(a)
The average time before molecules reach in left half of the box.
(a)
Answer to Problem 26P
The average time before molecules reach in left half of the box is
Explanation of Solution
Given:
The number of molecules is
The volume of the box is
Formula used:
The expression for average time is given as,
Here,
Calculation:
The average time for
Conclusion:
Therefore, the average time before molecules reach in left half of the box is
(b)
The average time before molecules reach in left half of the box.
(b)
Answer to Problem 26P
The average time before molecules reach in left half of the box is
Explanation of Solution
Given:
The number of molecules is
Calculation:
The average time for
Conclusion:
Therefore, the average time before molecules reach in left half of the box is
(c)
The average time before molecules reach in left half of the box.
(c)
Answer to Problem 26P
The average time before molecules reach in left half of the box is
Explanation of Solution
Given:
The number of molecules is
Calculation:
The average time for
The conversion of
Substitution of the conversion in equation (a) can be given as,
Conclusion:
Therefore, the average time before molecules reach in left half of the box is
(d)
The average time before molecules reach in left half of the box.
(d)
Answer to Problem 26P
The average time before molecules reach in left half of the box is
Explanation of Solution
Given:
The number of molecules is
Calculation:
The average time for
The conversion of
Substitution of the conversion in equation (2) can be given as,
Conclusion:
Therefore, the average time before molecules reach in left half of the box is
(e)
The physicist waiting time before all of the gas molecules in the vacuum chamber occupy only the left half of chamber and comparison with expected lifetime of the universe.
(e)
Answer to Problem 26P
The average time is
Explanation of Solution
Given:
The pressure at which best vacuum created is
The expected lifetime of the universe is
Formula used:
The expression for the ideal gas is given as,
Here,
The expression for the comparison is given as,
Calculation:
The number of moles in vacuum condition at
On further solving the above equation,
The average time of molecules in vacuum to occupy left half of the chamber can be calculated as,
The conversion of
Substitution of the conversion in equation (2) can be given as,
The comparison can be given as,
Conclusion:
Therefore, the average time is
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Chapter 19 Solutions
Physics For Scientists And Engineers
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