We are given the compressibility of water as 4 × 10⁻⁵ per unit atmospheric pressure, which means the fractional decrease in volume per unit increase in pressure is 4 × 10⁻⁵.
Given Data:
Initial volume of water, V = 100 cc
Change in pressure, ΔP = 100 atm
Compressibility, k = 4 × 10⁻⁵ per atm
Formula Used:
The volume change due to pressure is given by the relation:
ΔV = k × V × ΔP
where:
ΔV is the change in volume,
k is the compressibility,
V is the initial volume,
ΔP is the change in pressure.
Substituting the values:
ΔV = (4 × 10⁻⁵) × (100) × (100)
ΔV = 4 × 10⁻⁵ × 10⁴
ΔV = 4 × 10⁻¹ cc
Final Answer:
The change in volume is 0.4 cc, which corresponds to option (d) 4 × 10⁻¹ cc.
