Basically, I'm using the equation $\frac{F}{A} = -B\times \frac{\bigtriangleup V}{V_o} $. Originally I had to find the change in volume given an initial volume (B and pressure ($\frac{F}{A}$) were given to me.

Now it's giving me the final density and is asking for the initial density. How do I approach this?

## Best Answer

$$K=-\frac{dP}{\left(\frac{dV}{V}\right)}$$ $K$ is the bulk module, $P$ is the pressure, and $V$ is the volume. If $K$ is constant, then we have:$$\frac{dV}{V}=-\frac{dP}{K}$$$$\Rightarrow\;\ln\frac{V_2}{V_1}=\frac{P_1-P_2}{K}$$$$\frac{V_2}{V_1}=\frac{\rho_1}{\rho_2}$$ $\rho$ is the density.$$\Rightarrow\;\ln\frac{\rho_1}{\rho_2}=\frac{P_1-P_2}{K}$$$$\Rightarrow\;\rho_2=\frac{\rho_1}{e^\left(\frac{P_1-P_2}{K}\right)}=\frac{1003}{e^\left(\frac{-1.13\times10^8}{2.34\times10^9}\right)}=1052.62\;kg/m^3$$