Determine the estimated change in the density of water in the ocean at a depth of 400 m below the surface. The density of water at the surface is 1030 kg/m ^3 and the bulk modulus of water is 2 10^9 N/m ^2 .

Step-by-step solution

The change in pressure at a depth h is given by: P = g h The bulk modulus B relates the change in pressure to the fractional change in density: B = P Rearranging for the change in density : = P B = ^2 g h B Substituting the given values (using g = 9.8 m/s ^2 ): = (1030)^2 9.8 400 2 10^9 = 1060900 3920 2 10^9 = 4.158 10^9 2 10^9 2.08 kg/m ^3 Rounding to the nearest integer, the estimated change in density is 2 kg/m ^3 .