The bulk moduli of ethanol,mercury,and water | vedclass

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Question

(A) The bulk modulus $B$ is defined as $B = -\frac{\Delta P}{\Delta V/V}$,which implies the fractional compression $\frac{\Delta V}{V} = \frac{\Delta

Vedclass · Accepted Answer

Ethanol $>$ Water $>$ Mercury

Vedclass · Answer

(A) The bulk modulus $B$ is defined as $B = -\frac{\Delta P}{\Delta V/V}$,which implies the fractional compression $\frac{\Delta V}{V} = \frac{\Delta P}{B}$.For a constant pressure change $\Delta P$,the fractional compression $\frac{\Delta V}{V}$ is inversely proportional to the bulk modulus $B$ (i.e.,$\frac{\Delta V}{V} \propto \frac{1}{B}$).Given bulk moduli:$B_{	ext{ethanol}} = 0.9 	imes 10^9 \, Nm^{-2}$$B_{	ext{water}} = 2.2 	imes 10^9 \, Nm^{-2}$$B_{	ext{mercury}} = 25 	imes 10^9 \, Nm^{-2}$Since $B_{	ext{ethanol}} $\left( \frac{\Delta V}{V} ight)_{	ext{ethanol}} > \left( \frac{\Delta V}{V} ight)_{	ext{water}} > \left( \frac{\Delta V}{V} ight)_{	ext{mercury}}$Therefore,the correct order is Ethanol $>$ Water $>$ Mercury.

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