Volume & Density
Volume and density are inextricably linked physical properties that quantify how much space an object occupies and how tightly packed its mass is within that space. In metrology, precise measurement of these quantities is essential for everything from custody transfer of petroleum to formulating complex pharmaceuticals and characterizing new materials.
Volume
Volume is a derived SI unit, defined as length cubed (m³). However, in practical laboratory and industrial settings, the liter (L or dm³) is commonly used. Volume metrology is broadly divided into measuring the volume of solids (often regular geometric shapes) and the volume of fluids (liquids and gases).
The volume of a container intended to hold a specific amount of liquid is often determined gravimetrically. By filling the vessel with a pure liquid of known density (like highly pure water) at a specific temperature and weighing it, the internal volume can be calculated with extreme precision. This requires meticulous temperature control, as the density of water changes significantly with temperature.
Density and Specific Gravity
Density ($\rho$) is defined as mass ($m$) per unit volume ($V$): $\rho = m/V$. The SI unit is kg/m³. Density is a fundamental property of a substance, though it varies with temperature and pressure (especially for gases).
Specific Gravity (or Relative Density) is a dimensionless quantity representing the ratio of the density of a substance to the density of a reference material (typically water at 4°C for liquids and solids, and air for gases).
Note: Because volume expands or contracts with temperature, density is strongly temperature-dependent. High-precision density measurements must always state the reference temperature at which the measurement was taken.
Archimedes' Principle and Hydrostatic Weighing
Perhaps the most famous principle in density measurement is attributed to Archimedes: "Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object."
This principle is the basis for hydrostatic weighing, a highly accurate method for determining the density of solids and liquids.
- Density of a Solid: The solid is weighed in air, then suspended from a balance and completely submerged in a reference liquid of known density (like pure water or a fluorocarbon). The apparent loss of weight is equal to the buoyant force, from which the volume and thus the density of the solid can be calculated.
- Density of a Liquid: A solid sinker of known mass and exactly known volume is weighed in air and then suspended in the liquid under test. The buoyant force acting on the sinker determines the density of the liquid.
Pycnometry
A pycnometer is a vessel of precisely defined volume used to determine the density of liquids, and sometimes solid powders or granules.
- Liquid Pycnometer: A glass flask with a close-fitting ground glass stopper featuring a fine capillary tube. It is filled with the liquid under test, the stopper is inserted, and excess liquid is forced out through the capillary. By weighing the empty pycnometer and then the filled pycnometer, and knowing its exact volume (often calibrated using water), the liquid's density is determined.
- Gas Pycnometer (Helium Pycnometry): Used to measure the true volume (and thus true density) of solid samples, especially porous materials or powders where a liquid might not penetrate all pores or might dissolve the sample. It operates by measuring the pressure change of a known volume of inert gas (usually helium, due to its small atomic size) when it expands into a chamber containing the sample.
Oscillating U-Tube Density Meters
In modern industrial and laboratory settings, the oscillating U-tube meter is the standard for rapid, highly precise liquid density measurement.
The device consists of a hollow, U-shaped glass or metal tube. The liquid sample is introduced into the tube, which is then electronically excited to oscillate at its characteristic resonant frequency. This resonant frequency is directly related to the mass of the tube and its contents. Since the volume of the tube is fixed, the mass of the fluid changes the overall oscillating mass. By accurately measuring the period of oscillation, the density of the liquid can be calculated with exceptional precision (often to 5 or 6 decimal places).