Density is a fundamental physical property of matter, defined as the amount of mass contained within a given volume. The central question is whether this property changes with the size of an object. Understanding density involves examining its relationship with mass and volume to determine if it depends on an object’s overall dimensions.
Density as an Intrinsic Property
Density is an intrinsic, or intensive, property of a substance. This means its value does not change regardless of the amount or size of the material. For example, a small piece of pure gold has the same density as a large gold bar, assuming identical temperature and pressure conditions.
In contrast, properties like mass and volume are extrinsic, or extensive, meaning they depend on the quantity of matter. A larger sample will have greater mass and occupy more volume. However, when these two extensive properties are combined in the specific ratio that defines density, the result becomes an intrinsic property, independent of the sample’s size.
The Proportional Relationship of Mass and Volume
Density remains constant regardless of an object’s size due to the proportional relationship between its mass and volume for a given substance. As the volume of a material increases, its mass increases by the same proportion. This consistent ratio ensures that the density value, calculated as mass divided by volume (ρ = m/V), stays the same.
If a block of wood is cut in half, both the mass and the volume of each half are reduced by half. Yet, the ratio of mass to volume for each smaller piece remains identical to that of the original block. This demonstrates that while the individual quantities of mass and volume change with the size of the sample, their relationship, which defines density, does not. This principle applies to any homogeneous material, illustrating why density is a characteristic of the substance itself rather than the specific sample.
Density in Everyday Examples
Practical examples illustrate density’s independence from size. A small pebble of granite, for instance, possesses the same density as a massive granite boulder, typically ranging between 2.63 and 2.75 grams per cubic centimeter (g/cm³). The total mass and volume of the pebble are vastly different from the boulder, but the inherent compactness of the granite material remains constant.
Similarly, a single drop of pure water has a density of approximately 1.0 g/cm³ at 4°C, which is the same as that of a vast ocean, assuming similar temperature and pressure conditions. While deep ocean water can be slightly denser due to immense pressure, this effect is minor compared to changes caused by temperature and salinity. What changes with the amount of substance is the total mass and total volume, not the fundamental density of the material itself.