Answer:
That's going to depend on
-- starting temperature of the water
-- finishing temperature of the water
-- efficiency of the method you use to heat the water.
But we'll play the game.
Here are the numbers we're using:
Energy content of typical commercial grade natural gas in the US: 1,000 BTU per ft3
or 100,000 BTU per ccf.
Heat capacity of water: 1 BTU per pound-mass per degree Fahrenheit.
Density of water: 8.34 lb/gallon = 0.52125 lb-mass per cup
From this mash-up, we get
(1 cup) x (0.52125 lbm/cup) x (1 BTU/lbm-degree) / (100,000 BTU/ccf) = 0.0000052125 ccf per degree Fahrenheit
Example: To raise the temperature of 1 cup of water 100 degrees:
0.0000052125 x 100 = 0.052125 cubic foot of natural gas, IF all of the energy
in the natural gas could be transferred to the water.