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.
Given data,
Length of an edge of the solid copper cube, l = 10 cm = 0.1 m
Hydraulic pressure, p = 7.0 × 106 Pa.
Bulk modulus of copper, B = 140 × 109 Pa
Bulk modulus, B = p/(Δv/v)
Where,
Δv/v = volumetric strain
Δv = change in volume
v = original volume
Δv = pv/B
Original volume of the cube, v = l3
∴ Δv = pl3/B
⇒ 7× 106 × (0.1)3 / (140× 109)
⇒ 5× 10-8m3 = 5× 10-2 cm-3
Therefore, the volume contraction of the solid copper cube is 5× 10-2 cm-3