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


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