A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of $0.8 \mathrm{~cm}^{3}$. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ______ litre. (Take $1 \mathrm{~atm}=10^{5} \mathrm{~Pa}$)

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Elasticity & SHM

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

)

Answer: 4

The bulk modulus relates the pressure change to the fractional volume change through

B = - \frac{Δ P}{Δ V / V}

, so

V = \frac{B ∣Δ V ∣}{Δ P}

. With

Δ P = 4 atm = 4 \times 1 0^{5} Pa

∣Δ V ∣ = 0.8 cm^{3} = 0.8 \times 1 0^{- 6} m^{3}

and

B = 2 \times 1 0^{9} Pa

V = \frac{2 \times 1 0 ^{9} \times 0.8 \times 1 0 ^{- 6}}{4 \times 1 0 ^{5}} = 4 \times 1 0^{- 3} m^{3}

. The initial volume of the liquid was

4

litre.

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Integer answer