In winter, a house loses heat at a rate of lambda (T - T0) where T is the temperature inside the house. T0 the temperature outside, and lambda a positive constant, (a ) Suppose we want to keep the temperature inside constant by hooking up an ideal heat pump (a refrigerator) that transfers heat from the outside to the inside. If the power of the ideal heat pump is W, show that the steady state temperature is T = T0 + (1 + W/2 lambda. (b) If we just use a space heater which simply converts all input power to heat, what is the steady state temperature? (c) Discuss your answers. Which is more efficient, at keeping the house warm?
