Is a 9000 BTU heat pump roughly equivalent in cooling ability to a 9000 BTU window air conditioning unit?
If not, what is an approximate way to "translate" between the two, in order to obtain a heat pump with cooling ability equal to an X BTU window air conditioner?
9000 BTU/Hr is 9000 BTU/Hr - exactly the same, assuming you are looking at the heat pump's cooling capacity, which is often slightly different from its heating capacity.
The heat pump might be slightly more effective as it won't have the partly open window, but that's a minor effect.
