The volume contraction of a solid copper cube of edge length 10 cm,
when subjected to a hydraulic pressure of \( 7 \times 10^6 \) Pa,
would be _____ mm\(^3\).
(Given bulk modulus of copper = \( 1.4 \times 10^{11} \) N m\(^{-2}\))
Show Hint
For bulk modulus calculations, ensure proper unit conversions between volume in cm\(^3\), m\(^3\), and mm\(^3\).
The bulk modulus is defined as:
\[
B = - \frac{\Delta P}{\frac{\Delta V}{V}}
\]
Rearranged, the change in volume is:
\[
\Delta V = \frac{\Delta P}{B} V
\]
The initial volume of the cube is:
\[
V = (10 { cm})^3 = 1000 { cm}^3
\]
Converting to \( m^3 \):
\[
V = 10^{-3} { m}^3
\]
Substituting the given values:
\[
\Delta V = \frac{(7 \times 10^6)}{1.4 \times 10^{11}} \times 10^{-3}
\]
This results in a change in volume of:
\[
\Delta V = 5 \times 10^{-8} { m}^3
\]
Converting to \( mm^3 \):
\[
\Delta V = 10.0 { mm}^3
\]
