Assuming a 6K gallon pool. 50K heat pump., 200Kgas heater. Further assume 5dF (degrees F) demand daily (may be high, but just an assumption)
Heat Pump.
6,000 x 8.3 = 50,000 lb of water.
50,000 / 50,000 = 1 hour to raise temp 1dF ( this will be optimistic for a heat pump, heat pump efficiency varies dramatically with the air temperature, only reaching the listed BTU number when the air is quite warm)...but let's roll with it.
1 * 5dF = 5 hours of heating.
Heat pump consumes about 5,000W/hour per 100,000 BTU. So 2,500W per hour for 50K unit.
5 hours, 2,500W, $.18/kWh = ~$2.25/5dF. (You can use your own rate, I just took recent rate in Houston)
Gas heater
200,000 BTU * .8 efficiency =160K BTU
50,000 / 160,000 = .3125 hours to raise 1dF
Gas heater consume 1g/h/100K BTU
Hourly consumption = 2g/h total
.3125 *5dF = 1.5625 hours
1.5625 hours * 2g/H = 3.125g/day
3.125g/day = 4 Therms = 400 cubic feet
Gas is $25/thousand in Houston (average, without delivery $).
.4 x $25 = $10/Day
Heat pump $ may be a bit higher, because efficiency varies.
You can/should re-run with your rates.
Heat pumps are better at maintaining a constant temperature. Gas are better at raising temps rapidly.
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