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A double-plane window consists of two ...

A double-plane window consists of two glass sheets each of area `1 m^(2)` and thickness `.01 m` 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. The rate of heat flow through the window pane is (Given , ` K_("glass") = 0.8 W m^(-1) K^(-1)`, `K_("air") = 0.08 W m^(-1) K^(-1)`)

Text Solution

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`(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`
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