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Chapter 14: Q.5 (page 384)

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?

Short Answer

Expert verified

The mass of liquid is 2435 kg

Step by step solution

01

Given information

Diameter of vat = 1 m

so radius = 0.5 m

depth of liquid = 2.0 m.

The pressure at the bottom of the vat = 1.3 atm.

02

Explanation

Total pressure is calculated by

PTotal = Patm + hρg

PTotal = pressure at the bottom = 1.3 atm

Patm = atmospheric pressure = atm

h = depth of liquid = 2 m

ρ= density of liquid

g = gravitational acceleration

As given

PTotal=Patm+hρg=1.3atm⇒hρg=0.3atm

Substitute the value and find density

ρ=Phg=30397.52×9.8=1551kg·m-3

From basic mensuration find the volume of liquid

V=πr2h=3.14×(0.5)2×2=1.57m3

Now find the mass using Mass = Volume x Density

M=V×ρ=1.57×1551=2435kg

So the mass of liquid is 2435 kg.

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Most popular questions from this chapter

Cylinders A and B have equal heights. Cylinder A is filled with helium gas at 1.0 atm pressure and 0oC. The diameter of cylinder B is half that of cylinder A, and cylinder B is filled with glycerin. What is the ratio of the fluid mass in cylinder B to that in cylinder A?

It's possible to use the ideal-gas law to show that the density of the earth's atmosphere decreases exponentially with height. That is, ρ=ρ0exp⁡−z/z0, where Zis the height above sea level, ρ0is the density at sea level (you can use the Table 14.1value), and z0is called the scale height of the atmosphere.

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