Concept explainers
(i)
The factor by which the average kinetic energy of the molecules changes.
(i)
Answer to Problem 21.8OQ
Option (b), by a factor of
Explanation of Solution
Given info: The initial temperature of an ideal gas is
Formula to calculate the initial average kinetic energy of the gas molecules is,
Here,
Formula to calculate the final average kinetic energy of the gas molecules is,
Here,
Divide equation (2) by equation (1).
Substitute
Conclusion:
The average kinetic energy of the gas molecules increase by a factor of
The average kinetic energy of the gas molecules increase by a factor of
The average kinetic energy of the gas molecules increase by a factor
The average kinetic energy of the gas molecules increase by a factor of
The average kinetic energy of the gas molecules increase by a factor of
(ii)
The factor by which the rms speed of the gas molecules changes.
(ii)
Answer to Problem 21.8OQ
Option (c) a factor of
Explanation of Solution
Given info: The initial temperature of an ideal gas is
Formula to calculate the initial rms speed for the molecules of gas is,
Here,
Formula to calculate the final rms speed for the molecules of gas is,
Divide equation (5) by equation (4).
Substitute
Conclusion:
The rms speed of the gas molecules increase by a factor of
The rms speed of the gas molecules increase by a factor of
The rms speed of the gas molecules increase by a factor of
The rms speed of the gas molecules increase by a factor of
The rms speed of the gas molecules increase by a factor of
(iii)
The factor by which the average momentum changes.
(iii)
Answer to Problem 21.8OQ
Option (c) a factor of
Explanation of Solution
Given info: The initial temperature of an ideal gas is
Formula to calculate the initial average kinetic energy of the gas molecules is,
Here,
Formula to calculate the final average kinetic energy of the gas molecules is,
Here,
From equation (3), the relation between the final and average kinetic energy is given as,
Substitute
Formula to calculate the average momentum of a molecule is,
From the above equation the average momentum of a molecule that undergoes in a collision with particular wall is directly proportional to the average speed of a gas molecule. But from the equation (7), the final average speed of a gas molecule increases by a factor of
Conclusion:
The average momentum of a molecule is increase by a factor of
The average momentum of a molecule is increase by a factor of
The average momentum of a molecule is increase by a factor of
The average momentum of a molecule is increase by a factor of
The average momentum of a molecule is increase by a factor of
(iv)
The factor by which the rate of collision of molecules changes.
(iv)
Answer to Problem 21.8OQ
Option (c) a factor of
Explanation of Solution
Given info: The initial temperature of an ideal gas is
Formula to calculate the average rate of collision of molecules with the walls is,
From the above equation the time required for the collision of molecules is inversely proportional to the average speed of the gas molecules but from equation (7), the final average speed of a gas molecule increases by a factor of
Conclusion:
The rate of collision of molecules with walls change by a factor of
The rate of collision of molecules with walls change by a factor of
The rate of collision of molecules with walls change by a factor of
The rate of collision of molecules with walls change by a factor of
The rate of collision of molecules with walls change by a factor of
(v)
The factor by which the pressure of gas changes.
(v)
Answer to Problem 21.8OQ
Option (b) a factor of
Explanation of Solution
Given info: The initial temperature of an ideal gas is
Formula to calculate the pressure of
From the above pressure of gas is directly proportional to the average kinetic energy of the gas molecules but from equation (6), the final average kinetic energy of gas molecules increases by a factor of
Conclusion:
The pressure of gas change by a factor of
The pressure of gas change by a factor of
The pressure of gas change by a factor of
The pressure of gas change by a factor of
The pressure of gas change by a factor of
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Chapter 21 Solutions
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