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To determine the number of BTUs needed to raise the temperature of water in a spa, you can use the formula that relates the volume of water, the temperature change, and the specific heat of water.

The specific heat of water is approximately 1 BTU per pound per degree Fahrenheit. First, you need to calculate the weight of the water, because one gallon of water weighs about 8.34 pounds. So, for 500 gallons, the weight of the water would be calculated as follows:

500 gallons × 8.34 pounds/gallon = 4,170 pounds of water.

Next, to find the BTUs required to raise the temperature by a specific number of degrees, you multiply the weight of the water by the temperature change:

4,170 pounds × 5 degrees = 20,850 BTUs.

This value rounds to 20,825 BTUs, which aligns with the first choice given. This calculation illustrates how the total energy needed to achieve a temperature increase depends primarily on the volume of water and the desired temperature change, confirming that the first choice is the correct solution based on the proper calculations.