Two models of a windowpane are made, two identical glass panes of thickness `3 mm` are separated with an air gap of `3mm`. This composite system is fixed in the window of a room. The other model consists of a single glass pane of thickness `6mm`, the temperature difference being the same as for first model. the ratio of the heat flow for the double pane to that for the single pane is `(K_("glass") = 2.5 xx 10^(-4) cal//s.m.^(@)C` and `K_("air") = 6.2 xx 10^(-6)cal//s.m.^(@)C)`

Options

A. `1//20`
B. `1//70`
C. `31//1312`
D. `31//656`

Answer

D

Explanation

`R_(eq) = 2R_(g) +R_(air) = (2(3mm))/(k_(g)A) +((3mm))/(k_(air)A)`

`R = (6mm)/(k_(g).A)(i_(A))/(i_(B)) = ((DeltaT)/(R_(eq)))/((DeltaT)/(R)) = (R)/(R_(eq)) =`
`((6mm)/(K_(g).A))/((2(3mm))/(K_(g)A)+((3mm)/(K_(air)A))) =((1)/(K_(g)))/((2K_(air)+K_(g))/(2K_(g).K_(air)) )=(2K_(air))/(K_(g)+2K_(air))`