Concept explainers
(a)
To draw: The graph of the Maxwell speed distribution function versus speed with points at speed intervals of
(a)
Answer to Problem 62AP
The of the Maxwell speed distribution function versus speed with points at speed intervals of
Explanation of Solution
Introduction:
The Maxwell distribution curve is the graph between the distribution of speed and the change in speed or speed interval.
Given info: The number of molecules of oxygen in vessel is
Write the expression of Maxwell’s speed distribution function.
Here,
The mass of the molecules of oxygen is,
Here,
The molecular mass of the oxygen molecules in
Substitute
Substitute
Substitute the values of
|
|
0 | 0 |
100 | 1.64 |
200 | 5.86 |
300 | 10.88 |
400 | 14.78 |
500 | 16.33 |
600 | 15.39 |
700 | 12.7 |
800 | 9.31 |
900 | 6.13 |
1000 | 3.64 |
1100 | 1.961 |
1200 | 0.96 |
1300 | 0.43 |
1400 | 0.18 |
1500 | 0.07 |
On the basis of the table, a graph is plotted below;
(b)
The most probable speed from the graph.
(b)
Answer to Problem 62AP
The most probable speed is
Explanation of Solution
Given info: The number of molecules of oxygen in vessel is
The most probable speed occurs where
Conclusion:
Therefore, the most probable speed is
(c)
The average and rms speeds for the molecules and label these points on the graph.
(c)
Answer to Problem 62AP
The average and rms speeds for the molecules is
Explanation of Solution
Given info: The number of molecules of oxygen in vessel is
Write the expression of average velocity.
The mass of the molecules of oxygen is,
Substitute
The molecular mass of the oxygen molecules in
Substitute
Thus, the average speed is
Write the expression of rms velocity.
Substitute
Substitute
Thus, the rms velocity of the oxygen molecules is
The graph of Maxwell’s curve is shown below;
Figure (1)
The point
Conclusion:
Therefore, the average and rms speeds for the molecules is
(d)
The fraction of molecules with the speed in the range of
(d)
Answer to Problem 62AP
The fraction of molecules with the speed in the range of
Explanation of Solution
Given info: The number of molecules of oxygen in vessel is
The figure given below shows the Maxwell’s curve,
Figure 2
Write the expression of the fraction of molecules with the speed range from
Substitute
Conclusion:
Therefore, the fraction of molecules with the speed in the range of
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Chapter 21 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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