Question

If compressibility of material is $4\times {10}^{-5}$ per atm, pressure is $100$ atm and volume $100c{m}^3$ find a $\Delta V=$ ?

• A. $0.2c{m}^3$
• B. $0.8c{m}^3$
• C. $0.4c{m}^3$
• D. $0.6c{m}^3$

Answer 1

The correct option is C $0.4c{m}^3$

$\begin{array}{c}\text{Given,}\\ \text{compressibility of material}=4\times {10}^{-5}\text{per atm}\\ \text{volume}\left(v\right)=100{cm}^3={10}^{-4}{m}^3\\ \Delta v=?\end{array}$

$\begin{array}{c}\text{we know,}\\ \text{Bulk modulus (B)}=\frac{1}{\text{compressibility}}\\ \begin{array}{cc}& =\frac{1}{4\times {10}^5}\\ \beta =& 0.25\times {10}^5\text{atm}\\ \beta & =1.013\times {10}^{5}N/m^2\\ \beta & =2.533\times {10}^{9}N/m2\end{array}\end{array}$

$\begin{array}{c}\text{and}\\ \begin{array}{cc}\beta & =\frac{Pv}{\Delta v}\\ \Delta v& =\frac{Pv}{\beta }\\ \Delta v& =\frac{1.013\times {10}^7\times {10}^{-4}}{2.533\times {10}^9}\\ \Delta v& =0.4\times {10}^{-6}{m}^3\\ \Delta v& =0.4{cm}^3\end{array}\end{array}$