A Bathtub of Water

• Bathtub holds 9 cubic feet, 0.25 cubic meters, 250 kilograms

• person displaces 50 kg? -> 200 kg of heated water

• Inlet water 10C, tub water 40C

• 30C * 2e5 g * 4.184 J/calorie -> 25 MJ

• Gas is $1 per therm, or $1 per 63 MJ at 60% heating efficiency

• $0.40 per full bathtub, $160/year for a bath every night

Electric Resistance

• $0.12 per 3.6 MJ, 90% efficiency -> $1 per 27 MJ

• $0.93 per full bathtub, $340/year for a bath every night

Electric Heat Pump

• $0.12 per 3.6 MJ, 240% efficiency -> $1 per 72 MJ

• $0.35 per full bathtub, $130/year for a bath every night

• est $2000 purchase and install plus one service call -> 67 year payback

• If electric rates rise because of government renewable requirements, no savings at all over gas

Since renewables are not time-dispatchable, much of the "electric" power will be gas anyway, and generation efficiency is much less than heating efficiency. The environmental cost of actual renewables is similar to the direct use of gas.