A double-pane window consists of two glass sheets each of area `1m^(2)` and thickness `0.01m` separated by a `0.05 m` thick stagnant air space. In the steady state, the room glass interface and the glass outdoor interface are at constant temperature of `27^(@)C` and `0^(@)C`, respectively.
`(a)` Calculate the rate of heat flow through the window pane.
`(b)` Find the temperatures of other interfaces.
[Take: thermal conductivities as `K_(glass)=0.8Wm^(-1)K^(-1)` and `K_(air)=0.08Wm^(-1)K^(-1)`]

Explanation

`(a)` Total thermal resistance is
`R=(2t_(1))/(K_(1)A_(1))+(t_(2))/(K_(2)A_(2))`
Here,
`A_(1)=A_(2)=1m^(2)`, `t_(1)=0.01m`, `t_(2)=0.05m`,
`K_(1)=0.8Wm^(-1)K^(-1)`, `K_(2)=0.08Wm^(-1)K^(-1)`.
`:. R=(2(0.01))/((0.8)(1))+(0.05)/((0.08)(1))=0.65W^(-1)K`
Heat current `=(dQ)/(dt)=(DeltaT)/(R )=(27-0)/(0.65)=41.5W`
`(b)` `T_(1)=27-((dQ)/(dt))(t_(1))/(K_(1)A_(1))=27-0.52=26.48^(@)C`
`T_(2)=0+((dQ)/(dt))(t_(1))/(K_(1)A_(1))=0.52^(@)C`