Question

The pressure required to decrease the volume of 4000 cc of water by 0.05%: (Bulk modulus of water = \( 2.2 \times 10^9 \, \text{Nm}^{-2} \))

• A. \( 11 \times 10^6 \, \text{Nm}^{-2} \)
• B. \( 5 \times 10^5 \, \text{Nm}^{-2} \)
• C. \( 2.2 \times 10^6 \, \text{Nm}^{-2} \)
• D. \( 1.1 \times 10^6 \, \text{Nm}^{-2} \)

Hint:

The bulk modulus gives a measure of how much pressure is required to change the volume of a substance. A higher bulk modulus means the substance is more resistant to volume changes under pressure.

Answer 1

The Correct Option is D

Step 1: Understand the bulk modulus formula.
The bulk modulus \( B \) relates the pressure change \( \Delta P \) to the fractional change in volume \( \frac{\Delta V}{V} \) using the following formula: \[ B = \frac{\Delta P}{\frac{\Delta V}{V}} \] Where:
\( B \) is the bulk modulus,
\( \Delta P \) is the pressure change,
\( \frac{\Delta V}{V} \) is the fractional change in volume.

Step 2: Rearrange the formula to solve for \( \Delta P \).
We can solve for \( \Delta P \) by multiplying both sides of the equation by \( \frac{\Delta V}{V} \): \[ \Delta P = B \times \frac{\Delta V}{V} \]
Step 3: Substitute the given values into the formula.
Given:
Bulk modulus \( B = 2.2 \times 10^9 \, \text{Nm}^{-2} \),
Fractional change in volume \( \frac{\Delta V}{V} = 0.05% = 0.0005 \).
Substitute these values into the equation for \( \Delta P \): \[ \Delta P = (2.2 \times 10^9) \times 0.0005 \]
Step 4: Perform the calculation.
\[ \Delta P = 1.1 \times 10^6 \, \text{Nm}^{-2} \] Thus, the pressure required to decrease the volume is \( 1.1 \times 10^6 \, \text{Nm}^{-2} \). % Correct Answer Correct Answer:} (4) \( 1.1 \times 10^6 \, \text{Nm}^{-2} \)