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Reviewed CSCA Physics question · Standard

In the kinetic theory of gases, the pressure of an ideal gas is proportional to the average translational kinetic energy of the molecules and the number density. If the root-mean-square speed of the molecules is doubled while the number of molecules and the volume remain constant, what happens to the pressure of the gas?

  1. It becomes half as large.
  2. It becomes twice as large.
  3. It becomes four times as large.
  4. It remains the same.
Show the answer and explanation

Correct answer

C. It becomes four times as large.

Principle or equation

The pressure of an ideal gas is related to the average translational kinetic energy by P = (2/3)(N/V)K_avg, and K_avg = (1/2)m v_rms^2. Thus P is proportional to v_rms^2.

Why this answer is correct

Since N and V are constant, P ∝ K_avg ∝ v_rms^2. Doubling v_rms increases v_rms^2 by a factor of 4, so the pressure becomes four times as large.

Example

If v_rms is 300 m/s at pressure P, then at 600 m/s, v_rms^2 becomes (600/300)^2 = 4 times, so pressure becomes 4P.

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