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It takes 8.33 BTU to raise the temperature of water 1 degree F.
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U.S.gallon = 8.33 pounds of water. Therefore to raise the temperature by one degree F will require 8.33 BTU. The initial temperature of 50 F is inconsequential.
This is a pretty straightforward calculation. By definition, a BTU is the amount of energy required to raise one pound of water one degree F. But you have one gallon of water, which weighs approximately* 8.34 pounds. So, you'd need 8.34 BTU to increase one gallon of water one degree F. Note how the amount of time was not important. Whether you heat the water slowly or quickly doesn't matter. You will still require 8.34 BTU to raise the temperature of a gallon of water one degree F. * I say approximately because the weight of water varies slightly with its temperature. Water is at its densest at 4 degrees Celsius (39 degrees F). A gallon of water at temperatures above and below that value will weigh less.
114,000 BTU/gallon
A British Thermal Unit (BTU) is the amount of heat energy needed to raise the temperature of one pound of water by one degree F. 1 Gallon of Propane is 91,600 BTU's.
About 115K BTU per gallon.
It takes 8.34 BTU to heat 1 gallon of water 1 degree F. Take 8.34 BTU times number of gallons to determine energy needed to raise pool 1 degree F. Then multiply by how many degrees you need to raise the temperate of the current pool temperature to the desired temperature. Example: 8.34 * 30,000 gal = 250,200 BTU need to raise temperature 1 degree F Next multiple by the number of degrees to warm, say the pool is 55 F. 80F - 55F = 25F. 250,200 BTU * 25 F = 6.255 million BTUs to heat the pool to 80 F. This does not take into account the loss of energy to the surroundings but gives you a starting point to determine the energy needed to heat a mass of water.
0.0923Btu Specific heat of copper is 0.0923 Btu/lb F
btu = the amount of heat needed to raise one pound of water one degree F
114100 Btu
1 gallon of water weighs 8.34 pounds. It takes I BTU to change the temp of 1 pound of water 1 degree F. So for 1 gallon it takes 8.34 BTU. It takes 3412.14 BTU to equal 1 KWH. So 8.34 Btu x (1KWH / 3412.14 BTU) = 0.002444 KWH