Show me the steps to solve $1.$ The attic of a house is mechanically ventilated with a supply intake fan $($see Figure below$),$ providing a ventilation rate of $24$ cfm $($see Figure below$).$ The attic floor has an area of $\backslash (132\backslash$mathrm$\{$~m$\}^\{2\}\backslash )$ and the roof has a surface area of $\backslash (160\backslash$mathrm$\{$~m$\}^\{2\}\backslash ).$ The external temperature is $\backslash (0^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and external relative humidity is $\backslash (90\backslash \%\backslash ).$ The living area has an air temperature of $\backslash (22^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The house sits on a slab$-$on$-$grade; therefore, it can be assumed that the house envelope air leakages are through the ceiling and through the walls only. The house ceiling is airtight, except for a $3$ mm wide air gap around $($along the perimeter of$)$ the $\backslash (0\mathrm{.}6\backslash$mathrm$\{$~m$\}\backslash$times $0\mathrm{.}6\backslash$mathrm$\{$~m$\}\backslash )$ horizontal ceiling hatch.

The house is designed with exhaust ventilation. A fan exhaust $100$ cfm continuously from the house and maintains a measured house negative pressurize of $4$ Pa with respect to the attic and the exterior. The house has a volume of $\backslash (660\backslash$mathrm$\{$~m$\}^\{3\}\backslash ).$ Neglect the effects of wind and stack effect on your airflow calculations. The ceiling thermal resistance is $\backslash (4\mathrm{.}0\backslash$mathrm$\{$~m$\}^\{2\}\backslash$mathrm$\{$~K$\}/$ W $\backslash )($including films$).$ The roof has a thermal resistance of $\backslash (0\mathrm{.}36\backslash$mathrm$\{$~m$\}^\{2\}\backslash$mathrm$\{$~K$\}/\backslash$mathrm$\{$W$\}\backslash )($including films$).$

a$)$ Calculate the amount of air leakage from the house through the ceiling in $\backslash (\backslash$mathrm$\{$L$\}/\backslash$mathrm$\{$s$\}\backslash )$ : the air flow between the house and the attic around the ceiling hatch $($use the orifice equation with a discharge coefficient of $0\mathrm{.}65).$ Notice the direction of airleakage. Assume the temperature of the attic is $\backslash (5^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ The problem needs to be solved iteratively.

b$)$ Calculate the house air leakage through the walls of the house in $\backslash (\backslash$mathrm$\{$L$\}/\backslash$mathrm$\{$s$\}\backslash )$ : the airflow rate through the wall cracks $($house air mass balance$).$ Notice the direction of air leakage.

c$)$ Calculate the attic air flow rate through the attic exhaust damper in $\backslash (\backslash$mathrm$\{$L$\}/\backslash$mathrm$\{$s$\}\backslash )($attic air mass balance$).$ Notice the direction of air leakage.

d$)$ Calculate the temperature of the attic $($attic heat balance, see equation below$)$: leakage heat transfer through the ceiling $+$ conduction heat transfer through the ceiling $+$ conduction heat transfer through the roof $+$ ventilation heat transfer $+$ exhaust air heat transfer, equal to zero. Make sure you have the signs right!