Assume that WVUs Engineering Sciences Building ESB is always

Assume that WVU\'s Engineering Sciences Building (ESB) is always maintained at 27 degree C, while the outside temperature today is 12 degree C. The building is heated by means of a heat pump of the coefficient of performance (COP) gamma = 3.5, which provides the energy at an average rate of 100 kW. The electricity costs $0.13/kWh. Please find: The actual operating chi cost needed to maintain the ESB during a week (7/24). The minimum theoretical operating cost needed to maintain the ESB during a week. The potential cost to maintain the ESB during a week if the heat is provided by a resistor heater.

Solution

For heat pump COP = Heat supplied / Work input

3.5 = 100 / W

W = 28.57 kW

a)

Electricity cost = 28.57*0.13 = $3.71 / hr

For a week, electricity cost = 3.71*24*7 = $623.28

b)

Max COP = T_high / (T_high - T_low)

= (27+273) / (27-12)

= 20

So, 20 = 100/W

Min W = 100 / 20 = 5 kW

Electricity cost = 5*0.13 = $0.65 / hr

For a week, electricity cost = 0.65*24*7 = $109.20

c)

For 100 kW heat supply, electricity cost = 100*0.13 = $13 /hr

For a week, cost = 13*24*7 = $2184