COULD YOU FURTHER EXPLAIN HOW MANY BTU ARE REQUIRED TO RAISE THE TEMP OF500 GALLONS OF WATER FROM 70 DEGRESS TO 160 DEGREES FAHRENHIET

Answer 1

As Bob Pursley said

In general:
heat=mass*specificeheat*changetemp
or
heat in = mass of water * specific heat of water * (Final temp -original temp)

In these strange English units
weight in pounds is used for mass

weight = 500 gal * 8.31 pounds/gal = 4155 pounds

specific heat of water in these units = 1 BTU/pound

change in temp = 160 - 70 = 90 degrees F

so

BTU = 4155 * 1 * 90
= 373,950 BTU

Answer 2

There is no change of state in this problem. If you were changing water to vapor that would require an extra 970 btu/lb or 4,030,350 on top of the 373,950 grid.