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A quick doodle;

Gas heat can never be more than 100% efficient. Burn 1 btu, get a Btu into your living space. Burn a KWh, get a KWh into your house. (Yes, you can measure gas in KWh). New forced breather systems are in the 95% efficient range. Old chimney vented ones to out at 80%ish)

Even at 17F a new heat pump moves 2.5x. Put a Btu in, move 2.5 Btu into your house. Put a KWh in, move 2.5 into your house.

At 40F heat pumps move 4.5 units of heat for every 1 consumed—a huge reduction in energy use versus burning fuel

Help me out: how efficient is electric generation from gas? A Combined cycle gas plant is c. 50% efficient?

let’s call transmission & Distribution losses at 10%?

so

Burn gas, get .5 BTU of electricity

Transmit it, get .45 BTU delivered

Heat pump it at 17F, get 2.5 x .45 = 1.12 BTUs into your house, a net reduction of 10% (or close to 30% vs the typical 80% efficient home boiler)

then consider that heat pumps can use new solar and Cape Wind andit really is a net energy and cost win