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Question

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


A
0.2cm3
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B
0.8cm3
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C
0.4cm3
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D
0.6cm3
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Solution

The correct option is C $$0.4cm^3$$
$$ \begin{array}{l} \text { Given, } \\ \text { compressibility of material }=4 \times 10^{-5} \text {per atm } \\ \text { volume }(v)=100 \mathrm{~cm}^{3}=10^{-4} \mathrm{~m}^{3} \\ \qquad \Delta v=? \end{array} $$
$$ \begin{array}{l} \text { we know, } \\ \text { Bulk modulus (B) }=\frac{1}{\text { compressibility }} \\ \qquad \begin{aligned} &=\frac{1}{4 \times 10^{5}} \\ \beta=& 0.25 \times 10^{5} \text { atm } \\ \beta &=1.013 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2} \\ \beta &=2.533 \times 10^{9} \mathrm{~N} / \mathrm{m} 2 \end{aligned} \end{array} $$
$$ \begin{array}{l} \text { and } \\ \qquad \begin{aligned} \beta &=\frac{P v}{\Delta v} \\ \Delta v &=\frac{P v}{\beta} \\ \Delta v &=\frac{1.013 \times 10^{7} \times 10^{-4}}{2.533 \times 10^{9}} \\ \Delta v &=0.4 \times 10^{-6} \mathrm{~m}^{3} \\ \Delta v &=0.4 \mathrm{~cm}^{3} \end{aligned} \end{array} $$

Physics

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