Question

The Bulk of Ethanol, Mercury and water are given as $0.9,25$ and $2.2$ respectively in units of ${10}^{8}N{m}^{-2}.$ For a given value of pressure, the fractional compression in volume is $△V/V$. Which of the following statements about $△V/V$ for these three liquids is correct?

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

Answer 1

Answer: (D)

Ethanol > Water > Mercury

$\begin{array}{c}\text{Given, bulk modulus of ethanol}=0.9\times {10}^{8}N/m^2\\ \text{bulk modulus of mercury}=25\times {10}^{8}N/m^2\\ \text{bulk modulus of water}=2.2\times {10}^{8}N/m^2\\ \text{Also the pressure is fixed.}\end{array}$

$\begin{array}{c}\beta =-\frac{P}{\Delta V/V}\\ \therefore \frac{\Delta V}{V}=-\frac{P}{\beta }\\ \Rightarrow \frac{\Delta V}{V}\alpha +\frac{1}{\beta }\end{array}$

$\text{Also the pressure is fixed.}$

$\begin{array}{c}\text{Here - ve sign implies}\\ \text{there is decrease in}\\ \text{volume if pressure}\\ \text{is increased.}\end{array}$

$\begin{array}{c}\text{The order of}\frac{\Delta V}{V}\text{for ethanol, water}\\ \text{and mercury}\text{is as follows:}\\ \text{Ethanol}>\text{water}>\text{mercury}\end{array}$