$4.(20$ marks$)$

Figure Q$4$ represents a sunroom with $3$ external walls facing North, East and South, respectively and an internal wall containing a double door into the main dwelling facing west. The sunroom is to be maintained at $\backslash (18^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ throughout the heating season for an outside temperature of $\backslash (-2^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Assuming that the main dwelling is to be maintained at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ calculate the required heat input to the sunroom given the thermal properties of the building components given in Table Q$4.$ The floor and roof can be taken to be external components. The sunroom height can be taken to be $2\mathrm{.}7$ m $.$ Assume all glazed and door elements run to the full room height. Air exchange occurs from ambient to sunroom and sunroom to ambient.

Table Q$4$