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Here, ρ=1.00 g/cm^3
Compressibility "k" = 0.00005 per atm
= 0.00005 / 10^6 dyne/cm^2
= 5 × 10^−11 cm^2/dyne
Depth "h" = 3 km = 3 × 1000 × 100 cm
= 3 ×10^5 cm
Increases in pressure at depth 4 km of water is
ΔP = hρg = ( 3 x 10^5) × 1 × 980 dyne/cm^2
If ρ' is density at depth h, then
ρ' = ρ (1 + kΔP) = 1 [1 + (5×10^−11) × (3 × 10^5 × 980)]
ρ' = 1 + (5 × 10^−11 x 2940 x 10^5
ρ' = 1 + 14,700 x 10^-11+5
ρ' = 1 + 14,700 x 10^-6
ρ' = 1 +1.4 x 10^4-6
ρ' = 1 + 1.4 x 10^-2
ρ' = 1 + 0.0014 = 1.014 g /cm^3
Thus the density of the sea water at 3 km depth is 1.014 g /cm^3
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