What is the cost to heat the garage for 6 hours at these temperatures if the cost of electricity is $0.14/kWh?

Question

On a cold winter day, the outside temperature is -5.0 degrees C while the interior of a well-insulated garage is maintained at 20.0 degrees C by an electric heater. Assume the walls have a total area of 75 m^2, a thickness of 0.15 m, and a thermal conductivity of 0.042 W (m x C degrees).

Note:1 kWh=3.6 x 10^6 J.

Answer 1

Solve for Q, that's the total heat energy your electric heater must put out to replace the Q that's lost over six hours. Heat loss will be Q = kAt delT/H; where k = .042 thermal conductivity (W/m-deg), H = .15 m, A = 75 m^2, and delT = 20 - (-5) = 25 deg C. t = 6 hrs the time interval that delT must remain at 25 deg. (As delT = delC = delK, there is no need to convert to Kelvin for this.)

Thus, q = Q/hr = .042*75*25*1/.15 = Watts of energy needing replacement in an hour. So we have C = total cost = c*q*t/1000; where c = $.14/kWh the hourly cost of a kilo Watt of power and t = 6 hours. The 1/1000 factor converts Watts to kiloWatts, which is the unit costs are calculated by.

You can do the math. But watch the units, your hourly cost is per kW, while the q answer is in W; so you need to convert Watts to kiloWatts when doing the total cost C.