If hydrogen is widely available, surely someone will want to do this..
This is what the flame looks like:
(Efficiency isn't in the Carnot sense, and heat pumps move heat rather than generating heat... Semantics, but point stands.)
For example: I recall reading that it is more efficient (ie BTUs generated) to use natural gas peaker plants generating electricity to drive a heat pump than to run a furnace. (Except at very low temps where COP drops quickly.)
It’s more efficient to burn the gas in a grid power station, convert to electricity, and use the electricity to drive the heat pump, then it is to burn the gas for heat directly.
Another consideration is that you lose efficiency in converting chemical to electrical energy, plus there is a higher transport and distribution loss to factor in.
https://www.panasonicproclub.com/uploads/IE/catalogues/PIR%2...
Show a 4.5 cop for a 7C-35C range, dropping to 1.8 for a -7 to 55C range.
For 2C to 35C it’s still a cop over 3