Question

A copper bar of length $L$ and area of cross section $A$ is placed in a chamber at atmospheric pressure. If the chamber is evacuated, the percentage change in its volume will be (compressibility of copper is $8\times {10}^{-12}{m}^2/N$ and $1atm={10}^{5}N/m)$

• A. $8\times {10}^{-7}$
• B. $8\times {10}^{-5}$
• C. $1.25\times {10}^{-4}$
• D. $1.25\times {10}^{-5}$

Answer 1

The correct option is B $8\times {10}^{-5}$

$B=-V\frac{\Delta P}{\Delta V}$
Compressibility is given as inverse of Bulk modulus.
Thus, $8\times {10}^{-12}=-\frac{\frac{\Delta V}{V}}{\Delta P}$
or, $-\frac{\Delta V}{V}=8\times {10}^{-12}\times (0-{10}^5)=-8\times {10}^{-7}$

Therefore percentage change would be

$-\frac{\Delta V}{V}\times 100=-8\times {10}^{-5}$