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8.2 Density  (Page 4/3)

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  • Define density.
  • Calculate the mass of a reservoir from its density.
  • Compare and contrast the densities of various substances.

Which weighs more, a ton of feathers or a ton of bricks? This old riddle plays with the distinction between mass and density. A ton is a ton, of course; but bricks have much greater density than feathers, and so we are tempted to think of them as heavier. (See [link] .)

Density , as you will see, is an important characteristic of substances. It is crucial, for example, in determining whether an object sinks or floats in a fluid. Density is the mass per unit volume of a substance or object. In equation form, density is defined as

ρ = m V , size 12{ρ= { {m} over {V} } } {}

where the Greek letter ρ size 12{ρ} {} (rho) is the symbol for density, m size 12{m} {} is the mass, and V size 12{V} {} is the volume occupied by the substance.

Density

Density is mass per unit volume.

ρ = m V , size 12{ρ= { {m} over {V} } } {}

where ρ size 12{ρ} {} is the symbol for density, m size 12{m} {} is the mass, and V size 12{V} {} is the volume occupied by the substance.

In the riddle regarding the feathers and bricks, the masses are the same, but the volume occupied by the feathers is much greater, since their density is much lower. The SI unit of density is kg/m 3 size 12{"kg/m" rSup { size 8{3} } } {} , representative values are given in [link] . The metric system was originally devised so that water would have a density of 1 g/cm 3 size 12{1`"g/cm" rSup { size 8{3} } } {} , equivalent to 10 3 kg/m 3 size 12{"10" rSup { size 8{3} } `"kg/m" rSup { size 8{3} } } {} . Thus the basic mass unit, the kilogram, was first devised to be the mass of 1000 mL of water, which has a volume of 1000 cm 3 .

Densities of various substances
Substance ρ ( 10 3 kg/m 3 or g/mL ) size 12{ρ` \( "10" rSup { size 8{3} } `"kg/m" rSup { size 8{3} } `"or"`"g/mL" \) } {} Substance ρ ( 10 3 kg/m 3 or g/mL ) size 12{ρ` \( "10" rSup { size 8{3} } `"kg/m" rSup { size 8{3} } `"or"`"g/mL" \) } {} Substance ρ ( 10 3 kg/m 3 or g/mL ) size 12{ρ` \( "10" rSup { size 8{3} } `"kg/m" rSup { size 8{3} } `"or"`"g/mL" \) } {}
Solids Liquids Gases
Aluminum 2.7 Water (4ºC) 1.000 Air 1 . 29 × 10 − 3 size 12{1 "." "29" times "10" rSup { size 8{ - 3} } } {}
Brass 8.44 Blood 1.05 Carbon dioxide 1 . 98 × 10 − 3 size 12{1 "." "98" times "10" rSup { size 8{ - 3} } } {}
Copper (average) 8.8 Sea water 1.025 Carbon monoxide 1 . 25 × 10 − 3 size 12{1 "." "25" times "10" rSup { size 8{ - 3} } } {}
Gold 19.32 Mercury 13.6 Hydrogen 0 . 090 × 10 − 3 size 12{0 "." "090" times "10" rSup { size 8{ - 3} } } {}
Iron or steel 7.8 Ethyl alcohol 0.79 Helium 0 . 18 × 10 − 3 size 12{0 "." "18" times "10" rSup { size 8{ - 3} } } {}
Lead 11.3 Petrol 0.68 Methane 0 . 72 × 10 − 3 size 12{0 "." "72" times "10" rSup { size 8{ - 3} } } {}
Polystyrene 0.10 Glycerin 1.26 Nitrogen 1 . 25 × 10 − 3 size 12{1 "." "25" times "10" rSup { size 8{ - 3} } } {}
Tungsten 19.30 Olive oil 0.92 Nitrous oxide 1 . 98 × 10 − 3 size 12{1 "." "98" times "10" rSup { size 8{ - 3} } } {}
Uranium 18.70 Oxygen 1 . 43 × 10 − 3 size 12{1 "." "43" times "10" rSup { size 8{ - 3} } } {}
Concrete 2.30–3.0 Steam 100º C size 12{ left ("100""°C" right )} {} 0 . 60 × 10 − 3 size 12{0 "." "60" times "10" rSup { size 8{ - 3} } } {}
Cork 0.24
Glass, common (average) 2.6
Granite 2.7
Earth’s crust 3.3
Wood 0.3–0.9
Ice (0°C) 0.917
Bone 1.7–2.0
A pile of feathers measuring a ton and a ton of bricks are placed on either side of a plank that is balanced on a small support.
A ton of feathers and a ton of bricks have the same mass, but the feathers make a much bigger pile because they have a much lower density.

As you can see by examining [link] , the density of an object may help identify its composition. The density of gold, for example, is about 2.5 times the density of iron, which is about 2.5 times the density of aluminum. Density also reveals something about the phase of the matter and its substructure. Notice that the densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. The densities of gases are much less than those of liquids and solids, because the atoms in gases are separated by large amounts of empty space.

Take-home experiment sugar and salt

A pile of sugar and a pile of salt look pretty similar, but which weighs more? If the volumes of both piles are the same, any difference in mass is due to their different densities (including the air space between crystals). Which do you think has the greater density? What values did you find? What method did you use to determine these values?
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Source:  OpenStax, Physics of the world around us. OpenStax CNX. May 21, 2015 Download for free at http://legacy.cnx.org/content/col11797/1.1
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