Volume vs. Capacity

Date: 05/01/2002 at 18:55:51
From: Lydia Saxton
Subject: Volume vs. Capacity

Can you explain the difference between the terms "volume" and 
"capacity"? Most sources I've researched seem to lean toward reserving 
the use of the term "volume" for solids (measured in cubic units) and 
the term "capacity" for liquids. Is this accurate?  

Also, can you define the distinction between "weight" and "mass"? Many 
texts use these terms interchangeably. I know that weight is a 
function of gravity and mass has to do with atomic structure, which is 
not affected by gravity.  

Thanks for your elucidations!
A Math Coach for the Los Angeles Unified School District.

Date: 05/01/2002 at 23:01:11
From: Doctor Peterson
Subject: Re: Volume vs. Capacity

Hi, Lydia.

I would say that volume refers to the space taken up by an object 
itself, while capacity refers to the amount of a liquid or other 
pourable substance a container can (or does) hold. That more or 
less parallels what you have seen. I have never, however, seen both 
terms used of the same object without clarification; you wouldn't 
talk of the volume of a pitcher, meaning the amount of plastic it is 
made of, without carefully saying so, since it is so common to use 
the two terms interchangeably. My dictionary gives "capacity" as a 
synonymous definition of "volume," though the current edition has 
backed away from that somewhat; here's the online version:

    http://m-w.com/ 

    volume

    3 : the amount of space occupied by a three-dimensional object
    as measured in cubic units (as quarts or liters) : cubic capacity 

    capacity

    2 a : the potential or suitability for holding, storing, or
    accommodating b : the maximum amount or number that can be
    contained or accommodated <a jug with a one-gallon capacity>
    <the auditorium was filled to capacity>

In the dictionary's tables of units, as usual, "capacity" is used as 
the heading for "liquid measure" (gallons, etc.) and "dry measure" 
(bushels, etc.), and "volume" for cubic units. The former are used, 
as I suggested, to measure "pourable" substances, the latter for 
anything (since you can convert gallons to cubic feet to see how much 
space it takes up).

But while I would use the term "capacity" to describe the unit, I 
would not speak of the number of gallons of milk as the "capacity of 
the milk," but as its volume - since, as I said, "volume" refers to 
the amount of a substance itself, and the milk is not a container. So 
really, capacity applies not to the liquids, but to containers. It's 
the "units of capacity" that are used for liquids.

As for mass and weight, this should cover it:

   Mass vs. Weight
   http://mathforum.org/library/drmath/view/56250.html 

   Mass vs. Weight
   http://mathforum.org/library/drmath/view/56320.html 
    
   Mass versus Weight
   http://mathforum.org/library/drmath/view/56334.html 

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