Question

The deepest point in any ocean is in the Mariana Trench, which is about 11 km deep, in the Pacific. The pressure at this depth is huge, about 1.13 x 108 N/m2. (Take the bulk modulus of seawater to be 2.34 x 109 N/m2) (a) Calculate the change in volume of 0.900 m3 of seawater carried from the surface to this deepest point. 0.04346X m (b) The density of seawater at the surface is 1.03 x 103 kg/m3. Find its density at the bottom. 107kg/m3 (c) Is it a good approximation to think of water as incompressible? O Yes O No

Answer 1

Hey there!

The Bulk modulus can be given with the formula

Hey there! The Bulk modulus can be given with the formula B = -P/Delta V/V where, P is the pressure, Delta V/V is the ratio between change in volume Delta V to the initial volume V. We have V as 0.9 m^3 . P as 1.13 times 108 N/m^2 and B as 2.34 times 109 N/m^2 . Hence change in volume Delta V can be given as Delta V = -PV/B Delta V = -1.13 * 10^8 * 0.9/2.34 * 10^9 Hence Delta V = -0.04346 m^3 (negative)

where, P is the pressure, $\Delta V/V$ is the ratio between change in volume $\Delta V$ to the initial volume .

We have V as 0.9 m³ . P as 1.13 x 10⁸ N/m² and B as 2.34 x 10⁹ N/m² .

Hence change in volume $\Delta V$ can be given as

$\Delta V = -PV / B$

$\Delta V = -1.13 * 10^{8} * 0.9 / 2.34 * 10^{9}$

Hence

$\Delta V = -0.04346 m^{3}(negative)$

The calculation from your part was right. Except for the symbol :)

I hope the explanation helps... Feel free to comment and discuss further ... Cheers  :)