A $0\mathrm{.}75-$m x $1\mathrm{.}5-$m window is constr$$cted of $6-$mm$-$thick glass. On a cold night, the inside and outside surface temperatures of the glass are $16$deg C and $-24$deg C$,$ respectively.

$($a$)$ What is the rate of heat loss through the glass?

$($b$)$ The window is replaced by a double$-$paned window, in which two panes of glass are separated by an air space. If the spacing of the panes is $13$ mm and the glass surface temperatures in contact with the interior air space are $12$deg C and $-18$deg C$,$ what is the new rate of heat loss from the window? $($Hint: since the temperatures on the inside glass surfaces are given, you need only analyze conduction across$$the$$air$$gap$.)$