I am an electrical engineer that took two semesters of Thermodynamics about 4 decades ago. I am aware of the theory behind the Carnot cycle and such.
I live in a condo in the Boston area that is all-electric (except for a fireplace I am not using and has its flue closed up). Recently, I replaced the windowbox A/C with a windowbox A/C and heat pump. I have been using the heat pump solely to heat the apartment while the outside temps have been above 40 F.
The other heat is simple resistance heating, which I will call "100% efficient" even though the electricity was generated at a plant somewhere with a heat engine of far less efficiency. I look at the heat pump as being a way to recover some of the heat lost in that inefficiency because, theoretically, it is better than 100% efficient because the heat coming out of it is the sum of the electric power running it plus whatever energy taken from the outside air. I also know that this efficiency decreases as the outside temperature falls.
But now as winter is starting to close in, outside temps will become consistently below freezing. At what point is it not worth it to run the windowbox heat pump? Just asking if some HVAC sorta people know a rule of thumb regarding this.