Determine the volume contraction of a solid copper cube, $10 ext{ cm}$ on an edge, when subjected t

Question

Determine the volume contraction of a solid copper cube, $10	ext{ cm}$ on an edge, when subjected to a hydraulic pressure of $7.0 	imes 10^6	ext{ Pa}$. (Bulk modulus of copper $= 140	ext{ GPa}$)

Professor PC Thomas Classes · Answer

Original volume $V = (0.10	ext{ m})^3 = 10^{-3}	ext{ m}^3$. Contraction $\Delta V = \frac{\Delta P \cdot V}{B} = \frac{7.0 	imes 10^6 	imes 10^{-3}}{140 	imes 10^9} = \frac{7 	imes 10^3}{140 	imes 10^9} = 5 	imes 10^{-8}	ext{ m}^3$. In $	ext{cm}^3$, this is $5 	imes 10^{-8} 	imes 10^6 = 0.05	ext{ cm}^3$.