First slide

Elastic Modulie

Question

If compressibility of a material is 4×10^-5 per atm. If pressure is 100 atm and volume is 100 cm³, then find the value of $ΔV .$

Moderate

A

0.4 cm³
B

0.8 cm³
C

0.6 cm³
D

0.2 cm³

Solution

$Given, k = 4 \times 10^{- 5} per atm$
$\begin{array}{l} p = 100 atm \\ and V = 100 {cm}^{3} \\ = 100 \times 10^{- 8} m^{3} \\ ∵ Compressibility = \frac{1}{Bulk modulus of elasticity} \\ k = \frac{1}{Δp \frac{V}{ΔV}} = \frac{ΔV}{ΔpV} \\ ∴ ΔV = k (ΔpV) = 4 \times 10^{- 5} (100 \times 100 \times 10^{- 8}) \\ = 0.4 \times 10^{- 8} m^{3} = 0.4 {cm}^{3} \end{array}$

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