A bottle with a volume of 180 U. S. fluid gallons is filled at the rate of 1.6 g/min. (Water has a density of 1000 kg/m^3, and 1 U.S. fluid gallon = 231 in.^3.) In years, how long does the filling take?
To find out how long it takes to fill the bottle, we need to calculate the total amount of water that needs to be filled in the bottle, and then divide it by the filling rate.
First, let's convert the volume of the bottle from U.S. fluid gallons to cubic inches:
180 U.S. fluid gallons * 231 in^3/U.S. fluid gallon = 41,580 in^3
Since we are given the filling rate in grams per minute, we need to convert the bottle volume from cubic inches to cubic meters:
41,580 in^3 * 1 m^3/61023.7 in^3 = 0.6809 m^3
The density of water is given as 1000 kg/m^3. Therefore, the mass of the water to be filled in the bottle is:
0.6809 m^3 * 1000 kg/m^3 = 680.9 kg
Now, we need to convert the filling rate from grams per minute to kilograms per minute:
1.6 g/min * 1 kg/1000 g = 0.0016 kg/min
Finally, to find the time required to fill the bottle, we divide the mass by the filling rate:
680.9 kg / 0.0016 kg/min = 426,812.5 min
To convert minutes to years, we divide by the number of minutes in a year:
426,812.5 min / (60 min/hour * 24 hours/day * 365 days/year) ≈ 0.815 years
Therefore, it takes approximately 0.815 years to fill the bottle.