Chapter 14: Q. 2 (page 383)

Cylinders A and B have equal heights. Cylinder A is filled with helium gas at 1.0 atm pressure and 0^oC. 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?

Short Answer

Expert verified

The ratio is 1760: 1

Step by step solution

Given information

Cylinder A is filled with helium gas at 1.0 atm pressure and 0^oC.

The diameter of cylinder B is half that of cylinder A,

Cylinder B is filled with glycerin.

Explanation

The density is defined as Mass/Volume

ρ =M/V

Volume of cylinder is

$V = π r^{2} h$

$M_{A} = ρ_{A} \times V_{A} = ρ_{A} \times π r_{A}^{2} h M_{B} = ρ_{B} \times V_{B} = ρ_{B} \times π r_{B}^{2} h$

As given

$r_{B} = \frac{r_{A}}{2}$

Density of helium gas, ρ_A=0.179 kg/m³
Density of glycerine, ρ_B=1260 kg/m³

Now substitute values

$\frac{M_{B}}{M_{A}} = \frac{ρ_{B} \times π r_{B}^{2} h}{ρ_{A} \times π r_{A}^{2} h} = \frac{ρ_{B} \times r_{B}^{2}}{ρ_{A} \times r_{A}^{2}} \frac{M_{B}}{M_{A}} = \frac{1260 \times {(\frac{r_{A}}{2})}^{2}}{0.179 \times r_{A}^{2}} = 1760 : 1$

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Cylinders A and B have equal heights. Cylinder A is filled with helium gas at 1.0 atm pressure and 0^oC. 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?

Short Answer

Step by step solution

Given information

Explanation

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Cylinders A and B have equal heights. Cylinder A is filled with helium gas at 1.0 atm pressure and 0oC. 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?

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Linear Momentum

Waves Physics

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Magnetism

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Study anywhere. Anytime. Across all devices.

Cylinders A and B have equal heights. Cylinder A is filled with helium gas at 1.0 atm pressure and 0^oC. 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?