Newton’s Law of Cooling.
A building is maintained at temperature TH with a reversible heat pump operating between the building and a colder environment at temperature TC < TH. The heat pump consumes electrical power at a constant rate W. The building also loses heat according to Newton’s law of cooling, that is, at a rate a(TH – TC) where a is constant. Show that the building temperature is maintained at temperature
TH = TC + dW/dt (1/2a) [1 + sqrt( 1 + 4aTC/(dW/dt) )]
The Attempt at a Solution
Puzzled about how to start