Pool Heater Sizing and Heat-Up Time
Heat-up energy Btu = gallons x 8.34 x rise, and time = energy/(output x efficiency). A 20,000 gal pool +10 F takes 5.2 h on a 400,000 Btu/h gas heater at 80%, but 11.1 h on a 150,000 Btu/h heat pump. Ignores cover/standby losses. The equipment ratings govern.
Formula and source
Q_btu = gallons x 8.34 x dT; delivered = output x eff; hours = Q_btu / delivered.
The sensible water-heating relation (1 Btu raises 1 lb of water 1 F), by name.
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