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 _______ litre.
(Take 1 atm = 10⁵ Pa)

Solution

Physics sir · 3 steps

Bulk modulus is pressure change over fractional volume change, so solve it for V and keep SI units throughout.

1. Pressure change. The pressure rises from 1 atm to 5 atm, so Δ P = 4 atm = 4 × 10⁵ Pa. The volume change is Δ V = 0.8 cm³ = 0.8 × 10⁻⁶ m³.

   B = (Δ P)/(Δ V / V) ⇒ V = (B Δ V)/(Δ P)

2. Put in numbers. V = ((2 × 10⁹) × (0.8 × 10⁻⁶))/(4 × 10⁵) = 1600/(4 × 10⁵) = 4 × 10⁻³ m³.
3. So. Since 1 m³ = 1000 litre, the initial volume is 4 litre.

The common slip: 3.2. Using the final pressure 5 atm instead of the change 4 atm gives 3.2 litre, not 4.

The idea to keep. In bulk modulus problems, use the change in pressure, not the final pressure. Convert everything to SI first, then convert the volume to litres at the end.

Answer from the NTA final answer key. Solution by PrepWiser.