newtons law of cooling question?

Question

why does it take fewer BTU's of energy to keep a house 65 degrees F than it does to keep the same house at 68 degrees F when the temperature outside is 40 degrees?

Answer 1

The Newton's Law of cooling is empirical and states that the rate of heat exchange between a body at temperature T and the environment at temperature Ta is proportional to the temepature difference, i.e.

dQ/dt = K (T - Ta),

where K depends on the area, shape and conductive properties of the material and has dimensions:

[K] = [Q}/([t] [T]) = W/K

BTU is a measure of heat. The SI unit is joule (J).