Your physics processor failed you. The most efficient form of heat is and always will be heat pumps. They have a coefficient of performance that is positive for depending on the refrigerant gas from 2 to upwards of 8. This means for every kilowatt put into the system two to eight kilowatts of heat are delivered to the hot side heat sink. This is due to the second law of thermodynamics and irreversible phase change. Electric resistance heating can by definition never achieve greater than 1. Gas combustion is a first law process you lose right off the bat the HHV vs LHV of the fuel.Then you lose more across the heat exchanger due to the need to drive a thermal gradient. The end result is gas will NEVER EVER exceed a COP of .9 I don’t have time to undo what your physics prof failed to do right.
Google is your friend first look up heat pump COP and SEER ratings. Then look up Mitsubishi low temp inverter heat pumps that have COP above 2 for all temps above MINUS 5F thus ending the its too cold for heat pumps argument cold. The ground is also never far from 55 degrees anywhere in the Northern hemisphere below the.first line. Ground source heat pumps are the scientifically proven most efficient heat source in the planet.
With modern heat pumps using CO2 as the refrigerant gas you can have a positive COP down to.NEGATIVE 20F
The problem with heat pumps is the initial capital costs are much higher than a furnace but not so much more in climates where cooling via A.C.is needed then the heat pump does double.duty with the option of a high temp precondenser to draw 130+ degree hot water when in cooling mode giving hot water for free to the structure during the.cooling season.
Can’t use a heat pump when there is no power. But I sure as hell can light my gas log fireplace with a match and heat at least 80% of my house.
Oh, and no gas hookup means no gas stove either.... Have fun cooking that soy burger over a candle during a power outage.
We have a 1933 vintage Servel natural gas refrigerator at work. It has no moving parts to wear out, and it works better than any of the latest, greatest refrigerators out there.