Density is a physical property that is defined as a substance’s mass divided by its volume:
density = mass/volume or d = m/V
You are viewing: Why Is Density A Derived Unit
Density is usually a measured property of a substance, so its numerical value affects the significant figures in a calculation. Notice that density is defined in terms of two dissimilar units, mass and volume. That means that density overall has derived units, just like velocity. Common units for density include g/mL, g/cm3, g/L, kg/L, and even kg/m3. Densities for some common substances are listed in Table 1 “Densities of Some Common Substances”.
Because of how it is defined, density can act as a conversion factor for switching between units of mass and volume. For example, suppose you have a sample of aluminum that has a volume of 7.88 cm3. How can you determine what mass of aluminum you have without measuring it? You can use the volume to calculate it. If you multiply the given volume by the known density (from Table 1 “Densities of Some Common Substances”), the volume units will cancel and leave you with mass units, telling you the mass of the sample:
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7.88 cm3 × 2.7 g/cm3 = 21 g of aluminum
where we have limited our answer to two significant figures.
Density can also be used as a conversion factor to convert mass to volume—but care must be taken. We have already demonstrated that the number that goes with density normally goes in the numerator when density is written as a fraction. Take the density of gold, for example:
Although this was not previously pointed out, it can be assumed that there is a 1 in the denominator:
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That is, the density value tells us that we have 19.3 grams for every 1 milliliter of volume, and the 1 is an exact number. When we want to use density to convert from mass to volume, the numerator and denominator of density need to be switched—that is, we must take the reciprocal of the density. In so doing, we move not only the units but also the numbers:
This reciprocal density is still a useful conversion factor, but now the mass unit will cancel and the volume unit will be introduced. Thus, if we want to know the volume of 45.9 g of gold, we would set up the conversion as follows:
Note how the mass units cancel, leaving the volume unit, which is what we’re looking for.
Care must be used with density as a conversion factor. Make sure the mass units are the same, or the volume units are the same, before using density to convert to a different unit. Often, the unit of the given quantity must be first converted to the appropriate unit before applying density as a conversion factor.
Key Concepts and Summary
Density relates a substance’s mass and volume. Density can be used to calculate volume from a given mass or mass from a given volume.
Source: https://t-tees.com
Category: WHY
