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 $8\times {10}^{-12}{m}^2/N$ 1 atm = ${10}^{5}N/m^2$)

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

Answer 1

The correct option is A 8 x ${10}^{-7}$

$\text{Compressibility}\left(k\right)=\frac{1}{\beta \text{(bulk modulus)}}=8\times {10}^{-12}$

$\beta =\frac{1}{8\times {10}^{-12}}=\frac{dP}{\left(\frac{dV}{V}\right)}$

$\begin{array}{cc}\frac{dV}{v}& =8\times {10}^{-12}\times dP=8\times {10}^{-12}\times {10}^5=8\times {10}^{-7}\\ \frac{dV}{V}& =8\times {10}^{-7}\end{array}$