Question

The mass per unit volume of a substance is called density ( \[density=\dfrac{mass}{volume}\] ). Arrange the following in order of increasing density – air, honey, chalk, water, exhaust from chimneys, iron, and cotton.

Answer 1

Hint: It would give us a rough idea of the density to divide the given materials into solid, liquid and gaseous. Then arrange them in the order of increasing density i.e., gaseous $<$ liquid $<$ solid.

Complete step by step solution:
Consider the state of all the materials given for an intuition regarding the order.
- Gaseous: Air, exhaust from chimneys
- Liquid: Water, honey
- Solid: Chalk, cotton, iron
To arrive at the accurate ascending order, it will help to compare the density of the other materials with water.
- Air and exhaust from chimneys are in the gaseous state and have a density that is a lot less than that of water. Hence they will float above the water.
- Cotton, despite being a solid, will float on water due to large air pockets between the fibres. Thus, it will come before water in the order.
- Honey, chalk, and iron all have densities greater than water and therefore will sink in water.
Now, let us sort out the order of the materials that will come before water
- Cotton is denser than both the gaseous materials in this list on account of it being a solid.
- The exhaust from chimneys is denser than air. It has a lot of particulate matter packed in a small volume that increases its density.
Now, consider the densities of honey, chalk, and iron
- Honey is less dense than both chalk and iron since it is a liquid.
- Intuitively, chalk is less dense than iron.
So the final order of increasing density is
Air $<$ Exhaust from chimneys $<$ Cotton $<$ Water $<$ Honey $<$ Chalk $<$ Iron

Additional information:
The numerical densities of the given materials are:

Material	Density in ${kg}/{{{m}^{3}}}\;$
Air	1.225
Exhaust from chimneys	1.292
Water	997
Honey	1420
Chalk	2711
Cotton	450
Iron	7870

Note: Do not get confused between the densities of air and exhaust from chimneys, even though the exhaust will have a higher temperature and may lead you to believe that it is lighter than air, the abundance of particulate matter more than compensates for the high temperature and increases its density.