JEE Main 2025 Apr 8 Shift 2, Physics Q22: Properties of Fluids

JEE Main2025Apr 8, Shift 2Physics

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of $0.8$ cm $^{3}$ . If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ______ litre. (Take 1 atm $= 1 0^{5}$ Pa)

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Solution

Bulk modulus is defined as $B = - \frac{d P}{d V / V}$ , so $V = - B \cdot \frac{d V}{d P}$ .

Change in pressure: $d P = (5 - 1) \times 1 0^{5} = 4 \times 1 0^{5}$ Pa.

Change in volume: $d V = - 0.8 \times 1 0^{- 6}$ m $^{3}$ (negative since volume decreases under compression).

Substituting: $V = - 2 \times 1 0^{9} \cdot \frac{- 0.8 \times 1 0 ^{- 6}}{4 \times 1 0 ^{5}} = \frac{2 \times 0.8 \times 1 0 ^{3}}{4 \times 1 0 ^{5}} = 4 \times 1 0^{- 3}$ m $^{3}$ .

Converting to litres: $4 \times 1 0^{- 3}$ m $^{3} = 4$ L.

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JEE Main 2025 Apr 8 Shift 2, Physics Q22: Properties of Fluids

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