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If compressibility of material is $4 \times 10^{-5}$ per atm, pressure is 100 atm and volume is $100 \mathrm{~cm}^3$, then find $\Delta \mathrm{V}=$ ?
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The correct answer is:
$0.4 \mathrm{~cm}^3$
$\because$ Compressibility
$|\beta|=\frac{1}{\mid \text { Bulk modulus of elasticits } \mid}$
$|\beta|=\frac{\Delta \mathrm{pV}}{\Delta \mathrm{V}}$
or $\quad \beta=\frac{l}{\left(\frac{\Delta \mathrm{pV}}{\Delta \mathrm{V}}\right)}=\frac{\Delta \mathrm{V}}{\Delta \mathrm{pV}}$
$\begin{aligned} \therefore \Delta \mathrm{V}=\beta(\Delta \mathrm{p} . \mathrm{V}) & =4 \times 10^{-5}\left(100 \times 100 \times 10^{-6}\right) \\ & =0.4 \times 10^{-6} \mathrm{~m}^3=0.4 \mathrm{~cm}^3\end{aligned}$
$|\beta|=\frac{1}{\mid \text { Bulk modulus of elasticits } \mid}$
$|\beta|=\frac{\Delta \mathrm{pV}}{\Delta \mathrm{V}}$
or $\quad \beta=\frac{l}{\left(\frac{\Delta \mathrm{pV}}{\Delta \mathrm{V}}\right)}=\frac{\Delta \mathrm{V}}{\Delta \mathrm{pV}}$
$\begin{aligned} \therefore \Delta \mathrm{V}=\beta(\Delta \mathrm{p} . \mathrm{V}) & =4 \times 10^{-5}\left(100 \times 100 \times 10^{-6}\right) \\ & =0.4 \times 10^{-6} \mathrm{~m}^3=0.4 \mathrm{~cm}^3\end{aligned}$
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