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How to Calculate Specific Volume

There are a variety of constants thrown at high school students to calculate in their math and science classes. Many we use almost without a thought in our later years -- we measure our own weight with scales in our bathrooms, for example. We make rough evaluations of density when we're moving by trying to pick up that table we assumed must be light and quickly reassessing that it must be lined with lead. Some of these constants, however, are a little more obscure, and these are often forgotten until our children come asking for help on their physics homework.

Things You'll Need

  • Calculator
  • Sheet of paper
  • Writing utensil
  • Scale, if the mass of the item in question is not given
  • Graduated cylinder, or metric ruler or measuring tape if the volume of the item in question is not given
  • Item to be measured, if you have to make the measurements yourself
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Instructions

  1. Getting the Basic Measurements

    • 1

      Skip this part if you already know the mass and volume of your item. Otherwise, place the item on the scale, and take a reading of its mass. If your scale is in ounces or pounds, you must convert pounds to grams or kilograms in order to get an accurate mass. To convert pounds to kilograms, divide by 2.2 lb/kg. To convert ounces to grams, divide by 28.35 g/oz.

    • 2

      Measure the volume of your item by pouring it into the graduated cylinder, if it is a liquid or a particulate solid. This will give you a reading in milliliters (ml), which is equivalent to a volume in cubic centimeters.

    • 3

      Measure the volume of your item using a ruler or tape measure, if it is a solid. Depending on the shape of the object, you might find it easiest to take height, width and length and simply multiply them all together. If it is a more cylindrical shape, you might be best off taking the circumference (C) and height (h). Divide C by (2 * pi) to determine the radius (r). Then the volume is V = pi * r^2 * h. Similar mathematical manipulations can help you determine the volume of more irregular figures, depending on how accurate you desire the specific volume calculation to be.

    Calculating the Specific Volume

    • 4
      Many watermelons weigh roughly one kilogram.

      Make sure you know the units on all of your measurements. If your final calculation requires your answer to be in SI units, convert your previous measurements into cubic meters and kilograms. To convert cubic centimeters to cubic meters, multiply by 10^-6. To convert grams to kilograms, divide by 1000.

    • 5

      Divide the volume of your object by the mass of your object, keeping a close eye on the units. If you followed the step above, you now have a number with units of cubic meters per kilogram, or m^3/kg. This is the specific volume of your object, in the proper SI unit of specific volume.

    • 6

      Interpret this number in a variety of ways. Most properly, the specific volume represents the amount of space one "unit" of the item's mass takes up. If you used standard SI units, this means your number indicates the number of cubic meters one kilogram of your item would fill.

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