Determine the volume contraction of a solid copper cube, 10cm on … - Vidyadip

Question

Determine the volume contraction of a solid copper cube, 10cm on an edge, when subjected to a hydraulic pressure of $7.0 \times 10^6$ Pa.

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Answer

Given:$ L = 10cm = 0.1m K =$ bulk modulus of $Cu = 140 \times 10^9Pa P = 7 \times 10^6$
Pa $\Delta\text{V}=$ Volume contraction of solid copper cube = ?
$\therefore V = L^3 = (0.1)^3 = 0.001m^3$
. 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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