Question

The deepest point in any ocean is in the Mariana Trench, which is about 11 km deep, in the Pacific. The pressure at this depth is huge, about 1.13 108 N/m2. (Take the bulk modulus of seawater to be 2.34 109 N/m2) (a) Calculate the change in volume of 0.9 m3 of seawater carried from the surface to this deepest point. (b) The density of seawater at the surface is 1.03 103 kg/m3. Find its density at the bottom

Answer 1

Answer:

a)  ΔV = - 4.346 10⁻² , b)   ρ’= 1.082 10³ kg / m³

Explanation:

The volume module is defined as the ratio of the pressure and the unit deformation, with a negative sign, for the module to be positive

       B = - P / (ΔV/V)

a) The ΔV volume change

     ΔV/V = -P / B

     ΔV = - P V / B

     ΔV = - 1.13 10⁸ 0.9 /2.34 10⁹

     ΔV = - 4.346 10⁻²

b) Density at the bottom of the sea

On the surface

     ρ = m / V

      m = ρ V

     m = 1.03 10³ 0.9

     m = 0.927 10³ kg

Body mass does not change with depth

Deep down

    ρ’= m / V’

    ΔV = 4.346 10⁻²

    $V_{f}$- V₀ = 4,346 10⁻²

    $V_{f}$ = 0.0436 + Vo

    $V_{f}$= -0.04346 + 0.9

    $V_{f}$ = 0.85654 m³

    ρ’= 0.927 10³ / 0.85654

    ρ’= 1.082 10³ kg / m³