Question

Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 × 106 Pa.

Answer 1

Length of an edge of the solid copper cube, $l$ = $10 \;cm$ = $0.1 \;m$
Hydraulic pressure, $p$ = $7.0 \times 10^6$
Pa Bulk modulus of copper, $B$ = $140 \times 10^9$ $Pa$
Bulk modulus, $B$ = $\frac{P }{\frac{ \triangle V }{ V}}$
Where,
$\frac{\triangle V }{ V}$ = Volumetric strain
$\triangle V$ = Change in volume
$V$ = Original volume.
$\triangle V$ = $\frac{PV }{ B}$
Original volume of the cube,$V$ = $l^3$

$\therefore$ $\triangle V$ = $\frac{Pl^3 }{ B}$

= $\frac{7 \times 10^ 6 \times (0.1)^3 }{ 140 × 10 ^9}$

= $5 \times 10 ^{- 8}\; m^3$
= $5 \times 10^ {- 2}\; cm^{ - 3}$

Therefore, the volume contraction of the solid copper cube is $5 \times 10^ {- 2}\; cm^{ - 3}$.