Concept explainers
(a)
The gas having larger rms speed.
(a)
Answer to Problem 121P
The gas having larger rms speed is
Explanation of Solution
Given that the volume of nitrogen is
The average kinetic energy of the gaseous molecules in a container is proportional to the temperature. In the given situation, both the gases are at same temperature. Hence the average kinetic energy of both gases will be same.
Since the average kinetic energy is directly proportional to the mass of the molecule, the less massive molecule will have high rms speed in order to have same average kinetic energy.
Conclusion:
Among nitrogen and oxygen, nitrogen molecules are less massive. Thus, it will have larger rms speed than oxygen at same temperature.
Therefore, the gas having larger rms speed is
(b)
The temperature at which the oxygen gas will have same rms speed as nitrogen.
(b)
Answer to Problem 121P
The temperature at which the oxygen gas will have same rms speed as nitrogen is
Explanation of Solution
Given that the temperature of nitrogen gas is
Write the expression for the rms speed of a gas molecule.
Here,
Rewrite equation (I) for
Since the rms speeds are equal, equate the right hand sides of equations (II) and (III) and solve for
Conclusion:
Substitute
Therefore, the temperature at which the oxygen gas will have same rms speed as nitrogen is
(c)
The amount of heat that must flow into or out of the container of oxygen to change its temperature from
(c)
Answer to Problem 121P
Heat of
Explanation of Solution
Given that the volume of oxygen is
Write the expression for the molar specific heat at constant volume of an ideal diatomic gas.
Here,
Write the ideal gas law equation for the gas.
Here,
Solve equation (II) for
Write the expression for the heat energy required to change the temperature of the gas.
Here,
Use equation (I) and (III) in (IV) and expand the term
Here,
Conclusion:
Substitute
Therefore, heat of
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