A carpenter builds a solid wood door with dimensions $2\mathrm{.}10m0\mathrm{.}91m6\mathrm{.}0cm.$ Its thermal conductivity is $k=0\mathrm{.}120\frac{W}{m}*K.$ The air films on the inner and outer surfaces of the door have the same combined thermal resistance as an additional $1\mathrm{.}9$ cm thickness of solid wood. The inside air temperature is $21\mathrm{.}0C,$ and the outside air temperature is $-5\mathrm{.}0C.($a$)$ What is the rate of heat flow through the door? $($b$)$ By what factor is the heat flow increased if a window $0\mathrm{.}540$ m on a side is inserted in the door? The glass is $0\mathrm{.}5$ cm thick, and the glass has a thermal conductivity of $0\mathrm{.}80\frac{W}{m}*K.$ The air films on the two sides of the glass have a total thermal resistance that is the same as an additional $12\mathrm{.}0$ cm of glass. $(20$ points$)$