Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Question
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Chapter 17, Problem 27P

(a)

To determine

The rms speed of H2.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

The escape speed of gas molecules is 60km/s.

The temperature at the Jupiter surface is 150°C.

Formula used:

Write the expression for the rms speed of the molecule.

  vrms=3RTM ........ (1)

Here, vrms is the root mean square value o the molecule, R is the gas constant, T is the temperature and M is the molecular mass of the molecule.

Write the expression for the relation between Celsius and kelvin.

  T(K)=T(°C)+273.15 ........ (2)

Substitute 150°C in equation (2).

  T(K)=150°C+273.15T(K)=123.15K

Calculation:

Substitute 8.314J/molK for R , 123.15K for T and 2×103kg/mol for M in equation (1).

  vrms= 3( 8.314 J mol K )( 123.15K ) 2× 10 3 kg/ mol vrms=1.24km/s

Conclusion:

The rms speed of the H2 molecule is 1.24km/s

(b)

To determine

The root mean square speed of O2.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given:

The escape speed of gas molecules is 60km/s.

The temperature at the Jupiter surface is 150°C.

Formula used:

Write the expression for the rms speed of the molecule.

  vrms=3RTM

Here, vrms is the root mean square value of the molecule, R is the gas constant, T is the temperature and M is the molecular mass of the molecule.

Calculation:

Substitute 8.314J/molK for R , 123.15K for T and 32×103kg/mol for M in equation (1).

  vrms= 3( 8.314J/ molK )( 123.15K ) 32× 10 3 kg/ mol vrms=310m/s

Conclusion:

The root mean square speed of oxygen molecule is 310m/s .

(c)

To determine

The root mean square speed of CO2 .

(c)

Expert Solution
Check Mark

Explanation of Solution

Given:

The escape speed of gas molecules is 60km/s.

The temperature at the Jupiter surface is 150°C.

Formula used:

Write the expression for the rms speed of the molecule.

  vrms=3RTM

Here, vrms is the root mean square value of the molecule, R is the gas constant, T is the temperature and M is the molecular mass of the molecule.

Calculation:

Substitute 8.314J/molK for R , 123.15K for T and 44×103kg/mol for M in equation (1).

  vrms= 3( 8.314J/ molK )( 123.15K ) 44× 10 3 kg/ mol vrms=264m/s

Conclusion:

The root mean square speed of the CO2 molecule is 264m/s.

(d)

To determine

The elements found in the atmosphere of the Jupiter.

(d)

Expert Solution
Check Mark

Explanation of Solution

Given:

The escape speed of gas molecules is 60km/s.

The temperature at the Jupiter surface is 150°C.

Formula used:

Write the expression for the rms speed of the molecule.

  vrms=3RTM

Here, vrms is the root mean square value of the molecule, R is the gas constant, T is the temperature and M is the molecular mass of the molecule.

Calculate 20% of escape velocity for Jupiter.

  v=15vescape ........ (3)

Here, vescape is the escape velocity of the Jupiter.

Calculation:

Substitute 60km/s for vescape in equation (3).

  v=15(60km/s)v=12km/s

Conclusion:

The velocity on the Jupiter is greater than root mean square speed for the O2,

  CO2 , H2 . Thus, these molecules will be found in Jupiter.

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