Determine the volume contraction of a solid copper cube, 10 cm on an edge when subjected to hydraulic pressure of `7 xx 10^(6)Pa`. Bulk modulus of copper = 140 Gpa.

Explanation

Length of an edge of the solid copper cube, l = 10 cm = 0.1 m
Hydraulic pressure, p = `7.0xx10^(6)` Pa
Bulk modulus of copper, B = `140xx10^(9)` Pa
Bulk modulus, `B=((p)/(DeltaV))/(V)`
Where,
`(DeltaV)/(V)` = Volumetric strain
`DeltaV` = Change in volume
V = Original volume.
`DeltaV=(pV)/(B)`
Original volume of the cube, `V=l^(3)`
`thereforeDeltaV=(pl^(3))/(B)`
`=(7xx10^(6)xx(0.1)^(3))/(140xx10^(9))`
`=5xx10^(-8)"m"^(3)`
`=5xx10^(-2)"cm"^(-3)`
Therefore, the volume contraction of the solid copper cube is `=5xx10^(-2)"cm"^(-3)`.