One wall was built with $1\mathrm{.}5$ cm thick gypsum plaster on the inside, $20$ cm thick rough building brick in the middle, and $2\mathrm{.}5$ cm thick lime mortar on the outside. Indoor and outdoor temperatures are $22\backslash$deg C and $5\backslash$deg C respectively. The heat transfer coefficient is $10$ W$/$m$^2$K on the inner surface and $20$ W$/$m$^2$K on the outer surface. Heat loss is intended to be reduced by $80\%$ by insulating the wall externally with polyurethane foam. a$)$ Heat loss from uninsulated walls, b$)$ The thickness of the insulation, c$)$ Calculate the temperature of the surface facing the outside in both cases.

Bir duvar i$$te $1,5$ cm ka$$nl$$kta al$$ s$$va$,$ ortada $20$ cm kal$$nl$$kta kaba yap$$ tu$$las$$ve d$$ta $2,5$ cm kalnlkta kire$$li har$$ katmandan in$$a edilmi$$tir$.$ i$$ ve d$$ ortam scakl$$klar$$ sras ile $22\backslash$deg C ve $5\backslash$deg C'dir. Is$$ ta$$n$$m katsays$$ i$$ y$$zeyde $10$ W$/$m$^2$K$,$ d$$ y$$zeyde $20$ W$/$m$^2$K'dir. Duvar d$$tan poli$$retan k$$p$$k ile yal$$t$$larak $$s$$ kayb$\%80$ orannda azaltlmak istenmektedir.

a$)$ Yal$$t$$ms$$z duvardan $$s$$ kayb$$n$,$

b$)$ Yal$$t$$m kal$$nl$$n$$

c$)$ Her iki durumda d$$ ortama bakan y$$zeyin scakl$$n$$ hesaplay$$n$$z$.$