### Calculation Of Specific Gravity

Calculation Of Specific Gravity:-
The Specific Gravity (it is also written as sp.gr.) of a substance is the ratio of the weight of a given volume of the substance to the weight of an equal volume of some standard substance (which is taken as water at 4degreeC)

Obviously it is a pure number and processes no dimensions.

Hence the Specific gravity of a substance

=(the weight of volume  v   of the substance)/(the weight of volume   v  of the standard substance)

=(the weight of a unit volume of the substance)/(the weight of a unit volume of the standard substance)

=(the mass of a unit volume of the substance)/(the mass of a unit volume of the standard substance)     (as weight=mass*g)

=(the density of the substance)/(the density of standard substance)

This is the final step for Specific Gravity.

True specific gravity can be expressed mathematically as:
$SG_\text{true} = \frac {\rho_\text{sample}}{\rho_{\rm H_2O}}$
where $\rho_\text{sample}\,$ is the density of the sample and $\rho_{\rm H_2O}$ is the density of water.
The apparent specific gravity is simply the ratio of the weights of equal volumes of sample and water in air:
$SG_\text{apparent} = \frac {W_{A_\text{sample}}}{W_{A_{\rm H_2O}}}$
where $W_{A_\text{sample}}$ represents the weight of sample and $W_{A_{\rm H_2O}}$ the weight of water, both measured in air.
It can be shown that true specific gravity can be computed from different properties:

$SG_\text{true} = \frac {\rho_\text{sample}}{\rho_{\rm H_2O}} = \frac {(m_\text{sample}/V)}{(m_{\rm H_2O}/V)} = \frac {m_\text{sample}}{m_{\rm H_2O}} \frac{g}{g} = \frac {W_{V_\text{sample}}}{W_{V_{\rm H_2O}}}$

where $g$ is the local acceleration due to gravity, $V$ is the volume of the sample and of water (the same for both), ${\rho_\text{sample}}$ is the density of the sample, $\rho_{\rm H_2O}$ is the density of water and $W_V$ represents a weight obtained in vacuum.