   Chapter 10, Problem 56AP

Chapter
Section
Textbook Problem

A 1.5-m-long glass tube that is closed at one end is weighted and lowered to the bottom of a freshwater lake. When the tube is recovered, an indicator mark shows that water rose to within 0.40 m of the closed end. Determine the depth of the lake. Assume constant temperature.

To determine
The depth of the lake (h).

Explanation

Given info: The length of the glass tube ( L1 ) is 1.50 m. The length after the rise in water level ( L2 ) is 0.40 m. The initial pressure ( P1 ) is 1.013×105Pa . The final pressure is P2 .

Formula to calculate the final pressure is,

P2=P1+hρg (I)

• ρ is the density of water.
• g is the acceleration due to gravity.

From the Ideal gas law at constant temperature,

P2P1=V1V2 (II)

Formula to calculate the volume is,

V1=AL1V2=AL2 (III)

• A is the cross sectional area

From Equations (I), (II) and (III),

P1+hρgP1=L1L2

On Re-arranging,

h=(P1ρg)(L1L21)

Substitute 1

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