The Bulk moduli of Ethanol, Mercury and water are given as 0.9, 25 and 2.2 respectively in units of 109 Nm−2. For a given value of pressure, the fractional compression in volume is (Δ V)/(V). Which of the following statements about (Δ V)/(V) for these three liquids is correct? (a) Ethanol > Water > Mercury (b) Water > Ethanol > Mercury (c) Mercury > Ethanol > Water (d) Ethanol > Mercury > Water

Answer: (a). Fractional compression (Δ V)/(V) = P/B, so for the same P, (Δ V)/(V) ∝ 1/B. B: ethanol 0.9 water > mercury. So the answer is (a).

The Bulk moduli of Ethanol, Mercury and water are given as 0.9, 25… | JEE Main 2014 (11 Apr, Shift 1)

Q22JEE Main 2014 · 11 APR · SHIFT 1Easy

Bulk Modulus & Compressibility

The Bulk moduli of Ethanol, Mercury and water are given as 0.9, 25 and 2.2 respectively in units of 109 Nm−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?

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Answer: (a)

Fractional compression $\frac{\Delta V}{V} = \frac{P}{B}$ , so for the same $P$ , $\frac{\Delta V}{V} \propto \frac{1}{B}$ .
$B$ : ethanol $0.9$ < water $2.2$ < mercury $25$ (in $10^9\ \text{N m}^{-2}$ ).
Smallest $B$ compresses most: ethanol > water > mercury.
So the answer is (a).

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Bulk Modulus & Compressibility question from JEE Main 2014 (11 Apr, Shift 1)

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