A scientist creates a test room with a composition layered from the outside in as a $3$ inch thick layer of brick, a half inch layer of mortar, a $1$ inch thick layer of plywood, framing of hardwood $24$ s $($actual dimensions are $1\mathrm{.}5$ inch wide by $3\mathrm{.}5$ inch deep$)$ set on $10$ inch centers $(10$ inches from the center of one $24$ to the next$)$ with mineral fiber filled in between, with an interior cover of half inch plaster board, a quarter inch of mortar, and finished with $2$ cell deep tiles. How much energy would have to be added to a $12ft$ by $12ft$ room with $8ft$ ceilings to offset losses through the walls $($ignore the floor and roof$)$ on a $50$ degree day averaging $10mph$ if the $75$ degree interior temperature were to be maintained?