In the kinetic theory of gases, the pressure exerted by an ideal gas on the walls of its container is proportional to which of the following molecular quantities?
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Correct answer
B. The average of the squared speeds of the molecules
Principle or equation
For an ideal gas, pressure is given by p = (1/3) (N m / V) v_rms^2, where v_rms is the root-mean-square speed, which is the square root of the mean of the squared speeds. Therefore, pressure is proportional to the average of the squared speeds.
Why this answer is correct
The kinetic theory derivation shows that the force exerted by molecules on a wall depends on the change in momentum per collision and the collision rate, both involving the square of the speed. Summing over all molecules yields the mean of the squared speeds. Thus, pressure is proportional to the average of the squared speeds, not the average speed or the square of the average speed.
Example
If the rms speed of gas molecules doubles, the pressure increases by a factor of 4, because pressure is proportional to the mean squared speed.
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