Question #$4$

$[10$ points$]$

Three $2^{nd}$ year engineering students at Ontario Tech are living in a rented home on Dalhousie Crescent, and the cold winds herald the coming of final exams season. The three roommate engineers split utilities and want to find the best solution to heat the house while saving money. The house is to be maintained at $22C$ for comfort, while the outdoor air temperature is $5C.$ The house is estimated to be losing heat at a rate of $6,624k\frac{J}{h}r,$ and so the heater used must be capable of providing at least this much heat. The students are in a disagreement about how to best heat the home.

Michael proposes that the house should be heated through electric resistance heaters, which boast a $100\%$ thermal efficiency due to their complete conversion of electricity to heat. $($Assume the cost of electricity is a steady $11$ cents$/$kWh$)$

Jess says that an air$-$source heat pump could be used, since it will have a COP that allows it to move more energy than you provide it with. $($Assume the cost of electricity is a steady $11$ cents$/$kWh$)$

Dadrian suggests that instead of heating the home with expensive electricity, a highefficiency condensing natural gas furnace could be used. These furnaces are $95\%$ efficient, and are fueled by affordable natural gas $($Assume a higher heating value of $40\mathrm{.}6M\frac{J}{m^3}$ and a cost of $40\mathrm{.}5$ cents $\frac{?}{m^3})$

To help the students chose a heating solution for this house, you must:

a$)(2)$ Determine the electrical energy requirement for Michael's electric heaters and gas requirement for Dadrian's high$-$efficiency natural gas furnace.

b$)(3)$ Determine the COP, $Q_H,Q_L,$ and $W_{in}$ for Jess' air$-$source heat pump

c$)(3)$ Find the operating costs associated with these three options, and discuss the feasibility of the options. Evaluate the three heating options for their total cost in the month of December.

d$)(2)$ Imagine you are the project manager who will make the ultimate decision. Briefly describe how you will go about making that decision.