Converting Ounces to Ounces

Date: 06/03/2002 at 03:36:35
From: Jessica 
Subject: weight of mass and liquid?

I know this should be easy to figure out, but my roommate and I are 
having a small debate on weight.  I am a cocktail waitress here in 
Vegas and was trying to figure out the total weight of my tray if,
say, a mug of beer weighs 25oz.  

I figured an ounce is an ounce like when they say "what weighs more, a
ton of bricks or a ton of feathers? - neither, a ton is a ton." 

However my roommate started to convince me that liquid is weighed
differently, which I understand, but how is it converted?  I'm sorry
the question is so elementary, I have taken science and math classes,
but never did grasp any of it.

Date: 06/03/2002 at 09:14:26
From: Doctor Rick
Subject: Re: weight of mass and liquid?

Hi, Jessica.

I think the source of confusion here is that there are two different 
units called an "ounce". (Actually, there are more than that, but two 
are in common use today.) There is the ounce of weight, technically 
called the avoirdupois ounce, and the ounce of volume or capacity, 
called the fluid ounce.

When you say a mug of beer "weighs 25 oz.", you are probably 
referring to the volume of beer, not its weight. I don't have any 
beer around, but a can of soda is labeled "12 fl. oz.", meaning the 
soda in the can has a volume of 12 fluid ounces -- not a weight of 12 
avoirdupois ounces.

To "convert" volume (in fluid ounces) to weight (in avoirdupois 
ounces), we need to know the density of beer -- the weight of a unit 
volume of beer. 

The density of water is close to 1 av. oz. per fl. oz., but not 
quite. A gallon of water weighs 8.34 pounds. There are 128 fl. oz. in 
a gallon and 16 av. oz. in a pound, so

  128 fl. oz. of water weigh 8.34 * 16 av. oz.

and therefore 

  1 fl. oz. of water weighs 8.34 * 16 / 128 av. oz.

                            = 1.0425 av. oz.

Thus 25 fl. oz. of water weigh 25 * 1.0425 av. oz. = 26.0625 av. oz. 
The density of beer will be close to that of water, but we can't say 
exactly what it is. Here is a web site that lists several 
measurements of the density of beers:

  Density of Beer: The Physics Factbook, edited by Glenn Elert 
  http://hypertextbook.com/facts/2000/BlairElefant.shtml

It indicates that the density of beer is something like 5% greater 
than the density of water (1 g/cm). Thus 25 fl. oz. of beer will 
weigh closer to 27.4 av. oz.

Don't forget that this doesn't include the weight of the empty mug!

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/