A wall that is $2\mathrm{.}30$ m high and $3\mathrm{.}66$ m long has a thickness composed of $1\mathrm{.}00$ cm of wood plus $3\mathrm{.}00$ cm of insulation $($with the thermal conductivity approximately of wool$).$ The inside of the wall is $23\mathrm{.}0$C and the outside of the wall is at $5\mathrm{.}00$C$.$ The thermal conductivity of wood is $0\mathrm{.}130$ W$/($m$$K$)$ and that of wool is $0\mathrm{.}0380$ W$/($m$$K$).$

$1)$ What is the rate of heat flow through the wall? Use unit W$.$

$2)$ If half the area of the wall is replaced with a single pane of glass that is $0\mathrm{.}500$ cm thick, What is the rate of heat flow through the wall now? The thermal conductivity of glass is $0\mathrm{.}630$ W$/($m$$K$).$ Use unit kW$.$