$3.$ Two roommates head outside to take a break from working on their thermo homework and close the door of their dorm room $(\backslash (11^\{\backslash$prime$\}\backslash$mathrm$\{$x$\}15^\{\backslash$prime$\}\backslash )$ with a ceiling height of $\backslash (9^\{\backslash$prime$\}\backslash )).$ The air in the room is initially at $\backslash (70^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ and $14\mathrm{.}7$ psi $.$ They leave a fan running and return $2$ hours later $($they are devoted students, after all$)$ to find that the room temperature has increased to $\backslash (80^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ).$ Assume that the room is well sealed when the door is closed. Assume the air can be treated as an ideal gas, but do not assume constant specific heats.

a$.$ If the fan and other appliances in the room draw electricity at a rate of $300$ W $,$ determine the rate of heat transfer from the room, in Btu$/$hr$.$

b$.$ Determine the final air pressure in the room, in psia.