Density of Compressed Liquid
Category : JEE Main & Advanced
If a liquid of density \[\rho \], volume V and bulk modulus K is compressed, then its density increases.
As density \[\rho =\frac{m}{V}\] so \[\frac{\Delta \rho }{\rho }=\frac{-\Delta V}{V}\] ...(i)
But by definition of bulk modulus
\[K=\frac{-V\Delta P}{\Delta V}\]\[\Rightarrow \]\[-\frac{\Delta V}{V}=\frac{\Delta P}{K}\] ...(ii)
From (i) and (ii) \[\frac{\Delta \rho }{\rho }=\]\[\frac{{\rho }'-\rho }{\rho }=\frac{\Delta P}{K}\] [As \[\Delta \rho =\rho '-\rho \]]
or \[{\rho }'=\rho \left[ 1+\frac{\Delta P}{K} \right]\]\[=\rho [1+C\Delta P]\] \[\left[ \text{As }\frac{\text{1}}{K}=C \right]\]
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