PHYSICAL CHEMISTRY OF MILK

Module 3. Density

Lesson 6
DENSITY

6.1 Introduction

Density is one the important physical property of a matter. Density has a direct relationship with weight and volume of a substance. The knowledge about density is helpful in understanding the behavior of substance when placed in a different environment. The density of milk and milk products is used to convert volume into mass and vice versa, to estimate the solids content of milk and to calculate other physical properties (e.g. kinematic viscosity). The relationship of this property with the temperature will also be helpful in developing various processing techniques of milk products.

6.2 Definition

6.2.1 Density

Density is defined as the mass of a certain quantity of material divided by its volume. It is expressed in kg.m^-3 (SI units) or g.ml^-1. The symbol ρ used to express density. Since density closely depends on temperature it is usually denoted with temperature ρ ²⁰ meaning the density at 20^°C .

6.2.2 Specific gravity

The mass or weight of a certain volume of the product divided by the mass of an equal volume of water is known as specific gravity. Thus specific gravity (s.g) of a product can be obtained by using the formula.

s.g = ρ_{product /} ρ_water

The density of substance varies with temperature and pressure so it is necessary to specify the temperatures and pressures at which the densities or weights are determined. Usually the density measurement is made nominally at 1 atmosphere (1013.25 millibars /hectopascal )pressure. As the substances for which density is measured are incompressible liquids, the effect of atmospheric pressure on this property is negligible. As such the variations caused by changes in pressure are neglected. For true (in vacuo) specific gravity calculations, air pressure must be considered. Temperatures are specified by the notation T_s/ T_r with T_s representing the temperature at which the sample's density was determined and T_r the temperature at which the reference (water) density is specified. For example, s.g (20°C/4^°C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4^°C.

Relative density or specific gravity: It is customary to represent specific gravity or relative density of any liquid as below:

Where the superscript indicates temperature at which the density of the material is measured, and the subscript indicates temperature of the reference substance to which it is compared. There is appreciable variation in specific gravity with the change in temperature of both the fluids. As such it is necessary to know both the temperatures to get more reliable information.

6.3 Difference Between the Density and Specific Gravity

• Specific gravity i.e. relative density is a dimensionless quantity. It is mostly useful as a comparison but not in absolute units. Whereas density can measured in specific units.
• Specific gravity does not provide the actual difference in the mass of two substances since it is only on relative basis. It tends to be rather vague while the density will help in giving the exact mass of the product per unit volume.
• Specific gravity is more suitable for only liquids while density is for both solids and liquids.
• Measuring the specific gravity is simple and more convenient, less laborious and does not require any sophisticated equipment and quick results can be obtained, while the density needs specific equipment like pycnometer, sensitive balance and other materials.
• Specific gravity can be measured by people with minimum skill but density measurement requires specially trained individual for this purpose.
• In a given time, a large number of samples could be tested for specific gravity whereas only limited samples for density could be determined.
• Determination of specific gravity is more economical in comparison to the density determination

6.4 Methods for the Determination of the Density and Specific Gravity of Milk

A very common instrument for direct measurement of density of a liquid is the hydrometer, which measures the volume displaced by an object of known mass. A common laboratory device for measuring fluid density is a pycnometer; a related device for measuring the absolute density of a solid is a glass pycnometer. Another instrument used to determine the density of a liquid or a gas is the digital density meter - based on the oscillating U-tube principle.

6.4.1 Hydrometer

Hydrometer is an instrument used to measure the specific gravity (or relative density) of liquids; that is, the ratio of the density of the liquid compared to the density of water. The operation of the hydrometer is based on the Archimedes principle that a solid suspended in a fluid will be buoyed up by a force equal to the weight of the fluid displaced. Thus, the lower the density of the substance, deeper the hydrometer will sink.

A hydrometer is usually made of glass and consists of a cylindrical stem and a bulb filled with mercury or lead shot to make it float upright. The liquid to be tested is poured into a tall jar or measuring cylinder and the hydrometer is gently inserted / lowered into the liquid until it floats freely. The point at which the surface of the liquid touches the stem of the hydrometer is noted. Hydrometers usually contain a paper scale inside the stem, so that the specific gravity can be read directly. The scales may be Plato, Oechsle, or Brix, depending on the purpose.

Hydrometers may be calibrated for different uses, such as a lactometer for measuring the density (creaminess) of milk, a saccharometer for measuring the density of sugar in a liquid, or an alcohol meter for measuring higher levels of alcohol in spirits

6.4.2 Lactometer

A lactometer (or galactometer) is a hydrometer used to test relative density of milk. The specific gravity of milk does not give a conclusive indication of its composition since milk contains a variety of substances that are either heavier or lighter than standard substance i.e. water. Additional tests for fat content are necessary to determine overall composition of milk. Another instrument, invented by Doeffel, is two inches long, divided into 40 parts, with division beginning at the point to which it sinks when placed in water. (Fig. 6.1)

6.4.3 Pycnometer

A pycnometer (from Greek: πυκνός (puknos) meaning "dense"). A pycnometer is usually made of glass, with a close-fitting ground glass stopper with a capillary tube through it, for facilitating the escape of air bubbles from the apparatus. This device enables accurate measurement of a liquid's density in reference to an appropriate working fluid, such as water or mercury, using an analytical balance.(

The specific gravity of the liquid can easily be calculated if the weight of empty flask, flask with full of water, and flask with full of an experimental liquid are known. The particle density of a powder, for which the usual method of weighing cannot be applied, can also be determined with a pycnometer. The powder is added to the pycnometer and is then weighed, to get weight of the powder sample. The pycnometer is then filled with a liquid of known density, in which the powder is completely insoluble. The weight of the displaced liquid can then be determined, and hence the specific gravity of the powder.

6.4.4 Westphal balance

This balance is used to measure the specific gravity (or density) of liquids. This is usually supplied in its box, along with the characteristic U-shaped balancing masses and the plummet in the upper right-hand corner. The sliding top of the box has the decorative molding attached to it.

The arm is first balanced with the plummet totally immersed in water at 15.5^°C. The plummet has a built-in thermometer and has a known volume (equal to 5 gms of water at 15.5^°C) and mass (15g). A 5g mass is placed on the hook holding the plummet, and screw on the foot is adjusted until the index pointer on the end of the beam lines up with the point on the frame. The plummet is then completely immersed in the unknown liquid, and the system is rebalanced, using a series of riders on the nine equally paced notches on the beam, thus giving the value of the added mass for each decimal place. This gives the buoyant force of the liquid relative to water, and hence the specific gravity, which may be obtained to four decimal places.