Effect of pressure on bulk modulus Choose the correct statement about how the bulk modulus of a fluid changes as pressure increases.

Introduction:
The bulk modulus (K) measures a fluid’s resistance to uniform compression. This question assesses understanding of compressibility trends with pressure, especially in liquids where compressibility is small but not zero.

Given Data / Assumptions:

• Fluid is uniform and isotropic under hydrostatic compression.
• Temperature effects are neglected for simplicity.
• Small to moderate pressure ranges typical of engineering systems.

Concept / Approach:
Bulk modulus is defined as K = -V * (dP / dV) = dP / (dV/V). Physically, higher K means the fluid is “stiffer” (less compressible). For many liquids, as pressure increases, the incremental compressibility decreases, so the slope dP/d(ΔV/V) rises; equivalently, K increases with pressure. Although the rate of increase may be mild, the trend is well established for water and most engineering liquids over practical pressure ranges.

Step-by-Step Solution:

Verification / Alternative check:
Engineering handbooks show water’s bulk modulus near 2.1 GPa at atmospheric conditions and larger at several hundred bars, confirming the positive dependence on pressure.

Why Other Options Are Wrong:

• remains same: ignores observed pressure dependence.
• decreases: opposite of typical liquid behavior.
• first increases then decreases / first decreases then increases: no such general pattern for ordinary liquids in the common range.

Common Pitfalls:
Confusing compressibility (which decreases with pressure) with bulk modulus (its reciprocal trend). Also, extrapolating gas behavior directly to liquids without checking property models.

Final Answer:
increases