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Chapter 14: Q. 7 (page 384)

A 3.0-cm-diameter tube is held upright and filled to the top with mercury. The mercury pressure at the bottom of the tube— the pressure in excess of atmospheric pressure—is 50 kPa. How tall is the tube?

Short Answer

Expert verified

The height of tube is 0.38 m

Step by step solution

01

Given information

Diameter of tube =3.0-cm = 0.03 m

so radius is 0.015m

It is filled to the top with mercury.

The mercury pressure at the bottom of the tube—
the pressure in excess of atmospheric pressure—is 50 kPa.

02

Explanation

The pressure exerted by the mercury is given as

P = hρg ...............................(1)

p = 50 x 103 Pa

h = depth of liquid

ρ= density of liquid

g = gravitational acceleration

Calculate hρg , consider g = 9.8 m/s2 and density of mercury is 13.6 x103kg/m3

hρg= 50 x 103 Pa = h x 13.6 x103kg/m3 x 9.8 m/s2

h=50×103Pa(13.6×103kg/m3)×(9.8m/s2)h=0.38m

Height of tube = 0.38 m.

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Most popular questions from this chapter

One day when you come into physics lab you find several plastic hemispheres floating like boats in a tank of fresh water. Each lab group is challenged to determine the heaviest rock that can be placed in the bottom of a plastic boat without sinking it. You get one try. Sinking the boat gets you no points, and the maximum number of points goes to the group that can place the heaviest rock without sinking. You begin by measuring one of the hemispheres, finding that it has a mass 21gand a diameter of 8.0cm. What is the mass of the heaviest rock that, in perfectly still water, won't sink the plastic boat?

A 1.0-m-diameter vat of liquid is 2.0 m deep. The pressure at the bottom of the vat is 1.3 atm. What is the mass of the liquid in the vat?

The 1.0−m-tall cylinder in FIGURE P14.61 contains air at a pressure of 1atm. A very thin, frictionless piston of negligible mass is placed at the top of the cylinder, to prevent any air from escaping, then mercury is slowly poured into the cylinder until no more can be added without the cylinder overflowing. What is the height h of the column of compressed air?

Hint: Boyle's law, which you learned in chemistry, says p1V1=p2V2 for a gas compressed at constant temperature, which we will assume to be the case.

A 50-cm-thick layer of oil floats on a 120-cm-thick layer of water. What is the pressure at the bottom of the water layer?

A 3.0-cm-diameter tube is held upright and filled to the top with mercury. The mercury pressure at the bottom of the tube— the pressure in excess of atmospheric pressure—is 50 kPa. How tall is the tube?
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