Free tutorial in Basic Physics - Understanding Density


Do you want to learn about the concept of density and its importance in science and in our lives? This article gives a detailed understanding of this entity called density, one of the important physical characteristics of a material.

Introduction

Everything visible in the form of matter has some mass and some volume. We all must have observed that for the same mass, the volume of the material varies and sometimes varies drastically. For example, one kilogram of rice will fill only about 7 tea cups but one kilogram of rice husk will be almost occupying at least ten times more space (volume) than that. It is interesting to know what makes this difference in the volume of the materials having the same mass. We will learn in this lesson about the entity called density which explains about these varying physical characteristics related to the mass and volume of a particular material.

Mass and Volume

Mass and volume are the basic physical characteristics of a material. Mass is the amount of the material available in that body while volume is the space that it occupies. For example, 1 kilogram of ordinary wood takes a space of about 1600 cc (cubic centimeter) while 1 kilogram of iron weight takes only a space of about 130 ccs. It implies that iron is denser than that of wood and occupies a small space. Comparatively, in this example, it is occupying only about one-tenth of the space occupied by the same mass of wood.

The concept of density

Mass and volume are two very special physical characteristics of a material and when we combine these two in one then the concept of density is generated. By definition and also for simplicity we consider the mass of a unit volume of a material as its density and by knowing the density of a material we can know a lot of things about it. In a scientific depiction, this relationship of density with its mass and volume is represented as follows -
density (d) = mass (m) / volume (V)

Units of density

There are many representations of the unit of density but the most common are gram/cc and Kg/cubic metre. There is an old unit of density known as pounds/cubic feet which is still being used in some industries and that unit belongs to FPS (foot, pound, and second) system.

Density of water

1 kilogram (1000 gram) of water has a volume of about 1000 cc (1 litre) and using the above relationship between mass, volume, and density, it is evident that water density is = 1000 gram/1000 cc= 1 gram/cc. In SI system the unit will be Kg/cubic meter. We can calculate it in the SI system by dividing the mass of 1 cubic meter of water by its volume. That would come to approximately 1000 Kg/cubic meter. So in SI system, the density of water is 1000 Kg/cubic meter. The density of water slightly varies with temperature and if we measure it exactly with reference to a particular temperature then actually the exact density of water at room temperature of 20-25 degrees centigrade is 0.997 gram/cc or 997 Kg/cubic meter. With increase in temperature it slightly decreases and if we heat the water to almost boiling temperatures in the range 90-95 degree centigrade then it becomes 0.962 gram/cc, a little decrease in deed.

In the old FPS system, the density of water is 62.4 pounds/cubic feet. A pound is the unit of mass in the FPS system and the conversion between Pound and Kilogram is given by 1 Pound = 0.454 Kg (one pound is equal to almost very near to half a Kg).

Understanding water density gives us very interesting information. A large part of the Earth's surface is covered with oceans filled with water only. How this water is different from the rain water or the river water or the spring water or the underground water which we use in our daily life? Actually, sea water contains a lot of salt in it which is mainly common salt which we know and study in chemistry as Sodium Chloride (NaCl). The amount of salt is so much that only one litre of sea water contains approximately 35 grams of salt. This makes the density of sea water about 1.025 gram/cc or 1025 Kg/cubic meter. So one cubic meter of sea water will weigh about 25 Kg more than the one cubic meter of the common water that we use in our households! That is indeed an interesting observation.

Density of air

We all know that the materials can exist in various forms like liquid, solid, and gas. For example, water can be in ice form or water form, or steam form and their densities will differ from each other depending upon the ratio of their mass and volume in that state. Solid forms are generally denser than liquids and both of these states are denser than the gas state. For example air around us which we breathe round the clock is a gas mainly a mixture of Oxygen (21%) and Nitrogen (78%) along with a little Carbon dioxide and other gases (1%). It has a very low density about 0.00123 gram/cc or 1.23 Kg/cubic meter. It would be interesting to note that the air in our living room with a size of 5 meters x 4 meters x 3 meters is approximately 74 Kg.

How to find the density of a material

We will now go through some methods which are generally followed for finding the density of a material. For this, we have to get two things one is the mass of the item and the second is its volume. Mass can be found by a weighing scale, it is easy to do so. As regards volume we can find it through calculations for the symmetrical bodies and other methods for irregular bodies. For symmetrical bodies volume can be found by using some mathematical formula. For example, if we want to find out the volume of a cylindrical body then we use the formula pi x (r square) x h where pi = 3.14, r is the radius of the base of the cylinder, and h is the height of the cylinder. Another example is a spherical body. For a spherical body, the volume is given by the formula 4 x pi x (r cube) / 3 where pi = 3.14 and r is the radius of the sphere. Similarly, a rectangular block has a volume equal to length x width x height. So, in mathematics, as we have a formula for the volume of symmetrical bodies, we can find out the volume of these symmetrical bodies using these formulas.

What about the volume of irregular bodies like a piece of stone. For this, we have to use certain other methods to find out the volume. One such method is to use a graduated beaker in which some water is there and we can read its volume from the graduated scale given on the side wall of the beaker. Once we dip the stone in the water and it sinks to the bottom then the level of water goes up depending upon the volume of the stone. The stone will displace the water equal to its own volume only. So, by subtracting the earlier level of water from the later level we get the volume of stone. Once we have got the mass and volume of an item then using the basic relationship density = mass/volume we can obtain the value of density for that material.

Please note that density is the characteristic of a material. It does not change with the shape and quantity of the material. The density of iron is the same whether it is an iron rod or an iron plate. This is an important point to understand and remember.

Floating of bodies in liquids

An iron piece sinks in water but an iron ship floats in the sea. What makes a body float in a liquid? Actually when a body is immersed in a liquid then its mass remains the same but due to the upthrust of the liquid, its apparent weight is reduced. The great scholar Archimedes found that if a body is fully or partially immersed in a liquid then its apparent weight is reduced and the reduction is equal to the weight of displaced liquid. So ships and other such floats are designed in such a way that they become like a bowl and do not sink in the ocean. Their apparent weight is reduced to a great extent as they displace a large amount of water.

Density of some common substances

Let us now see comparatively as what are the densities of the various common substances belonging to gas, liquid, and solids respectively. Some of these are as follows -
  • Carbon dioxide gas - 0.002 g/cc
  • Oxygen gas - 0.0014 g/cc
  • Kerosine - 0.8 g/cc
  • Alcohol - 0.08 g/cc
  • Milk - 1.03 g/cc
  • Honey - 1.42 g/cc
  • Blood - 1.6 g/cc
  • Granite - 2.65 g/cc
  • Aluminium - 2.7 g/cc
  • Iron - 7.87 g/cc
  • Copper - 8.6 g/cc
  • Mercury - 13.6 g/cc
  • Gold - 19.3 g/cc
  • Platinum - 21.4 g/cc

Conclusion

Density is the physical characteristic of a substance and it can be determined by finding the mass and volume of the item. Density also gives an idea about the heaviness of a material. For example Copper is heavier than Aluminium and Gold is heavier than Iron. Density is the characteristic physical property of a material.

Frequently Asked Questions

Can something have a density equal to zero?
If a thing exists it would have a mass and volume and however small those are, it would have a density.
What is the density of Earth?
Earth is almost a huge spherical body and has a solid crust below which there is a transition state and further below that molten lava (at a high temperature) is there. The average density of Earth is 5.51 gram/cubic centimetre.
If we compress a gas, will its density increase?
Yes. We are packing more gas in the same volume so its mass will increase leading to increase in its density.
What is a hydrometer?
It is an instrument for measuring the density of liquids.


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