At a depth of about 1030 m in the sea, the pressure has increased by 100 atmospheres (to 1.0 × 10⁷ N/m²). By how much has 1.0 m³ of water been compressed by this pressure? The bulk modulus of water is 2.3 × 10⁹ N/m². A) 2.3 × 10^-3 m³ B) 3.3 × 10^-3 m³ C) 4.3 × 10^-3 m³ D) 5.3 × 10^-3m³ E) 6.3 × 10^-3 m³

Question

Quizplus · Accepted Answer

We can use the formula for bulk modulus:

B = -V(dP/dV)

where B is the bulk modulus, V is the volume, and (dP/dV) is the pressure change per unit volume. Rearranging this formula, we can solve for the change in volume:

-dV/V = dP/B

We can plug in the given values:

dP = 100 atm = 10132500 N/m^2
B = 2.3 × 10^9 N/m^2
dV/V = -10132500/2.3 × 10^9 = -0.004403

So the compression of 1.0 m of water is:

dL = dV = (-0.004403) x (1.0 m) = -0.004403 m = 4.4 x 10^-3 m

Since the volume has decreased, the length has also decreased by the same amount. Thus, the answer is:

Choice C) 4.3 × 10^-3 m

At a Depth of About 1030 M in the Sea