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

Answer:

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 / (∆V/V)

Where,

∆V/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 × 10-8 m3 = 5 × 10-2 cm-3

Therefore, the volume contraction of the solid copper cube is 5 × 10–2 cm–3.

Answer 2

Answer:

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 / (∆V/V)

Where,

∆V/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 × 10-8 m3 = 5 × 10-2 cm-3

Therefore, the volume contraction of the solid copper cube is 5 × 10–2 cm–3.