Two models of a windowpane are made. In one model, two identical glass panes of thickness 3 mm are separated with an air gap of 3 mm. This composite system is fixed in the window of a room The other model consist of a single glass pane of thickness 3 mm, the temperature difference being the same as for the first model. the ratio of the heat flow fot the double pane to that for the single pane is
(`K_("glass")=2.5 xx10^(-4)cal//s.m.^(@)C` and `K_("air")=6.2 xx10^(-6)cal//s.m.^(@)C`).

Options

A. `1//20`
B. `1//70`
C. `1//100`
D. `1//50`

Answer

D

Explanation

`R_(eq)=2Rg+R_(air)=(2(3mm))/(k_gA)+((3mm))/(k_(air)A)`
`R=(3mmi_A)/(k_gAi_B)=((DeltaT)/(R_(eq)))/((DeltaT)/(R))`
`=(R)/(R_(eq))=((3mm)/(K_gA))/((2(3mm))/(K_gA)+((3m)/(K_(air)A)))`
`=((1)/(K_g))/((2K_(air)+K_g)/(K_gK_(air)))=(K_(air))/(K_g+2K_(air))`