Question

Determine the volume contraction of a solid copper cube, $10cm$ on an edge, when subject to a hydraulic pressure of $7\times {10}^6$ $Pa.$ $K$ for copper $=140\times {10}^9$ Pa.

Answer 1

$x$ for copper $=\frac{\text{Volumeteric stain}}{\text{Volumeteric stain}}=\frac{P}{\Delta v/v}=\frac{pv}{\Delta v}$

$\Rightarrow \Delta v=\frac{pv}{x}=\frac{7\times {10}^6}{140\times {10}^9}\times {\left(\frac{10}{100}\right)}^3=\frac{1}{2}\times \frac{{10}^6}{{10}^{13}}=5\times {10}^{-8}{m}^3$