Question

Bulk modulus of a liquid is $ 2 \times 10^9 \, \text{Pa} $. Initially and final pressure are 1 atm and 5 atm respectively. Find the initial volume of the liquid if change in volume is 0.8 cm$^3$.

• A. \( 2 \times 10^3 \, \text{cm}^3 \)
• B. \( 4 \times 10^3 \, \text{cm}^3 \)
• C. \( 2 \times 10^{-4} \, \text{cm}^3 \)
• D. \( 4 \times 10^{-3} \, \text{cm}^3 \)

Hint:

Bulk modulus relates pressure change and volume change. Use this relationship to calculate the initial volume when the pressure change and final volume change are known.

Answer 1

The Correct Option is B

The bulk modulus \( B \) is defined as the ratio of the change in pressure to the relative change in volume: \[ B = -\frac{\Delta P}{\frac{\Delta V}{V}} \] Rearranging to find the initial volume \( V \): \[ V = -\frac{\Delta P}{B} \times \frac{\Delta V}{V} \] We are given: - \( B = 2 \times 10^9 \, \text{Pa} \) - \( \Delta P = P_2 - P_1 = 5 \, \text{atm} - 1 \, \text{atm} = 4 \, \text{atm} = 4 \times 10^5 \, \text{Pa} \) - \( \Delta V = 0.8 \, \text{cm}^3 \) Substituting the known values into the equation: \[ V = \frac{4 \times 10^5 \times 0.8}{2 \times 10^9} \] \[ V = 4 \times 10^3 \, \text{cm}^3 \] Thus, the initial volume is \( 4 \times 10^3 \, \text{cm}^3 \).