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Density: Definition, Calculation, Relative Density, Specific Gravity and Variation

Density: Definition, Calculation, Relative Density, Specific Gravity and Variation

Take the example of foam balls and rubber balls. Foam balls do not hurt when hit with because of their low density; their molecules occupy more volume in comparison to rubber balls; which have low density owing to the compact nature of rubber. Density is the amount of space which a substance or an object occupies. An object to have high density, if it occupies more space despite having lesser mass. You have a solid ball and a hollow ball in front of you. Why do you find it difficult to lift the solid ball? It has higher density in comparison to the hollow ball.Oil floats on water due to its low density.

What do you observe from the following figure? Water floats on honey because water is less dense compared to honey;however oil floats on water due to two reasons: 1) it is immiscible with water 2) It is less dense than water


Fig. showing three liquids floating one above another.

Table of contents

  • What is density?
  • Unit of density
  • Relative density(or)specific gravity
  • Density of two or more liquids
  • Effect of temperature on density
  • Effect of pressure on density
  • Practice problems
  • FAQs

What is density?

Density of a liquid or a solid material is defined as the mass per unit volume. Mathematically, it can be expressed as 

From the above equation, it is clear that a body having heavier mass, but occupying lesser volume, has higher density. It is a scalar quantity.

 Unit of density

The unit of density is and its dimensional formula is

Note: CGS unit of density is or

.

Consider two spheres having densities and being dipped in water having density . Let us assume the second sphere is least dense i.e., 

The sphere having lesser density floats on at the top, while that having greater density sinks.

Relative density

Relative density or specific gravity is the ratio of density of the liquid to the density of water at . Since it is a ratio of two quantities,it has no unit.

Density of two or more liquids

Suppose let us mix two different liquids of densities and having masses and are mixed together. Then the density of the mixture 

If ; then

Effect of temperature on density

When the temperature of a liquid increases, then its density reduces. Why so? This is because with increase in temperature , the volume increases()

Let be the density of the liquid at temperature and be the density at C.

Then, 

,where is the change in temperature denotes the coefficient of volume expansion. From the above equation it is clear that density reduces with increase in temperature. A common observation seen in the behaviour of the substances is that they expand when heated as the density decreases and vice versa when the material is cooled. This is how substances generally react to heat. 

Let us now look at how water behaves when heated. The general tendency of cold water remains unchanged until . The density of water gradually increases as you cool it. When you reach , its density reaches a maximum. What water does next will astound you. When you cool it further to make some ice, i.e. , water expands with a further drop in temperature, meaning the density of water decreases when you cool it from to . The below graph explains this behaviour. The effect of this expansion of water is that the coldest water is always present on the surface. Since water at is the heaviest, this water settles on the bottom of the water body and the lightest, i.e. the coldest layer, accumulates on the top layer. So in the winter, the top of the water is always the first to freeze over. Since ice and water both are bad conductors of heat, this top layer of ice insulates the rest of the water body from the cold of the winter, thereby protecting all life in the water body. Now you can truly comprehend how essential the anomalous behaviour of water is for life.


Fig shows variation of density with temperature for water

Effect of pressure on density

Now what will happen if the pressure is increased instead of temperature? Since pressure is inversely proportional to volume,

and  

∴ As pressure increases, density increases

Solved examples

Q. Two liquids having densities and ,having volumes and , are mixed together. Find the density of the mixture?

A. 

; =() ;

Q. Why does ice float on water?

A. Ice floats over water because it is about 9% less dense than liquid water. It is so because molecules form an ordered crystal through the hydrogen bonding. This ordered crystal spaces the various molecules farther and farther apart. Soon they are farther apart than when they were a liquid, which makes ice less dense than water.

Q. Three liquids of densities and are given; and it is known that

Which of the fluids can be placed at the bottom in a container?

A. Since ; liquid has the highest density followed by liquid and then liquid 2. So liquid 3 will be at the bottom.

Q. A liquid has a density of at . Find its density if temperature is increased by ? []

A.

FAQs

Q. Why do clouds float in the sky?
A. Clouds float in the air because of their low density.

Q. When ice melts its density will increase or decrease?
A. Density of water increases from 0 to 4 degree celsius. So when ice melts its density increases. 

Q. What will be the temperature of water at the bottom of the lake whose upper surface is frozen and turned into ice?
A. Frozen upper surface floats on the surface of water because it has lower density compared to water. Also water has maximum density at degree celsius so at the bottom of lake temperature of water will be .

Q. Why does the density of liquid change with temperature?
A. Heating a substance causes molecules to speed up and spread slightly further apart, occupying a larger volume that results in a decrease in density. Cooling a substance causes molecules to slow down and get slightly closer together, occupying a smaller volume that results in an increase in density.

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