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What is the root mean square speed of gas molecules directly proportional to?

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Question: What is the root mean square speed of gas molecules directly proportional to?

Options:

  1. The square root of the temperature.
  2. The square of the temperature.
  3. The mass of the gas molecules.
  4. The volume of the gas.

Correct Answer: The square root of the temperature.

Solution: 

The root mean square speed of gas molecules is directly proportional to the square root of the absolute temperature, as given by the equation v_rms = sqrt(3kT/m).

What is the root mean square speed of gas molecules directly proportional to?

Practice Questions

Q1
What is the root mean square speed of gas molecules directly proportional to?
  1. The square root of the temperature.
  2. The square of the temperature.
  3. The mass of the gas molecules.
  4. The volume of the gas.

Questions & Step-by-Step Solutions

What is the root mean square speed of gas molecules directly proportional to?
  • Step 1: Understand that the root mean square speed (v_rms) is a measure of the average speed of gas molecules.
  • Step 2: Know that temperature is a measure of how hot or cold something is, and in this case, we are using absolute temperature (T).
  • Step 3: Recognize that the equation v_rms = sqrt(3kT/m) shows the relationship between v_rms, temperature (T), and other constants (k and m).
  • Step 4: Identify that in the equation, the square root of the absolute temperature (sqrt(T)) is part of the formula for v_rms.
  • Step 5: Conclude that since v_rms is proportional to sqrt(T), it means that as the absolute temperature increases, the root mean square speed of gas molecules also increases.
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