Question #7a3a0

1 Answer
May 27, 2015

Density is independent of changes done to the mass or the volume of a substance because it expresses the ratio between mass and volume.

Density is defined as mass per unit of volume, i.e. how much mass of your substance you get per, say, #"cm"^3#.

#rho = "mass"/"volume"#

If you remove some of that mass, you'll also reduce the volume your substance occupies, since the mass you remove has a volume of its own. This means that the density of a substance is independent of changes in mass or volume.

So, let's say you have substance that has a density of #"1 g/cm"^3#, so 1 gram of your substance fits exactly into 1 cube like this one

When you have 2 g of your substance, the total volume it will occupy will of course be 2 cubes. The density will be equal to

#rho = "2 g"/"2 cm"^3 = "1 g/cm"^3#

If add 0.5 g more, the total volume of the substance will be 2 and 1/2 cubes, which means that

#rho = "2.5 g"/"2.5 cm"^3 = "1 g/cm"^3#

And so on.

The same goes for removing mass. If you start with your 1-g cube and remove 0.5 g, you'll be left with a volume of 1/2 cube. That's why density is independent of changes in mass and volume, because you can't change one without changing the other.

Keep in mind, a substance's density is not actually constant, but it can be assumed to be constant for most solids and liquids at normal pressure and temperature variations.