Final answer:
At a depth of 7 km in the ocean, the change in specific volume is -0.307 m^3/kN, the specific volume is 9.743 kN/m^3, and the specific weight is 97.43 kN/m^3.
Step-by-step explanation:
To determine the change in specific volume, we can use the formula:
Δv = -v * ΔP / K,
where Δv is the change in specific volume, v is the specific volume at the surface, ΔP is the change in pressure, and K is the bulk modulus. In this case, the depth is 7 km and the pressure at that depth is 71.6 MPa.
With the given values, we can calculate the change in specific volume:
Δv = -10.05 kN/m^3 * (71.6 MPa - 0) / (2.43 GPa) = -0.307 m^3/kN.
To find the specific volume at 7 km depth, we can use the formula:
v = v0 + Δv,
where v0 is the specific volume at the surface. Using the given values, we get:
v = 10.05 kN/m^3 + (-0.307 m^3/kN) = 9.743 kN/m^3.
The specific weight at 7 km depth can be calculated using the formula:
w = γ * v,
where w is the specific weight, γ is the specific weight at the surface, and v is the specific volume at the given depth. Substituting the values, we get:
w = 10.05 kN/m^3 * 9.743 kN/m^3 = 97.43 kN/m^3.