Calculation of Bulk Modulus of Water:

Given: Initial volume (V) = 100.0 litre, Final volume = 100.5 litre, Pressure increase (Δp) = 100.0 atm

Step 1: Calculate the change in volume. Since pressure increases, volume should decrease. The change in volume (compression) = 100.5 - 100.0 = 0.5 litre (magnitude)

Step 2: Convert pressure to SI units. Δp = $100.0 \times 1.013$ × 10⁵ Pa = $1.013 \times 10$⁷ Pa

Step 3: Apply the bulk modulus formula. B = -Δp/(ΔV/V) = Δp × V/|ΔV| B = ($1.013 \times 10$⁷ × 100.0)/0.5 B = $1.013 \times 10$⁷ × 200 B = $2.0 \times 10$⁹ Pa (or 2.0 GPa)

Comparison with Air: From Table 8.3, bulk modulus of air (at STP) = $1.0 \times 10$⁻⁴ GPa = $1.0 \times 10$⁵ Pa

Ratio: B_water/B_air = ($2.0 \times 10$⁹)/($1.0 \times 10$⁵) = $2.0 \times 10$⁴

Water has a bulk modulus approximately 20,000 times larger than air.

Explanation for Large Ratio:

The large difference arises from the molecular structure. Water molecules are bound with their neighbours through strong intermolecular forces (hydrogen bonding), making water relatively incompressible. In contrast, air molecules are very poorly coupled to their neighbours with negligible intermolecular forces, making gases highly compressible. As stated in the text, "Gases are about a million times more compressible than solids!" and liquids fall between solids and gases in terms of compressibility. The tight coupling between neighbouring atoms/molecules in liquids resists volume change under pressure, resulting in a much higher bulk modulus compared to gases.