What is Density?
The measure of the denseness in a specific given area of a material is known as its density. It is basically a measure of how tightly matter is packed together. It is a unique property of an object. Archimedes, a Greek scientist, discovered the principle of density. By knowing the formulas and the units, one can easily calculate the density of an object. It is most commonly denoted by or sometimes D.
Density- Examples
Heavy or hard materials are supposed to be dense such as iron, platinum, rocks, minerals, and so on. Materials like glass, bamboo, styrofoam are not dense materials. In matter, liquids are denser than gases and solids are denser than liquids. In the case of gases, particles can move freely all over the place while in the case of solids particles can collide with each other.
Density- Formula
Density is calculated by mass over volume, which can be written as-
\[Density = \frac{Mass}{Volume}\]
\[\rho = \frac{m}{v}\]
where \[\rho\] denotes density
m denotes mass and v volume
Density- SI and Other Units
The density of all different substances is also different which means the density of substances would weigh differently for the same volume of different substances. Therefore, the density of each substance is specific. The standard value for calculating density is taken as 1 g/cm3 which is the approximate density of water. Though, the SI unit of density is taken as kg/m3.
Density can also be expressed in terms of liters, metric tons, as listed below-
t/m3- metric ton per cubic meter
g/mL- gram per milliliter
kg/L- kilogram per liter
g/cm3- gram per cubic centimeter
mg/m3- megagram per cubic meter
kg/dm3- kilogram per cubic decimeter
In the CGS system, the density of objects is measured in g/cm3.
Types of Density
Usually, the density is of two types, one is absolute density, and the other is relative density. Relative density is also known as specific gravity, which is the ratio of the density of a material to the density of reference material. Usually, the reference material is water. Specific gravity is a relative quantity with no units.
Absolute density refers to the mass of any substance per unit volume of a material. It is usually expressed in g/cm3.
To find the density of an object, measure the mass of the material and divide it by the volume it covers, since the density of water is 1 gm/cm3 - the ratio of the density of the material to that of water is 1:£ (Density of water is 1 gm/cm3 at 4°C.)
For example, the density of gold is 19.32 g/cm3, and so the specific gravity is 19.32.
Units of Density
Units of density are g/cm3
The SI units of density are kg/m3.
Other density units - Gram /litre (g/l),
Gram /millilitres
Applications of Density in Real Life
Let's get an idea with an example from real life.
Suppose you have two balloons. One is filled with air, and the other one is filled with coke. Coke is much denser because the atoms take up less space as they move around less. The air balloon contains atoms that are colliding around very quickly, and this makes the atoms take up more space or less density. Thus, the balloon with air is light and the balloon with water is heavy.
Usually, density plays a crucial role in many applications, life tubes we find on beaches or in swimming pools are designed to float on water so that people can swim without sinking, just by holding those air-filled tubes. Life tubes are filled with air which is less dense than water so it always floats. Another application is, ships can float because they have ballast tanks that hold air, and these tanks provide large volumes with little mass, hence decreasing the density of the ship. Combined with the buoyant force, this reduced density helps the ship to float over water. Submarines dive below the surface of the water by emptying their ballast tanks.
Solved Examples
1. Calculate the density of water if it has a volume of 1m3 and mass of 1160 Kg.
Ans: Given-
Mass = m = 1160 Kg
Volume = v = 1m3
Solution:
\[Density = \frac{Mass}{Volume}\]\[\rho = \frac{m}{v}\]
Density = 1160/1
Density = ρ = 1160 kg/m3
2. You have a rock with mass of 60g and density 2 g/cm3. Calculate its volume.
Ans: We know that Density = ρ = Mass/Volume
Volume = v = Mass/Density
Let’s substitute the values given.
Volume = 60/2 = 30cm3
3. If the density of diamond is 3.5 g/cm3, what will be the mass of diamond having a volume of 0.5 cm3?
Ans: Given:
Density = ρ = 3.5 g/cm3
Volume = v = 0.5 cm3
Solution:
We know that Density = mass/ volume
Mass = Density * volume
Let’s substitute the values and find the value of Mass
Mass = 3.5 * 0.5
Mass = 1.8g
FAQs on Unit of Density
1. What is the SI unit of density and how is it derived?
The SI unit of density is kilograms per cubic meter, written as kg/m³. This unit is derived from the fundamental SI units for mass (kilogram, kg) and length (meter, m). Since density is defined as mass divided by volume (which is length cubed), its unit becomes the unit of mass divided by the unit of volume (kg/m³).
2. What is the formula used to calculate the density of a substance?
The formula to calculate the density of a substance is: Density (ρ) = Mass (m) / Volume (V). In this formula, 'ρ' (rho) is the symbol for density, 'm' represents the mass of the substance, and 'V' represents the volume it occupies. To get an accurate result, you must use consistent units for mass and volume.
3. Besides kg/m³, what are other common units used to measure density?
While kg/m³ is the official SI unit, several other units for density are commonly used in different contexts, especially in chemistry and daily applications. These include:
- Gram per cubic centimeter (g/cm³): This is the standard CGS (Centimetre-Gram-Second) unit. It's convenient because the density of water is approximately 1 g/cm³.
- Gram per millilitre (g/mL): This is numerically equivalent to g/cm³, as 1 cm³ is equal to 1 mL.
- Kilogram per litre (kg/L): This is also numerically equivalent to g/cm³.
4. How do temperature and pressure affect the density of most substances?
Temperature and pressure are key factors that affect a substance's density by changing its volume.
- Temperature: For most substances, increasing the temperature causes them to expand, which increases their volume. Since density is mass divided by volume, an increase in volume leads to a decrease in density. Conversely, cooling a substance generally increases its density.
- Pressure: Increasing the external pressure on a substance (especially gases and, to a lesser extent, liquids) compresses it, reducing its volume. This reduction in volume leads to an increase in density.
5. Why does ice float on water if they are both made of H₂O?
Ice floats on water due to a unique property of water known as its anomalous expansion. As water cools, it becomes denser, but only down to 4°C. Below this temperature, as it freezes into ice, its molecules arrange themselves into a rigid, open-crystal lattice structure. This structure takes up more space than the molecules in liquid water, making ice about 9% less dense than liquid water. Because it is less dense, it floats.
6. What is the difference between density and relative density?
The key difference lies in what they measure and their units. Density is an absolute property of a substance, defined as its mass per unit volume (e.g., kg/m³ or g/cm³). In contrast, relative density (or specific gravity) is a ratio that compares the density of a substance to the density of a reference substance, which is usually water. Since it's a ratio, relative density is a dimensionless quantity and has no units.
7. What are some important real-world applications of the concept of density?
The concept of density is crucial in many real-world applications, including:
- Shipbuilding: A ship made of steel (which is much denser than water) floats because its hollow shape displaces a large volume of water, making its overall average density less than that of water.
- Hot Air Balloons: A hot air balloon rises because heating the air inside it makes it expand and become less dense than the cooler, denser air outside.
- Purity Testing: The density of a pure substance like gold is a known constant. By measuring the density of an object, one can help determine its purity.
- Layering of Liquids: Immiscible liquids with different densities, like oil and water, will separate into layers, with the least dense liquid floating on top. This principle is important in managing oil spills.
8. How is density used to check the purity of milk?
The density of pure milk is relatively constant, typically ranging from 1.028 to 1.032 g/mL. Adding water to milk (adulteration) will decrease its density because water is less dense than milk. A device called a lactometer, which works on the principle of buoyancy, is used to measure the specific gravity of milk. A reading outside the standard range indicates that the milk may be adulterated with water or other substances.
