Chapter 3: Q25E (page 611)

In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about $7 \times 10^{9}$ people)?

Short Answer

Expert verified

$6.39 \times 10^{- 6} m$ is the length of the side of the cube.

Step by step solution

Calculation of volume

Given data:

$T = 273 K, P = 1.01 \times 10^{5} P a, N = 7 \times 10^{9}$

Putting the equation;

$V = \frac{N \times K \times T}{P} = \frac{7 \times 10^{9} \times 1.381 \times 10^{- 23} \times 273}{1.01 \times 10^{5}} V = 2.61 \times 10^{- 16} m^{3}$

Calculation of length

Now the length is

$L^{3} = V L = \sqrt[3]{V} = \sqrt[3]{2.61 \times 10^{- 16}} = 6.39 \times 10^{- 6} m$

$6.39 \times 10^{- 6} m$ is the length of the side of the cube.

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In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about $7 \times 10^{9}$ people)?

Short Answer

Step by step solution

Calculation of volume

Calculation of length

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In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about7×109people)?

Short Answer

Step by step solution

Calculation of volume

Calculation of length

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physics of Motion

Circular Motion and Gravitation

Thermodynamics

Engineering Physics

Conservation of Energy and Momentum

Medical Physics

Study anywhere. Anytime. Across all devices.

In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about $7 \times 10^{9}$ people)?