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

Answers (1)
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.