A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to a change of volume of 0.8 cm3. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was \underline\hspace2cm litre. (Take 1 atm = 105 Pa)

Properties of Matter PYQ — JEE Main 2025 · 8 Apr · Shift 2 · Q71 with Solution

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Correct answer: 4

The bulk modulus $B$ is

B = -\frac{\Delta P}{\Delta V/V}

Taking magnitudes,

B = \frac{\Delta P\, V}{\Delta V}

So,

V = \frac{B\,\Delta V}{\Delta P}

Bulk modulus:
$B = 2\,\text{GPa} = 2\times 10^9\,\text{Pa}$
Pressure change: The liquid is compressed from $1\,\text{atm}$ to $5\,\text{atm}$ , so
$\Delta P = 4\,\text{atm} = 4\times 10^5\,\text{Pa}$
Change in volume:
$\Delta V = 0.8\,\text{cm}^3 = 0.8\times 10^{-6}\,\text{m}^3 = 8\times 10^{-7}\,\text{m}^3$

V = \frac{(2\times 10^9)(8\times 10^{-7})}{4\times 10^5}

First simplify numerator:

2\times 10^9 \cdot 8\times 10^{-7} = 16\times 10^2 = 1600

Thus,

V = \frac{1600}{4\times 10^5} = 4\times 10^{-3}\,\text{m}^3

Since

1\,\text{m}^3 = 1000\,\text{L}

we get

V = 4\times 10^{-3}\times 1000 = 4\,\text{L}

The initial volume of the liquid was

\boxed{4}

litre.