How to Calculate Relative Density: Step-by-Step Methods for Students
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 Explained: Physics Made Simple
1. What is relative density and why is it also called specific gravity?
Relative density is a measure that compares the density of a substance to the density of a standard reference substance. It is a dimensionless quantity because it is a ratio of two similar physical quantities. For liquids and solids, the reference substance is almost always pure water at 4°C. It is also known as specific gravity, a term more common in engineering fields, but both represent the same concept of comparing a substance's density to that of water.
2. What is the key difference between density and relative density?
The primary difference lies in what they measure and how they are expressed. Here's a breakdown:
- Nature of Measurement: Density is an absolute property of a substance, defined as its mass per unit volume. Relative density is a comparative measure, showing how many times denser a substance is compared to water.
- Units: Density has units, such as kilograms per cubic meter (kg/m³) or grams per cubic centimetre (g/cm³). Relative density, being a pure ratio, has no units.
- Value: The numerical value of density depends on the unit system (e.g., iron's density is ~7850 kg/m³ or 7.85 g/cm³), while its relative density is a single number (~7.85).
3. What is the formula used to calculate the relative density of a substance?
The relative density (R.D.) can be calculated using the ratio of densities or the ratio of masses of equal volumes. The most common formula is:
R.D. = Density of the Substance / Density of Water at 4°C
Alternatively, if you measure the mass of the substance and the mass of an equal volume of water, the formula is:
R.D. = Mass of the Substance / Mass of an Equal Volume of Water
4. How can you find the absolute density of a substance if you know its relative density?
You can calculate the absolute density of a substance by rearranging the relative density formula. To do this, you multiply the substance's relative density by the known density of water.
Density of Substance = Relative Density × Density of Water
For example, if the relative density of aluminium is 2.7, its absolute density in the SI system is 2.7 × 1000 kg/m³ = 2700 kg/m³.
5. How does relative density help determine if an object will float or sink in water?
Relative density provides a simple rule for buoyancy in water:
- If the Relative Density > 1, the substance is denser than water and will sink. (e.g., Iron, with R.D. ≈ 7.85)
- If the Relative Density < 1, the substance is less dense than water and will float. (e.g., Wood, with R.D. < 1)
- If the Relative Density = 1, the substance has the same density as water and will remain suspended or fully submerged without sinking.
6. Why is water at 4°C specifically chosen as the reference substance for relative density?
Water at 4° Celsius (277 K) is chosen as the standard reference for two key reasons:
- Maximum Density: Water achieves its highest, most stable density at this temperature. Above and below 4°C, its density decreases. Using the point of maximum density provides a consistent and universally reproducible standard for scientific and engineering calculations.
- Abundance and Accessibility: Water is a readily available, inexpensive, and safe substance, making it a practical choice for a global standard.
7. What is the dimensional formula for relative density?
The dimensional formula for relative density is [M⁰L⁰T⁰]. This is because relative density is the ratio of two quantities with the same dimensions (density). The dimensional formula for density is [M¹L⁻³]. When you divide one by the other, the dimensions cancel out:
[M¹L⁻³] / [M¹L⁻³] = [M¹⁻¹ L⁻³⁻⁽⁻³⁾ T⁰⁻⁰] = [M⁰L⁰T⁰]
This confirms that relative density is a dimensionless physical quantity.
8. Is it possible for the numerical value of a substance's density and its relative density to be the same?
Yes, this is possible but only within the CGS (Centimetre-Gram-Second) system of units. In the CGS system, the density of water is defined as 1 g/cm³. Since relative density is the ratio of the substance's density to the density of water, dividing by 1 results in the same numerical value. For example, mercury's density is 13.6 g/cm³, and its relative density is 13.6. This is not true in the SI system, where the density of water is 1000 kg/m³.
9. What are some common instruments used to measure the relative density of substances?
Different instruments are used depending on whether the substance is a liquid or a solid. Common examples include:
- Hydrometer: A device that floats in a liquid to measure its relative density directly. The depth to which it sinks indicates the liquid's specific gravity.
- Pycnometer (or Relative Density Bottle): A small glass bottle with a precise volume, used to accurately measure the density and relative density of both liquids and solid powders.
- Hydrostatic Balance: This method uses Archimedes' principle to determine relative density by weighing a solid in air and then when it is fully submerged in water.
