C,

T2 = 14.0°C

( Q/t ) = Keff A ( T1 - T2 ) / ( tglass + tgap + tglass )

Keff = 1 / ( 1 / Kglass + 1 / Kair + 1 / Kglass )

Keff = 1 / ( 1 / 1.05 + 1 / 6.025 + 1 / 0.025 )

Keff = 0.02386 W/mk

Q/t = 0.02386 X ( 22 - ( -14 ) ) / ( 0.7 + 1 + 0.7 ) X 10-2

( Q/t )air = 143.16 J/s

b )

t = 1.4 cm

( Q/t ) = K A ( T1 - T2 ) / t

= 1.05 X 4 X ( 22 - ( - 14 ) ) / 0.014

( Q / t )glass = 10800 W

( Q/t )air < ( Q / t )glass

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