A double pan window used for insulating a room thermally from outside consists of two glass sheets each of area 1 `m^(2)` and thickness `0.01m` separated by `0.05` m thick stagnant air space. In the steady state, the room-glass interface and the glass-outdoor interface are at constant temperatures of `27^(@)C` and `0^(@)C` respectively. The thermal conductivity of glass is `0.8 Wm^(-1)K^(-1)` and of air `0.08 Wm^(-1)K^(-1)`. Answer the following questions.
(a) Calculate the temperature of the inner glass-air interface.
(b) Calculate the temperature of the outer glass-air interface.
(c) Calculate the rate of flow of heat through the window pane.

Answer

`41.6 W , 26.48^(@)C, 0.52^(@)C`

Explanation

Heat flow for three sections will be same.
`therefore (27-theta)/(((L)/(KA))_(1st"pane")) = (theta_(1)-theta_(2))/(((L)/(KA))_(A.S.))= (theta_(2) - 0)/(((L)/(KA))_(2nd"pane"))`
`implies Q_(1) = 26.48^(@)C , Q_(2) = 0.52^(@)C`
Heat flow rate `(d theta)/(dt) = (27-theta)/(((L)/(KA))_(1st "pane")) = (27-26.48)/((0.01)/(0.8xx1)) = 41.6 "watt"`