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$1)$ Infiltration and heating$/$cooling loads $(50$ total points$)$

A $2-$story single$-$family detached home with a total floor area of $\backslash (2400\backslash$mathrm$\{$ft$\}^\{2\}\backslash )($i$.$e$.,\backslash (1200\backslash$mathrm$\{$ft$\}\_\{2\}\backslash )$ per floor$)$ and $10-$foot$-$high ceilings located in Chicago, IL$,$ had a blower door test conducted to determine its envelope airtightness. The test revealed an effective envelope leakage area of $\backslash (240\backslash$mathrm$\{$in$\}^\{2\}\backslash ).$ Assume the indoor temperature and RH are tightly controlled and held constant at $\backslash (75^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ and $\backslash (50\backslash \%\backslash$mathrm$\{$RH$\}\backslash )$ throughout the year. Assume that windows and doors are always closed for simplicity. Using hourly data for a typical meteorological year $($TMY$)$ in Chicago $($posted on Blackboard with this assignment$),$ answer the following:

a$.$ Estimate the hourly air exchange rate $($in units of $\backslash (1/\backslash$mathrm$\{$h$\}\backslash ))$ due to infiltration alone $($ignoring open doors$/$windows or any mechanical fans$)$ for every hour of the year using the 'basic' infiltration model in Chapter $16$ of the ASHRAE Handbook of Fundamentals. You can assume Shelter Class $5.$ Provide a graph of air exchange rate versus time for every hour of the year, and report summary statistics including the annual average, standard deviation, and minimum and maximum values. $(25$ pts$)$

b$.$ Estimate the total annual sensible$,$ latent, and total heating and cooling loads due to air infiltration based on your modeled infiltration rates. Hint: first calculate these loads on an hourly basis and then sum them over the year to calculate total anmual loads $($in units of million BTU$).$ You can also use average values for the latent heat of vaporization of water and the specific heat capacity of air; or you can instead use the 'air latent heat factor' approach for latent loads presented in Chapter $17$ of the ASHRAE Handbook of Fundamentals $($either is appropriate$).(25$ pts$)$