Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 20, Problem 27PQ

(a)

To determine

The most probable speed, average speed and rms speed for the oxygen gas.

(a)

Expert Solution
Check Mark

Answer to Problem 27PQ

The most probable speed of oxygen gas is 390m/s , average speed of the oxygen gas is 440m/s and rms speed for the oxygen gas is 480m/s .

Explanation of Solution

Write the expression for the most probable speed of gas molecules.

  vmp=2kBTm                                                                                                         (I)

Here, vmp is the most probable speed of the gas molecules, kB is the Boltzmann constant, T is the temperature and m is the mass of the molecule.

Write the expression for the average speed of gas molecules.

  vav=8kBTπm                                                                                                          (II)

Here, vav is the average speed of the gas molecules.

Write the expression for the rms speed of gas molecules.

  vrms=3kBTm                                                                                                        (III)

Here, vav is the average speed of the gas molecules.

Conclusion:

The mass of oxygen molecule is 32u , temperature of the gas is 22°C and Boltzmann constant is 1.38×1023J/K .

Convert mass 32u into kilogram.

  m=32u×1.66×1027kg1u=5.31×1026kg

Convert 22°C into Kelvin scale.

  22°C=(22+273)K=295K

Substitute 5.31×1026kg for m . 295K for T and 1.38×1023J/K for kB in equation (I) to get vmp .

  vmp=2(1.38×1023J/K)(295K)(5.31×1026kg)=390m/s

Substitute 5.31×1026kg for m . 295K for T and 1.38×1023J/K for kB in equation (II) to get vav .

  vav=8(1.38×1023J/K)(295K)π(5.31×1026kg)=440m/s

Substitute 5.31×1026kg for m . 295K for T and 1.38×1023J/K for kB in equation (III) to get vrms .

  vrms=3(1.38×1023J/K)(295K)(5.31×1026kg)=480m/s

Therefore, the most probable speed of oxygen gas is 390m/s , average speed of the oxygen gas is 440m/s and rms speed for the oxygen gas is 480m/s .

(b)

To determine

The most probable speed, average speed and rms speed for the nitrogen gas.

(b)

Expert Solution
Check Mark

Answer to Problem 27PQ

The most probable speed of nitrogen gas is 420m/s , average speed of the nitrogen gas is 470m/s and rms speed for the nitrogen gas is 510m/s .

Explanation of Solution

Rewrite equations from part(a).

Write the expression for the most probable speed of gas molecules.

  vmp=2kBTm                                                                                                         (I)

Here, vmp is the most probable speed of the gas molecules, kB is the Boltzmann constant, T is the temperature and m is the mass of the molecule.

Write the expression for the most average speed of gas molecules.

  vav=8kBTπm                                                                                                          (II)

Here, vav is the average speed of the gas molecules.

Write the expression for the rms speed of gas molecules.

  vrms=3kBTm                                                                                                        (III)

Here, vrms is the rms speed of the gas molecules.

Conclusion:

The mass of oxygen molecule is 28u .

Convert mass 28u into kilogram.

  m=28u×1.66×1027kg1u=4.65×1026kg

Substitute 4.65×1026kg for m . 295K for T and 1.38×1023J/K for kB in equation (I) to get vmp .

  vmp=2(1.38×1023J/K)(295K)(4.65×1026kg)=420m/s

Substitute 4.65×1026kg for m . 295K for T and 1.38×1023J/K for kB in equation (II) to get vav .

  vav=8(1.38×1023J/K)(295K)π(4.65×1026kg)=470m/s

Substitute 4.65×1026kg for m . 295K for T and 1.38×1023J/K for kB in equation (III) to get vrms .

  vrms=3(1.38×1023J/K)(295K)(4.65×1026kg)=510m/s

Therefore, the most probable speed of nitrogen gas is 420m/s , average speed of the nitrogen gas is 470m/s and rms speed for the nitrogen gas is 510m/s .

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Chapter 20 Solutions

Physics for Scientists and Engineers: Foundations and Connections

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