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Chapter 1: Q52P (page 393)

The deepest point known in any of the earth鈥檚 oceans is in the Marianas Trench, 10.92 km deep. (a) Assuming water is incompressible, what is the pressure at this depth? Use the density of seawater. (b) The actual pressure is1.16脳108Pa ; your calculated value will be less because the density actually varies with depth. Using the compressibility of water and the actual pressure, find the density of the water at the bottom of the Marianas Trench. What is the percent change in the density of the water?

Short Answer

Expert verified

(a)1.10脳108Pa

(b)1.08脳103kg/m3

Step by step solution

01

Given information:

p=1.16脳108Pa,h=10.92脳103m

02

Concept/Formula used:

The variation in pressure due to depth is given by

P=P0+蚁gh

Where,

蚁Is density of fluid and

h Is depth

03

Pressure calculation in depth

(a)

Density of seawater蚁=1.03脳103kg/m3

p0=pair+蚁gh=1.01脳105Pa+1.03脳103kg/m39.80m/s210.92脳103m=1.10脳108Pa
04

Density of water at bottom

(b)

螖V=鈭�(螖p)V0尾=鈭�1.10脳108Pa1.00m32.2脳109Pa=鈭�鈭�0.050m3鈭�V=V0+螖V=1鈭�0.05=0.950m3蚁=mV=1.03脳103Kg0.950m3=1.08脳103kg/m3

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