Question

The Bulk moduli of Ethanol, Mercury and water are given as $0.9,25$ and $2.2$ respectively in units of ${10}^9/N{m}^{-2}$. For a given value of pressure, the fractional compression in volume is $\frac{\Delta V}{V}$. Which of the following statements about $\frac{\Delta V}{V}$ for these three liquids is correct?

• A. $Mercury>Ethanol>Water$
• B. $Ethanol>Mercury>Water$
• C. $Water>Ethanol>Mercury$
• D. $Ethanol>Water>Mercury$

Answer 1

The correct option is D $Ethanol>Water>Mercury$

The bulk modulus of elasticity for a fluid is given by $K=\frac{\Delta P}{\Delta V/V}$
Thus higher is the value of $K$, lower is the value of $\frac{\Delta V}{V}$
Hence, the order will depend on their bulk modulus of elasticity.
Hence, it follows the order,
$Mercury<Water<Ethanol$