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 \(5 \times 10^ {- 2}\; cm^{ - 3}\).