5 Facts On Density And Specific Gravity: Relation,How To Find


Density and specific gravity are the physical entity that describes the volumetric characteristics of the given substance. In this post, you will learn more about density and specific gravity.

Density defines mass of a substance at unit volume, and specific gravity is also a density compared with density of another substance as a reference. Specific gravity is the ratio of weight per unit volume of a material with weight per unit volume of another reference substance. However, both density and specific gravity are interconnected.

Water is used as a reference substance for solids and liquids to measure specific gravity. Dry air is used as a reference substance for gasses to measure specific gravity. The following section will know the relation and differences between density and specific gravity.

File:Hydrometer en.png - Wikimedia Commons
Hydrometer used to measure density and specific gravity Image credits: Wikimedia commons

Density and specific gravity relation

The specific gravity and density are interconnected to one another. The relation between density and specific gravity is given as

[latex]\rho\propto SG[/latex] ; where ρ is the density and SG is the specific gravity.

The above expression explains that the change in the density directly corresponds to the specific gravity. If density increases, the specific gravity also increases.

We can also roughly check the density of a given solid or liquid using the value specific gravity calculated with water reference.

  • For any substance whose measured specific gravity is less than one means, the density of that substance is less than water and floats on the water.
  • Suppose if measure specific gravity is more than 1, then density is greater than the water and sinks in water.

Since, in most cases, water is used as a reference substance, the value of specific gravity and density are almost equal. From the accurate calculation, it is found that the density is a bit less than the specific gravity.

Density and specific gravity difference

Since we know the definition of density and specific gravity, both seem alike, but there are some differences in their basic characteristics as well as in their measurements. Some differences between density and specific gravity are given in the below table.

DensitySpecific gravity
DefinitionDensity defines the weight of the given substance per unit volume.Specific gravity defines the ratio of densities of two substances in which one is referred to as a reference substance.
SI unitThe density id denotes by the symbol ρ, and its SI unit of density is kg/m3.Specific gravity does not have SI units because we are taking the density of two equivalent substances, in which units are canceled out.
RepresentationDensity represents the absolute value of the substance in one dimension.Specific gravity represents the relative value in one dimension.
Terms used in the calculationOnly the mass of the substance and volume are essential for the calculation.In order to calculate the specific gravity density of a given substance and the density of the reference substance is needed. So it is essential to know mass and volume if the density is not given.
ApplicationsDensity has applications in the field of science and industries and is also widely used in everyday life.Specific gravity has application only in scientific and industrial areas. It is not so commonly used in daily life.

How does density affect specific gravity?

We know that density and specific gravity are correlated, such that any change in the density would definitely affect the specific gravity.

Density is very responsive to temperature and pressure. The density value varies linearly for small variations in temperature and pressure. Since specific gravity corresponds to density, the change in density with temperature and pressure ensures a change in specific gravity.

The density is proportional to the change in the pressure and inversely corresponds to the temperature. That means an increase in the pressure increases the density at a constant temperature, consequently increasing specific gravity.

File:Water density on pressure for various temperatures.svg - Wikimedia  Commons
Variation of density with pressure and thus affecting specific gravity
Image credits: Wikimedia commons

Density and specific gravity formula

Specific gravity gives the density of a given substance in reference to another substance; the formula gives it.

[latex]SG=\frac{\rho_{sub}}{\rho_{ref}}[/latex]

The density of the given substance is given by the ratio of its mass and volume as

[latex]\rho=\frac{m}{V}[/latex]

Together, we can write specific gravity as

[latex]SG=\frac{\left(\frac{m}{V}\right)_{sub}}{\left(\frac{m}{V}\right)_{ref}}[/latex]

The above expression gives the formula describing how density and specific gravity relate to each other.

How to find density from specific gravity?

If you are provided with the substance’s specific gravity, you can easily find the density. The steps to be followed are given below.

  • Step 1: Find the water’s density at a given temperature and pressure.
  • Step 2: substitute the values in the expression of specific gravity.
  • Step 3: multiply the values of specific gravity and density of the reference object, which gives the density of the required substance.

The specific gravity of a solid substance is 14.87; find its density.

Since the given object is solid, the reference substance will be water.

[latex]SG=\frac{\rho_{sub}}{\rho_{water}}[/latex]

The density of the water is 1000kg/m3. Substituting, we get

14.87=[latex]\frac{\rho_{sub}}{1000kg/m^3}}[/latex]

ρsub=14.87×1000kg/m3

ρsub=14870kg/m3

How to calculate gas density from specific gravity?

The dry is considered the reference substance to find the gas density. Steps given below help you to find the density from specific gravity.

  • Step 1: find the density of the dry air initially.
  • Step 2: multiply the density of dry air and give specific gravity of the substance, which gives you the density of the given substance.

ρgas=SG×ρair

Example given below helps you understand clearly.

Find the density of a gas whose specific gravity is 0.00126.

The density of the air is 1.20kg/m3

ρgas=SG×ρair

ρgas=0.00126×1.20kg/m3

ρgas=1.512×10-3kg/m3.

How to find density with relative density?

Relative density defines the ratio of densities of two substances that are relative to one another. We can also say that it is the ratio of densities between a substance lying in the vicinity of another substance.

In some contexts, the relative density is also referred to as specific gravity. If you know the relative density of an object, then density can be calculated by using the formula; [latex]RD=\frac{\rho_{sub}}{\rho_{ref}}[/latex]

The problem solved below explains how to calculate density from relative density.

Some solved problems on density and specific gravity

Calculate the specific gravity of iron rods in water whose density is 7870kg/m3.

Solution:

Since the iron rod is in water, the density of the water is 1000kg/m3.

The specific gravity is given by

[latex]SG=\frac{\rho_{sub}}{\rho_{water}}[/latex]

Substituting the value of density of iron rod and water in the equation,

[latex]SG=\frac{7870}{1000}[/latex]

SG=7.87

Calculate the specific gravity of an object in the water of mass is 55g and volume is 22m3.

Solution:

Given –the mass of the object m=50g

The volume of the object V=22m3.

The density of the water=1000kg/m3.

The density of the given object is given by

[latex]\rho_{obj}=\frac{m}{V}[/latex]

Substituting the values

[latex]\rho_{obj}=\frac{50}{22}[/latex]

ρobj=2.27g/m3=2270kg/m3.

The specific gravity is

[latex]SG=\frac{\rho_{obj}}{\rho_{water}}[/latex]

[latex]SG=\frac{2270}{1000}[/latex]

SG=2.27.

An object is immersed in oil with a relative density of 2.3. The same oil is floating in water with a specific gravity of 0.92. Calculate the density of the object in oil.

Solution:

Given –the relative density of an object with respect to oil RD=2.3

The specific gravity of oil SG=0.92

The density of water ρw=1000kg/m3

The density of oil is calculated as

ρoil=SG×ρw

ρoil=0.92×1000kg/m3

ρoil=920kg/m3.

The density of the object is calculated as

ρobj=RG× ρoil

ρobj=2.3× 920

ρobj=2116kg/m3.

Calculate the specific gravity of a gas whose density is 1.5kg/m3.

Solution:

Since they are asking to calculate the specific gravity of gas, the reference medium should be dry air whose density is 1.205kg/m3 at normal temperature and pressure.

The density of the gas is given as 1.

The specific gravity for given gas is

[latex]SG=\frac{\rho_{gas}}{\rho_{air}}[/latex]

[latex]SG=\frac{1.5kg/m^3}{1.205kg/m^3}}[/latex]

SG=1.244.

Calculate the density and specific gravity of a substance in water whose mass is 63g and volume is 28m3.

Solution:

Given -the mass of the substance m=63g

The volume of the substance V=28m3

We are only provided with mass and volume of the substance and density has to be calculated using the formula.

[latex]\rho_{sub}=\frac{m}{V}[/latex]

[latex]\rho_{sub}=\frac{63g}{28m^3}[/latex]

ρsub=2.25g/m3=2250kg/m3

The specific gravity of the substance is given by the formula

SG=\frac{\rho_{sub}}{\rho_{water}}

SG=\frac{2250kg/m^3}{1000kg/m^3}

SG=2.25.

Summary

From this post you have learnt how density and specific gravity depends on one another. And to find specific gravity, knowing one of them is density of substance and reference substance is must.

Keerthi Murthi

I am Keerthi K Murthy, I have completed post graduation in Physics, with the specialization in the field of solid state physics. I have always consider physics as a fundamental subject which is connected to our daily life. Being a science student I enjoy exploring new things in physics. As a writer my goal is to reach the readers with the simplified manner through my articles. Reach me – keerthikmurthy24@gmail.com

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