Density

Density

To understand density better, let us assume that the mass of the flask be 80g. So, the mass of the flask filled with water is 330g and the mass of flask filled with kerosene is 280g. Mass of water only is 250g and kerosene only is 200g. Mass per unit volume of water is 250/250cm³. This is 1g/cm³. Mass per unit volume of kerosene is 200g/250cm³. This is 0.8g/cm³. The result 1g/cm3 and 0.8gcm³ are the densities of water and kerosene respectively. Therefore the density of a substance is the mass per unit volume of a given substance.

The SI unit of density is kilogram per meter cubic (kg/m3) also gram per centimeter cubic (g/cm3). The symbol for density is rho (ρ).

Example 1.7

A silver cylindrical rod has a length of 0.5 m and radius of 0.4 m. Find the density of the rod if its mass is 2640 kg.

Solution:

Mass of the cylinder = 2640 kg

Volume of the cylinder = πr²h = 3.14 × (0.4)² × 0.5 = 0.2512 m3

Density = mass/volume = 2640 kg/0.2512 m3 = 10509 kg m–3

1. Relative Density

We can compare the densities of two substances by finding their masses. But generally density of a substance is compared with the density of water at 4°C because density of water at that temperature is 1g/cm³. Density of any other substance with respect to the density of water at 4°C is called the relative density. Thus relative density of a substance is defined as ratio of density of the substance to density of water at 4°C. Mathematically, relative density (R.D)

Since the volume of the substance is equal to the volume of water,

Thus, the ratio of the mass of a given volume of a substance to the mass of an equal volume of water at 4°C also denotes relative density.

2. Measurement of relative density

Relative density can be measured using Pycnometer (Fig. 1.15) also called density bottle. It consists of ground glass stopper with a fine hole through it. The function of the hole in a stopper is that, when the bottle is filled and the stopper is inserted, the excess liquid rises through the hole and runs down outside the bottle. By this way the bottle will always contain the same volume of whatever the liquid is filled in, provided the temperature remains constant. Thus the density of a given volume of a substance to the density of equal volume of referenced substance is called relative density or specific gravity of the given substance. If the referenced substance is water then the term specific gravity is used.

3. Floating and sinking

Whether an object will sink or float in a liquid is determined by the density of the object compared to the density of the liquid. If the density of a substance is less than the density of the liquid it will float. For example a piece of wood which is less dense than water will float on it. Any substance having more density than water (for example, a stone), will sink into water.

Example

You have a block of a mystery material, 12 cm long, 11 cm wide and 3.5 cm thick. Its mass is 1155 grams. (a) What is its density? (b) Will it float in a tank of water, or sink?

Solution:

(a) Density = Mass/ Volume  = 1155g / [12 cm × 11 cm × 3.5 cm]

= 1155 g / 462 cm³ = 2.5 g cm^–3

(b) The mystery material is denser than the water, so it sinks.

4. Application of principle of flotation

Hydrometer

A direct-reading instrument used for measuring the density or relative density of the liquid is called hydrometer. Hydrometer is based on the principle of flotation, i.e., the weight of the liquid displaced by the immersed portion of the hydrometer is equal to the weight of the hydrometer.

Hydrometer consists of a cylindrical stem having a spherical bulb at its lower end and a narrow tube at is upper end. The lower spherical bulb is partially filled with lead shots or mercury. This helps hydrometer to float or stand vertically in liquids. The narrow tube has markings so that relative density of a liquid can be read directly.

The liquid to be tested is poured into the glass jar. The hydrometer is gently lowered in to the liquid until it floats freely. The reading against the level of liquid touching the tube gives the relative density of the liquid.

Hydrometers may be calibrated for different uses such as lactometers for measuring the density (creaminess) of milk, saccharometer for measuring the density of sugar in a liquid and alcoholometer for measuring higher levels of alcohol in spirits.

Lactometer

One form of hydrometer is a lactometer, an instrument used to check the purity of milk. The lactometer works on the principle of gravity of milk.

The lactometer consists of a long graduated test tube with a cylindrical bulb with the graduation ranging from 15 at the top to 45 at the bottom. The test tube is filled with air. This air chamber causes the instrument to float. The spherical bulb is filled with mercury to cause the lactometer to sink up to the proper level and to float in an upright position in the milk.

Inside the lactometer there may be a thermometer extending from the bulb up into the upper part of the test tube where the scale is located. The correct lactometer reading is obtained only at the temperature of 60°C. A lactometer measures the cream content of milk.

More the cream, lower the lactometer floats in the milk. The average reading of normal milk is 32. The lactometers are used highly at milk processing units and at dairies.

Activity

Take two identical flasks and fill one flask with water to 250 cm3 mark and the other with kerosene to the same 250 cm3 mark. Measure them in a balance. The flask filled with water will be heavier than the one filled with kerosene. Why? The answer is in finding­ the mass per unit volume of ­kerosene and water in respective flasks.