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

The length of the edge of a copper cube is 10 cm and the applied hydraulic pressure is 7.0× 10 6  Pa.

The bulk modulus of copper is 140× 10 9  Pa.

The bulk modulus of copper is given by the equation,

β= Δp ΔV V ΔV= ΔpV β = Δp L 3 β

Substituting the values in the above equation, we get:

ΔV= 7.0× 10 6  Pa ( 10× 10 −2  m ) 3 140× 10 9  Pa =5× 10 −8   m 3 =5× 10 −8   m 3 × 10 6   cm 3 1  m 3 ≈0.058  cm 3

Hence, the volume contraction of the solid copper is 0.058  cm 3 .