Question

The fractional change in the volume of a glass slab when subjected to hydraulic pressure of 14 atm is (Bulk modulus of glass = \( 40 \times 10^9 \, \text{Nm}^{-2} \))

• A. \( 1.44 \times 10^{-5} \)
• B. \( 3.54 \times 10^{-5} \)
• C. \( 2.74 \times 10^{-5} \)
• D. \( 3.14 \times 10^{-5} \)

Hint:

For pressure-volume relationship, use the formula \( \Delta V = \frac{\Delta P}{B} \) where \( B \) is the bulk modulus.

Answer 1

The Correct Option is B

The fractional change in volume is given by the formula: \[ \Delta V = \frac{\Delta P}{B} \] Where: - \( \Delta P \) is the pressure, - \( B \) is the bulk modulus. We are given: - \( \Delta P = 14 \, \text{atm} = 14 \times 1.013 \times 10^5 \, \text{Pa} \), - \( B = 40 \times 10^9 \, \text{Nm}^{-2} \). The fractional change in volume is: \[ \Delta V = \frac{14 \times 1.013 \times 10^5}{40 \times 10^9} \approx 3.54 \times 10^{-5} \] Thus, the fractional change in volume is \( \boxed{3.54 \times 10^{-5}} \).