Farnsworth House Heat Loss
Example in-class problem

Q in BTU per hr measures how much heat is transferred from warm interior of building to cold outdoors. This is exactly the amount of Q that the buildings heating system must supply.

In lieu of open doors, windows, most heat is transferred by:

Q_c = conduction

Q_r = radiation

Q_c = direct transmission of heat through walls and ceiling from inside to outside (imagine gluing an electric blanket to one side of a partition – after a while the other side will become warm as the blankets heat is transmitted through the wall).

Q_r = net radiation in infrared part of electromagnetic spectrum from the exterior wall and roof surfaces to the sky. Note that every object (living or not) above temp of absolute zero radiate electromagnetic energy. Terrestrial objects radiate in the infrared part of the spectrum.

Q_c = A_roof * (T_outside - T_inside) / R_roof + A_roof * (T_outside - T_inside) / R_roof

Q_R = Sigma * (T_sky⁴ - T_outside⁴) * (E_facade*A_facade + E_roof*A_roof)

Q_total = Q_C + Q_R

Consider conditions during a Fall night:
T_outside = 40 ^oF,
T_inside = 72 ^oF

How much heat, Q, is being lost to the outside?
Compare answers to space heaters and air conditioners (typical space heaters and AC units provide 2,000 – 12,000 BTU / hr of heating or cooling).

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