Heat escapes from my house by conduction through the walls and roof. The rate of heat loss, q_loss in kJ/hr, is proportional to the difference between the inside temperature and the outside temperature:
q_loss=k(Tinside - Toutside),
where k = 740 kJ/(°C. hr). The volume of my house is approximately 870 m^3 and the temperature inside is uniform. The "heat capacity" of the house is 3300 kJ/°C. That is, 3300 kJ raises the temperature of my house 1°C.
(A) At what rate must I heat my house (in kJ/hr) to maintain a steady temperature of 20°C (68°F) when the outside temperature is -5°C (23°F)?
(B) The heater in my house can supply heat at a maximum rate of 5.2 x 104 kJ/hr. I wish to keep the temperature in my home at a steady 20°C (68°F). What is the lowest outside temperature in °C that will still allow me to maintain an inside temperature of 20°C?
(C) Air leaks into (and leaks out of my house at a rate of 0.10 m/s. What heating rate (in kJ/hr) do I need to maintain a steady temperature of 20°C inside if the outside temperature is -5°C? You may assume that the volumetric flow rate of 0.10 m/s is referenced to 20°C.