Exact Weight of One Gallon of WaterDate: 08/15/2001 at 14:50:20 From: Davis Subject: Exact weight of one gallon of water? What is the exact weight of one gallon of water? The best answer I can get is 8.33 or 8.34 - it depends what source I go to. I have looked up this problem on different sites and have used search engines, but the resources available only give me decimals up to hundreds. I'd like to get it as close as I can. I work in the fire service and this information would be very helpful to me. Thanks, Davis Date: 08/15/2001 at 15:46:55 From: Doctor Rick Subject: Re: Exact weight of one gallon of water? Hi, Davis. Your question can be stated: "What is the density of water in pounds per gallon?" The density varies with temperature and pressure, though only slightly. Here is a reference that gives the density of water in grams per milliliter at various temperatures and (I presume) 1 atmosphere pressure: Density / Vapor Pressure of Water (North Carolina State University) http://www.ncsu.edu/chemistry/resource/H2Odensity_vp.html At 70 degrees F (close to 21 degrees C) the density is 0.9979955 g/mL. We can convert this to lb/gal as follows: 0.9979955 g 1000 mL 3.785411784 L 1 lb ----------- * ------- * ------------- * ----------- = 8.328676 lb/gal 1 mL 1 L 1 gal 453.59237 g I got the exact conversion factors from "How many? A Dictionary of Units of Measurement," by Russ Rowlett: http://www.unc.edu/~rowlett/units/ The density of water varies from 0.9991026 g/mL at 15 C to 0.9956502 g/mL at 30 C according to the NCSU site, so the figure I have calculated will vary from 8.337915 to 8.309104 lb.gal over this temperature range. You can see why figures of 8.3 and 8.4 are given: to be more accurate requires knowledge of the temperature. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ Date: 08/15/2001 at 16:00:59 From: Doctor Rob Subject: Re: Exact weight of one gallon of water? Thanks for writing to Ask Dr. Math, Davis! The weight will vary some with the temperature of the water. To begin, we know that by definitions, 1 gallon = 231 in^3*(2.54 cm/in)^4/(1 cm^3/ml), = 3785.411784 ml, exactly. Now it is just a matter of multiplying by the density d in g/ml of water at the temperature you want, and then converting to pounds by dividing by exactly 453.59237 g/lb. Thus the answer to 12 significant figures is 1 gallon of water weighs 8.34540445202*d pounds. Here is a Web site that will allow you to learn the value of d for the temperature: Measurement: Frequently asked questions - Fred Senese http://antoine.frostburg.edu/chem/senese/101/measurement/faq.shtml Select the last question under Density: "How do I find water's density at different temperatures?" Enter the temperature in degrees Celsius and see the density d. Use this and the formula above to get the temperature-adjusted weight in pounds. Since d can only be measured to six significant figures, you should round off your answer to that level of accuracy. I hope this helps. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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