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Reviewed CSCA Physics question · Easy

In a sample of an ideal gas at constant temperature, the root-mean-square speed of the molecules is v_rms. If the absolute temperature of the gas is increased by a factor of 4, what is the new root-mean-square speed?

  1. 2 v_rms
  2. 4 v_rms
  3. v_rms / 2
  4. 16 v_rms
Show the answer and explanation

Correct answer

A. 2 v_rms

Principle or equation

The root-mean-square speed of gas molecules is proportional to the square root of the absolute temperature: v_rms = sqrt(3kT/m).

Why this answer is correct

Since v_rms is proportional to sqrt(T), if T is multiplied by 4, v_rms is multiplied by sqrt(4) = 2.

Example

If v_rms = 500 m/s at 300 K, at 1200 K it becomes 1000 m/s.

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