Relative Density Measurement
The density of a substance can be defined as the mass of a substance per unit volume i.e. Density = Mass of substance/Volume of substance, It is one of the basic physical properties of a substance that can be used along with its other unique properties to characterise it and every substance has a different density Its unit is kg/m3. Relative density on the other hand can be defined as the ratio of the density of a substance to the density of the standard substance. Relative Density is also called Specific Gravity. Given below are some of the substances whose relative densities are mentioned at room temperature.
Usually water at 4 oC (used as a standard for a liquid or solid and the air is used for gas). It is a unitless quantity. Relative density finds its huge application in the petroleum industry where the products obtained are based on the measurements done according to the relative densities of the liquids. In this topic, we will discuss more on the relative density formula, the relative density of solid, etc.
Relative Density Formula
The density of the substances varies with pressure and temperature so it is necessary to specify the pressure and the temperatures at which the densities and the masses are to be determined.
It is said that measurements are done mostly at 1 atmosphere which is 101.325 kPa ignoring the variations caused by changing weather patterns and external affairs. But as we know relative density refers to highly incompressible aqueous solutions so the other incompressible substances like petroleum products that show variations in density caused by pressure are mostly neglected at least where apparent relative density is to be measured.
The formula of relative density or \[R.D = \frac{ \text{Density of Substance}}{ \text{Density of Water}}\]
\[R.D = \frac{(\rho_{substance})}{(\rho_{reference})}\]
Relative density is a dimensionless quantity. If a substance is said to have a relative density less than one then it is less dense compared to a reference substance. If it is greater than 1 then it is denser than the reference substance. If the density which is relative is exactly 1 then the densities are equal. Similarly, the relative density of solid can be calculated as:
\[Relative Density= \frac{ \text{(Loss of weight of solid in the air)}}{( \text{Loss of weight of solid in water)}}\]
In this topic, we have understood what is relative density in physics. Let's understand some of its uses and factors affecting the measurements.
SI Unit of Relative Density
Since relative density is the ratio of two same quantities, therefore there is no SI unit of relative density. Relative density is a dimensionless quantity.
Applications of Relative Density
The major application of relative density is in the petroleum industry where the products obtained are mostly based on the measurements done according to the relative densities of the liquids under process.
Heavy molecular weight hydrocarbons can be converted to low molecular weight hydrocarbons such as gasoline, jet fuel, and diesel based on the chemical processes involving the measurements based on relative densities of compounds.
It is used for determining the density of an unknown substance from the known density of another substance.
It is also used by geologists to find out the mineral content of the rock.
Testing the purity of a substance (Eg: gold)
Solved Examples of Density and Relative Density
Find the density of a block of ice if its mass is 500 kg and volume is 5 metre cube.
Answer: Mass of the block of ice = 500 kg
The volume of the block of ice= 5 metres cube
The density of the block of ice= Mass of the block of ice/ Volume of the block of ice
= 500 kg/ 5 m3
= 100 kg/ m3
Therefore, the density of a block of ice is 100 kg/ m3.
Find the density of a 3500 kg cuboid whose length, breadth and height are 22 metres, 10 metres, and 12 metres respectively.
Answer: Mass of the cuboid= 3500kg
Volume of the cuboid= l x b x h where l is length, b is breadth and h is the height.
= 22 x 10 x 12
= 2640 m3
Density of the cuboid= Mass of the cuboid/ Volume of the cuboid
= 3500 kg / 2640 m3
= 1.326 kg/m3
Therefore, the density of the cuboid is 1.326 kg/ m3
Find the density of natural oil whose specific gravity is 0.65. Express the answer in kg/m3.
Answer: As we know, specific gravity is relative density, therefore,
Relative Density of the oil= 0.65
Density of water= 1000 kg/ m3
Relative Density= Density of natural oil/ density of water
Density of oil= Relative density x density of water
= 0.65 x 1000
= 650 kg/ m3
Therefore, the density of the natural oil is 650 kg/ m3.
Factors Affecting Measurement of Relative Density
Air Bubbles: A small bubble with a diameter of 1 mm can yield a 0.5 mg increase and those with 2 mm can yield a 4 mg increase. So, make sure that the solid object or sinker immersed in the liquid is not adhered to by air bubbles.
Solid Matter Sample: A sample with a very large volume immersed in the fluid will result in an increase in the level of fluid within the pitcher of the glass.
Temperature: Solids are generally not affected by temperature changes so that the corresponding density changes are not relevant. However, according to the Archimedes Principle, while determining the density of a liquid or a solid, its temperature is taken into consideration. The temperature change affects liquids greater and causes changes in the density in the order of 0.1 to 1 per oC.
Measurement of Relative Density
Hydrometer: It is an instrument that is used to determine the relative density or specific gravity. It works on the model of the Archimedes Principle. Archimedes' principle states that any body, which is partially or fully immersed in the water, is acted upon by an upward force called the buoyant force. This force is equal to the weight of the liquid displaced by the object which is immersed in the water. The hydrometer is kept in the hydrometer jar which has the liquid. When the level of the sample liquid in the jar aligns with a point on the hydrometer scale, that tells the relative density of the liquid.
Pycnometer: This device is used to determine the specific gravity of various liquids. The steps to determine the relative density of a liquid requires measurement of the empty flask first. The flask is weighed with the reference liquid and then finally weighed with the testing liquid. These weights are used together to find the relative density. These weights are used to calculate the relative density of the liquid. Pycnometers can also be used for measuring the density of solids and gases also.
FAQs on Relative Density
1. Explain What is the Difference Between Density and Define Relative Density?
The term density is said to be the property of matter which is represented as a ratio of mass to a volume of a substance which is the unit volume of matter and its unit is kg/m3 On the other hand, specific gravity which is also known as relative density definition physics is said to be a measure of density with respect to a density of pure water (reference substance). It is a unitless quantity.
2. Explain How You Convert Relative Density to Density? What Are Some Methods to Calculate RD?
The R.D of a substance can be calculated by dividing the density of a substance by the density of water. If the Relative density of iron is 8.5, The Density of a substance can be calculated by multiplying the Relative Density that is the R.D. of the substance with the Density of water.
Some methods commonly used to determine the relative density of any substance based upon its type are:
Buoyancy methods
Hydrometer (for liquid substances)
Hydrostatic balance (for liquid and solid substances)
Immersed body method (for solid substances)
Pycnometer methods
Air comparison pycnometer (for solids)
Oscillating densitometer
3. Calculate the Relative Density of the Liquid From the Given Information.
The Mass of Empty Relative Density Bottle = 24.5g
The Mass of Relative Density Bottle Filled with Water = 56.2g
The Mass of Relative Density Bottle Filled with Liquid = 51.2 g
Relative density of the liquid can be given by:
(Mass Of Relative Density Bottle Filled With Liquid)−(Mass Of Empty Relative Density Bottle) /(Mass Of Relative Density Bottle Filled With Water)−(Mass Of Empty Relative Density Bottle)
Simplifying this we get:
(51.2−24.5)/ (56.2−24.5)
K = 26.7/36.7
K = 0.84
4. What is Archimedes Principle and how to derive it?
Archimedes’ principle was given by the great Greek mathematician, Archimedes. The principle states that any body, which is partially or fully immersed in the water, is acted upon by an upward force called the buoyant force. This force is equal to the weight of the liquid displaced by the object immersed.
Derivation
As we already know,
Density= Mass/ Volume which implies that
Mass = Density × Volume which can also be written as p × V
Here, p = density and V = volume.
Weight of the displaced fluid will be calculated as-
W = M × g
W = p × V × g
Here. W is the weight, p is the density, V is the volume and g is the acceleration due to gravity.
Therefore, this can be written as-
The loss of weight of the object = weight of the fluid displaced = p × V × g
Therefore, the Thrust Force is,
Thrust = p × V × g