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Exact Weight of One Gallon of Water


Date: 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/   
    
Associated Topics:
High School Physics/Chemistry
Middle School Terms/Units of Measurement

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