The Bulk modulus of a fluid is given by 25 GPa. What is the compressibility (Pa⁻¹) of that fluid?
Try it first: pick an option, then read the explanation.
Correct answer: B. 4 × 10⁻¹¹
Asked in SSC JE 29-01-2018 (Evening Shift)
Detailed Explanation
Compressibility measures the fractional decrease in volume per unit increase in hydrostatic pressure. It is defined mathematically as the reciprocal of the bulk modulus of elasticity.
Given \(K = 25\text{ GPa} = 25 \times 10^9\text{ Pa}\):
\[ \beta = \frac{1}{K} = \frac{1}{25 \times 10^9\text{ Pa}} = 0.04 \times 10^{-9}\text{ Pa}^{-1} = 4 \times 10^{-11}\text{ Pa}^{-1} \]
Why “4 × 10⁻¹¹” Is Correct
Dividing 1 by 25 × 10⁹ Pa gives 0.04 × 10⁻⁹ = 4 × 10⁻¹¹ Pa⁻¹, corresponding to option (b).
| Property | Formula | SI unit | Standard value (water, 4°C) |
|---|---|---|---|
| Density ρ | m/V | kg/m³ | 1000 kg/m³ |
| Specific weight γ | ρg | N/m³ | 9810 N/m³ |
| Specific gravity S | ρ/ρ_water | — | 1.0 |
| Specific volume v | 1/ρ | m³/kg | 0.001 m³/kg |
| Bulk modulus K | −dp/(dV/V) | Pa | 2.06 GPa |
| Compressibility β | 1/K | Pa⁻¹ | 4.85 × 10⁻¹⁰ Pa⁻¹ |
Why the Other Options Are Wrong
- A. 4 × 10⁻⁹: 4 × 10⁻⁹ results from using 0.25 GPa instead of 25 GPa.
- C. 25 × 10⁻⁹: 25 × 10⁻⁹ confuses the bulk modulus numerical value with its reciprocal.
- D. 25 × 10⁻¹¹: 25 × 10⁻¹¹ repeats the numerical prefix 25 without performing the reciprocal.
Key Point
Compressibility β = 1 / K; 1 / (25 × 10⁹) = 4 × 10⁻¹¹ Pa⁻¹.
Key Concepts for Students
- Bulk modulus K has dimensions of pressure [M L⁻¹ T⁻²].
- Compressibility β has dimensions [M⁻¹ L T²].
- Water has K ≈ 2.06 GPa and β ≈ 4.85 × 10⁻¹⁰ Pa⁻¹ under ambient conditions.
Practice more: this is question 34 in Properties of Fluid MCQs – Part 3. Try the whole set and check every answer instantly.