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Oxford study proves heat pumps triumph over fossil fuels in the cold
(www.nationalobserver.com)
This is a most excellent place for technology news and articles.
Most gas furnaces use forced air blowers to distribute the heat. You're not running that on a small battery.
I was thinking about the water heater and radiators, totally forgot forced air blowers - you're right.
Here in Canada it's common to use geothermal heat pumps with floor heating. Even in a power outage the floor will retain their heat for much longer than conventional heating system can.
And if worst comes to worst, it's not hard to run them off a generator, although I've never known anyone who has ever needed to.