A room has a window fitted with a single `0.1mxx2.0m` glass of thickness 2mm. (a) Calculate the rate of heat flow through the closed window when the temperature inside the room is `32^(@)C` and that outside is `40^(@)C` . (b) The glass is now replaced by two glasspane, each having a thickness of `1mm` and separated by a distance of `1mm`. Calculate the rate of heat flow under the same condition of temperature. Thermal conductivity of window glass `=1.0Js^(-1)m^(-1).^(@)C^(-1)` and that of air `=0.025Js^(-1)m^(-1).^(@)C^(-1)` .

Explanation

`A = 1 xx 2 = 2 m^(2), L = 2 xx 10^(-3) m, K_(g) = 1 W//m.^(@)C`
`R_("glass") = R = (L)/(K_(g) A) = (2 xx 10^(-3))/(1 xx 2) = 10^(-3).^(@)C//W`
Heat current `i= (40 - 32)/(R ) = (8)/(10^(-3)) = 8000 W`
`R_("glass") = R = (L//2)/(K_(g) A) = (1 xx 10^(-3))/(1) = 1 xx 10^(-3).^(@)C//W`
`R_("air") = R' = (L//2)/(K_(a) A) = (1 xx 10^(-3))/(0.025 xx 2) = 20 xx 10^(-3).^(@)C // W`
`R_(eq) = 2 R + R' = 21 xx 10^(-3) .^(@)C // W`
Heat current `i = (40 - 32)/(21 xx 10^(-3)) = 381 W`