Question
Determine the volume contraction of a solid copper cube, 10cm on an edge, when subjected to a hydraulic pressure of 7.0 × 106 Pa.
✓
Answer
Given: L = 10cm = 0.1m
K = bulk modulus of Cu
= 140 × 109 Pa
P = 7 × 106 Pa
$\Delta\text{V}=$ Volume contraction of solid copper cube = ?
$\therefore$ V = L3 = (0.1)3 = 0.001m3.
Using formula, $\text{K}-\frac{\text{P}}{\big(\frac{\Delta\text{V}}{\text{V}}\big)}$
We get $\Delta\text{V}=-\frac{\text{PV}}{\text{K}}=\frac{7\times10^6\times0.001}{140\times10^9}\text{m}^3$
$=-\frac{1}{20}\times10^{-6}\text{m}^3$
$=-0.05\times10^{-6}\text{m}^3$
$=-5\times10^{-2}\text{cm}^3$
Here negative sign shows volume contraction.
K = bulk modulus of Cu
= 140 × 109 Pa
P = 7 × 106 Pa
$\Delta\text{V}=$ Volume contraction of solid copper cube = ?
$\therefore$ V = L3 = (0.1)3 = 0.001m3.
Using formula, $\text{K}-\frac{\text{P}}{\big(\frac{\Delta\text{V}}{\text{V}}\big)}$
We get $\Delta\text{V}=-\frac{\text{PV}}{\text{K}}=\frac{7\times10^6\times0.001}{140\times10^9}\text{m}^3$
$=-\frac{1}{20}\times10^{-6}\text{m}^3$
$=-0.05\times10^{-6}\text{m}^3$
$=-5\times10^{-2}\text{cm}^3$
Here negative sign shows volume contraction.
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