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Relative Density

  • Last Updated : 20 May, 2021

Density is defined as the amount of mass in a unit volume of matter, for every substance has a different density. Through this article, we will cover what is relative density, calculations related to the relative density, and the density of various substances. 

Observe how the different liquids form different layers. The different substance poses a different density, meaning that for the same volume different substances weigh different, so the heavier substances tend to settle at the bottom, like in the case of honey and in the case of lighter material like oil, they tend to float at the top.

Relative Density

We define the density of a substance as the mass of a unit volume of substance. The SI unit of density is given as kilogram per meter cube (kgm-3). The density of any given substance under specified conditions always remains the same. The density of any substance is its characteristic properties. It is mainly different for different substances. For an instance, the density of metal gold is 19300 kg m-3 while water is 1000kgm-3. The density of any given sample of a substance can help us to determine its purity. It is always easy to express the density of a substance in comparison to water.

The difference between the specific gravity or relative density and density is that at room temperature and pressure, 1gram per 1 cubic cm is the density of water this density is treated as a standard, and the density of any other material (usual liquids) is always calculated relative to this which is called the relative density or specific gravity.



Therefore, specific gravity is the ratio of the mass of a substance to that of a reference substance. Given below is the formula to calculate it.

Relative density = Density of substance/Density of water

It has no units as it is a ratio of similar quantities.

The specific gravity of a substance tells whether the object will float or sink, it provides us the idea about relative mass or relative density. It is considered that if the given specific gravity of a substance is below 1 then it will float and if it is greater than 1 it will sink.

Following is the table showing different density of materials.

SubstanceDensity(kgm-3)
WATER1000
DIESEL860
GASOLINE725
SILVER10500
GOLD19300
AIR1.18
MERCURY13600
BLOOD1600
COPPER8900

As we can observe from the table different materials are having different density values. It is to be noted that these measurements are made based on a certain temperature and pressure. Because changing the physical conditions may give a different value of density each time as the density is dependent upon that factors.

Factors affecting Relative Density

As stated above the relative density is a ratio of the density of a substance with respect to the density of water. Hence, any change in the density of either substance or water will influence the relative density ratio therefore following are the factors that affect the density of any substance and indirectly affect relative density.

  • Temperature– The density is mass per unit volume it will change if the volume changes as the mass doesn’t change until we add some more of the same material to it. Increasing the volume of substance will decrease the density and vice versa is also true. We can change the volume if we heat or cool the substance. It will accordingly change its density therefore volume is inversely proportional to density. And so the temperature increase is also inversely proportional to the density as it increases the volume if the temperature is increased.
  • Pressure- For instance imagine we take a glass of water from earth to space, where it vaporizes as soon as possible due to the absence of pressure. However, its density decreases since the volume has increased. As we go on increasing the pressure the density also increases proportionally as the force of attraction between the molecules strengthens and the intermolecular spaces become less hence increasing its density. So we can say pressure is directly proportional to the density of the material.
  • Nature of substance- As from the formula it is clear that density is a characteristic property of any material and hence the relative density is totally dependent upon the nature of substance as well as of water at a certain temperature.

Different ways to calculate Relative Density:



  • Buoyancy Method
  • Hydrometer
  • Hydrostatic Balance
  • Immersed Body Method
  • Pycnometer Method
  • Air Comparison Pycnometer Method for Solids
  • Oscillating Densitometer

Hydrometer

The relative density of any liquid is taken out using a hydrometer. A bulb is completely attached to a stalk of constant cross-sectional area. The hydrometer is first floated in the reference liquid (in light blue), and the displacement (the level of the liquid in stalk) is marked (with a blue line). The reference could be in practice water.

The hydrometer is then floated in a liquid of unknown density. The change in displacement is then noted. In the example depicted, the hydrometer has dropped in the green liquid; therefore its density is lower than that of the reference liquid. It is important that the hydrometer floats in both liquids. The application of simple physical principles like the change in displacement can help determine the relative density.

Pycnometer

A Pycnometer is used to determine the density of a liquid. It is usually made of glass, with a fitting ground glass stopper with a capillary tube through it, so that air bubbles may escape from the apparatus. It enables a liquid’s density to be calculated by reference to an appropriate working fluid, such as water or mercury.

If the flask is empty, full of water, and full of a liquid whose relative density is needed, the relative density can easily be calculated. The particle density is also calculated with a Pycnometer. The Pycnometer is filled with a liquid of known density, in which the powder of known weight is completely insoluble. The weight of the displaced liquid is calculated, and hence the relative density of the powder.

Digital density meters

Hydrostatic Pressure-based Instruments:

It uses Pascal’s Principle which states that the pressure difference between two points within a vertical column of any liquid or fluid is dependent upon the vertical distance between the two given points, the density of the fluid, and the gravitational force. This is widely used for tank gaging applications as a convenient means of liquid level measure and approximation and density measure.

Vibrating Element Transducers:

It requires a vibrating element in contact to be placed with the fluid of interest. The resonant frequency of that particular element is measured and is related to the density of the fluid by a characterization that depends completely upon the design of the element. In new laboratories for precise measurements of relative density oscillating U-tube meters are used. Therefore, they are used in the brewing, distilling, pharmaceutical, petroleum, and other industries.

Ultrasonic Transducer:

Ultrasonic powerful waves are passed from a taken source, through the fluid of our interest, and into a metal detector which measures the acoustic spectroscopy of the traveling waves. Fluid properties such as density and viscosity can be determined from the spectrum.



Radiation-based Gauge:

Radiation is passed from a distant source, through the fluid of our interest, and into a scintillation detector, or counter. As whenever the fluid density increases, the detected flow radiation or the “counts” will decrease. The source is typically taken to be the radioactive isotope cesium-137, with a half-life of about 30 years. An advantage of this is that the instrument is not required to be in contact with the fluid.

Buoyant Force Transducer:

The buoyancy force generated by a float in a uniform liquid is equal to the weight of the liquid that is displaced by the float. Since buoyancy force is linear the measure of the buoyancy force usually yields a measure of the density of the liquid. When the object head is immersed vertically in the liquid, the float moves somewhat vertically and the position of the float controls the position of a very effective permanent magnet whose displacement is sensed usually by a concentric array of Hall-effect linear displacement sensors. The output coming signals of the sensors are mixed in a dedicated electronics machine which provides a single output voltage whose magnitude is a direct linear measure of the quantity which is to be measured.

Sample Problems

Question 1: It is given that the relative density of silver is 10.8. The density of water is1000 kgm-3. What is the density of silver in SI unit?

Solution:

Given,

Relative density of silver = 10.8

Density of water = 1000 kgm-3.

We know that,



Relative density =Density of silver/Density of water

Density of silver= Relative density \times Density of water

Density of silver= 10.8 x 103kgm-3.

Hence, the density of silver is 10800kgm-3

Question 2: What is the relative density and its SI unit?

Answer: 

The relative density or specific density is the ratio of density of a substance with respect to the density of water at 40 C. Since the units for both the numerator and denominator in the ratio are same, they cancel each other. Therefore, relative density has no units. The density of any substance defined as mass per unit volume. Hence, its SI unit is: kg/m3.

Question 3: State the difference between density and volume?

Answer:

Volume – States that how much space a material or substance takes up. Mass – It is a measurement of the amount of matter present in an object or substance. Density – It is defined as how much space a material or substance takes up (its volume) with respect to the amount of matter in that object or material (its mass).

Question 4: It is given that the density of mercury is 13600 kgm3. The density of water is1000 kgm3. What is the relative density of mercury in SI unit?

Solution:

Given,

Density of mercury = 13600kgm-3

Density of water = 1000 kgm-3.

We know that,

Relative density =Density of mercury/Density of water 

\therefore Relative density =13600/1000 = 13.6

Hence the relative density of mercury is 13.6.

Question 5: It is given that density of iron is 7800 kgm-3. The density of water is1000 kgm-3. What is the relative density of iron in SI unit? Is it greater than relative density of mercury which is 13.6? Will an iron rod sink in it or float?



Solution:

Given,

Density of iron = 7800kgm-3.

We know that,

Relative density =Density of mercury/Density of water

Relative density =\frac{7800}{1000 }= 7.8

Hence, the relative density of iron is 7.8.

As its relative density is lower than mercury it will float in it.

Question 6: It is given that density of diesel is 860 kgm-3. The density of water is 1000 kgm-3. What is the relative density of diesel in SI unit?

Solution:

Given,

Density of diesel = 860 kgm-3

We know that,

Relative density =Density of diesel/Density of water

Relative density =\frac{860}{1000 } = 0.86

Hence the relative density of diesel is 0.86

Question 7: It is given that density of gold is 19300 kgm-3. The density of water is 1000 kgm-3. What is the relative density of gold in SI unit? Will it float in mercury with a relative density of 13.6 and in water with 1?

Solution:

Given,

Density of gold = 19300kgm-3

We know that,

Relative density =Density of gold/Density of water

Relative density =\frac{19300}{1000 } = 19.3

Hence the relative density of gold is 19.3.

So it will not float in both mercury and water as it has a greater density.

Question 8. It is given that density of copper is 8900 kgm-3. The density of water is1000 kgm-3. What is the relative density of copper in SI unit?

Solution:

Given,

Density of copper = 8900 kgm-3

We know that,



Relative density =Density of copper/Density of water

Relative density =\frac{8900}{1000 }=8.9

Hence the relative density of iron is 8.9

Question 9: It is given that density of iron is 7800 kgm-3. The density of water is1000 kgm-3. What is the relative density of iron in SI unit? Is it greater than relative density of mercury which is 13.6? Will an iron rod sink in it or float? What will happen with a rod made of gold with density of 19300?

Solution:

Given,

Density of iron = 7800kgm-3

Density of gold = 19300kgm-3

We know that,

Relative density =\frac{Density of gold}{Density of water }

Relative density =\frac{19300}{1000 } = 19.3

Hence the relative density of gold is 19.3.

Also the relative density of mercury can be found.

Relative density =Density of mercury/Density of water 

Relative density =\frac{7800}{1000 }= 7.8

Hence the relative density of iron is 7.8.

As iron has a relative density that is lower than mercury it will float in it and the rod of gold will sink as it has a greater relative density.

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