Q15  Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of $7.0 \times 10 ^ 6 Pa$

S Sayak

Bulk modulus of copper is $B_{C}=140GPa=1.4\times 10^{11}Nm^{-2}$

Edge of copper cube is s = 10 cm = 0.1 m

Volume Of copper cube is V = s3

V = (0.1)3

V = 0.001 m3

Hydraulic Pressure applies is $P=7.0\times 10^{6}Pa$

From the definition of bulk modulus

$\\B_{C}=\frac{P}{\frac{\Delta V}{V}}\\ \frac{\Delta V}{V}=\frac{P}{B_{C}}\\ \frac{\Delta V}{V}=\frac{7\times 10^{6}}{1.4\times 10^{11}} \frac{\Delta V}{V}=5\times 10^{-5}$

The volumetric strain is $5\times 10^{-5}$

Volume contraction will be

$\\\Delta V=Volumetric\ Strain\times Initial\ Volume\\ \Delta V=5\times 10^{-5}\times 10^{-3}\\ \Delta V=5\times 10^{-8}m^{3}\\ \Delta V=5\times 10^{-2}cm^{3}$

The volume contraction has such a small value even under high pressure because of the extremely large value of bulk modulus of copper.

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