# Specific Gravity or Relative Density

## Definition:

Specific gravity or Relative Density of a substance is the ration of the density of that substance to the density of a reference substance. We can calculate the specific gravity of liquid and gas assuming the reference substance as water and air respectively.

## 1.     Specific gravity of Liquid

Specific gravity of liquid is defined as the ratio of density of the liquid at a standard or any temperature to the density of water at some standard reference temperature at atmospheric pressure. We take water as reference as the specific gravity of water [(S.G)water] is 1.

Mathematically,

Specific Gravity of liquid = (S.G)liquid = (density of liquid at any temperature) / (Density of water at some standard temperature)

For scientific purpose the distilled water is taken as reference.
For industrial purpose the normal water is taken as reference.

Standard reference temperature = 4°C
Atmospheric pressure = 760 mm of Hg

As per American Petroleum Institute (API), Standard reference temperature = 15.6°C or 60°F

As per International standard Organization (ISO), standard reference temperature = 15°C or 59°F

## 2.     Specific Gravity of Gas

The specific gravity of gas can be defined in either of two ways.

(i)                  Real Specific Gravity: The ratio of the density of the gas (ρgas ) to the density of air (ρair ) at a particular temperature and pressure is called the Real Specific Gravity.

Mathematically,
(S.G)gas = (ρgas / ρair) T,P

(ii)           Ideal Specific Gravity: Ratio of the molecular weight of the gas (Wgas) to the                                  molecular weight of air (Wair), is called the Ideal Specific Gravity.

Mathematically,
(S.G)gas = (Wgas / Wair)

◘ At normal atmosphere, temperature and pressure, the real specific gravity [(RSG)gas] and the Ideal Specific Gravity [(ISG)gas] of Gas are same, except- Steam, Carbon di oxide and some gases.
PROOF:

Ideal Gas Law = PV=nRT

P= pressure
V= volume
n= number of moles
R= Gas constant=8.314
T= temperature

For Real Gas = PV=nZRT

Z is defined as the ratio of the volume of the gas to the volume occupied by the same number of moles of ideal gas, at particular temperature and pressure.

Z = (Volume of real gas) / (Volume of same no. of moles of ideal gas)
Z is called the Compressibility factor.

PV=nZRT
PV = [m/Mw] ZRT
m/V = (PMW)/(ZRT)
ρ = (PMW)/(ZRT)
ρgas = [P (MW)gas]/ (ZgasRT)…………….(I)
ρair = [P (MW)air]/ (ZairRT)……………….(II)

Now,

(RSG)gas = ρgas / ρair

Putting the values of (I) and (II) in this equation,

(RSG)gas = [(MW)gas/(MW)air] * [ Zair/Zgas]

(RSG)gas = (ISG)gas * [Zair/Zgas]……………….(III)

At normal atmosphere, temperature and pressure,

Zair = Zgas

From equation (III),

(RSG)gas = (ISG)gas

Hence proved.

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