Question

12.1) A home is heated with an air-to-air heat pump. The manufacturer reports a COP of 3.1 for the heat pump. If the home is losing 25,600 Btu/hr, and electricity costs $0.085 per kWhr, what is the daily cost of heating this home?

12.2) Assume the homeowner from problem 15.1 investigates upgrading the home heating system to a geothermal system with a COP of 4.3. What is the new hourly cost of operation?

Answer 1

$\beta$ = COP = 3.1

rate of losing heat , P = 25600 Btu/hr = 7502.6 watt

t = time = 24 x 3600 = 86400 sec

Energy lost daily = Q₂ = 7502.6 x 86400 = 6.5 x 10⁸ J

using the formula

$\beta$ = Q₂/(Q₁ - Q₂)

3.1 = (6.5 x 10⁸ ) / (Q₁ - 6.5 x 10⁸)

Q₁ = 8.6 x 10⁸ J

Q₁ = 8.6 x 10⁸ J (1 kWh / 3.6 x 10⁶)

Q₁ = 238.88 kWh

daily cost = 0.085 x 238.88 = $20.298