Question 13 of 13beginner🔧 ApplyNumerical3 marks

How much should the pressure on a litre of water be changed to compress it by 0.10%?

Correct Answer

Given:

  • Volume of water = 1 litre
  • Compression = 0.10% = 0.001 (fractional change)
  • Bulk modulus of water, B = 2.2×102.2 \times 10⁹ N m⁻² (from Example 8.5)

Formula: The bulk modulus is defined as: B = -p/(ΔV/V)

Calculation: Rearranging the formula: p = -B × (ΔV/V)

Since compression of 0.10% means ΔV/V = -0.001

p = -2.2×102.2 \times 10⁹ × (-0.001) p = 2.2×102.2 \times 10⁶ N m⁻² (or Pa)

Answer: The pressure should be changed by 2.2×102.2 \times 10⁶ Pa to compress water by 0.10%.

Exercise: EXERCISES | Q: 8.16
For More Understanding

Explanation

This question applies the bulk modulus concept from Section 8.5.3. The bulk modulus of water (2.2×102.2 \times 10⁹ N m⁻²) is provided in Example 8.5 within the context. The negative sign in the bulk modulus formula accounts for the fact that an increase in pressure causes a decrease in volume. For a 0.10% compression, the fractional volume change is -0.001, and substituting into the formula gives the required pressure change of 2.2×102.2 \times 10⁶ Pa.

Solution Steps

  1. Step 1: Identify bulk modulus of water from context: B = 2.2×102.2 \times 10⁹ N m⁻²

  2. Step 2: Convert percentage compression to fractional change: 0.10% = 0.001

  3. Step 3: Apply bulk modulus formula: B = -p/(ΔV/V)

  4. Step 4: Rearrange to find pressure: p = -B × (ΔV/V)

  5. Step 5: Substitute values: p = -2.2×102.2 \times 10⁹ × (-0.001) = 2.2×102.2 \times 10⁶ Pa

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