A house has a rectangular base and a roof that peaks along a line above the center of the house and parallel to the length of the house. This roof slopes downward from the peak to each edge at an angle of $37\mathrm{.}0\backslash$deg with the horizontal. The length of the front of the house is $10\mathrm{.}0$ ?meters. The width of the house is $8\mathrm{.}00$ ?meters. The height from the front of the house up to the edge of the roof is $5\mathrm{.}00$ ?meters.

The average thermal conductivity of the walls $($including the windows$)$ ?and roof of the house depicted in the figure is $0\mathrm{.}480$ ?W$/($m $·\backslash$deg C$),$ ?and their average thickness is $21\mathrm{.}0$ ?cm$.$ ?The heat of combustion $($that is$,$ ?the energy provided per cubic meter$)$ ?of natural gas is $3\mathrm{.}89?10\mathrm{⁷}$ ?J$/$m$3.$

$($a$)$

How many cubic meters of gas must be burned each day to maintain an inside temperature of $25\mathrm{.}0\backslash$deg C in this house if the outside temperature is $0\mathrm{.}0\backslash$deg C$?$ ?Disregard radiation and the energy transferred by heat through the ground.

?m$3$

$($b$)$

How will the answer to part $($a$)$ ?be affected $($increase or decrease the gas requirements$)$ ?by the inclusion of thermal conduction through the floor; radiation incident on the roof, walls and windows during the daytime; operation of appliances, computers, entertainment systems; and leakage of air through cracks around doors and windows.

$($i$)$

thermal conduction through the floor

increase

decrease

$($ii$)$

radiation incident on the roof, walls and windows during the daytime

increase

decrease

$($iii$)$

operation of appliances, computers, entertainment systems

increase

decrease

$($iv$)$

leakage of air through cracks around doors and windows

increase

decrease

Your team has been hired by a major builder who is designing simple homes for a new ho winter months. The figure shows the house you are currently working on. 37.0 5.00 m 8.00 m 10.0 m