If a gas water heater was able to produce 25000 btu/hr, how long would it take to heat 30 gal of water from 70f to 140f

You need the specific heat of water in BTU per gallon deg F

Well the specific heat of water is ONE BTU per POUND deg F
and a gallon is about 8.33 pounds of water
so
C = 8.33 BTU/(gal deg F)
SO WE NEED
btu = 8.33 * 30 * 70 = 17496 btu

17497 BTU = 25000 t
so
t = 0.7 hours
or
42 minutes

To calculate the time it takes to heat 30 gallons of water from 70°F to 140°F using a gas water heater with a heat output of 25000 BTU/hr, we need to consider the specific heat capacity of water and the heat formula. Here's how you can calculate it:

1. Determine the temperature difference:
ΔT = Final temperature - Initial temperature
ΔT = 140°F - 70°F
ΔT = 70°F

2. Convert gallons to pounds:
Water density is approximately 8.34 pounds per gallon.
30 gallons * 8.34 lbs/gal = 250.2 lbs

3. Calculate the heat required:
Heat = Mass of water * Specific heat capacity of water * Temperature difference
The specific heat capacity of water is approximately 1 BTU/lb°F.
Heat = 250.2 lbs * 1 BTU/lb°F * 70°F
Heat = 17,514 BTU

4. Determine the time required:
Time (hrs) = Heat required / Heat output of the water heater
Time = 17,514 BTU / 25000 BTU/hr
Time ≈ 0.70 hours or 42 minutes

So, it would take approximately 42 minutes to heat 30 gallons of water from 70°F to 140°F using a gas water heater with a heat output of 25000 BTU/hr.