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If the RMS speed of a gas is 400 m/s at 300 K, what will be the RMS speed at 600

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Question: If the RMS speed of a gas is 400 m/s at 300 K, what will be the RMS speed at 600 K?

Options:

  1. 400 m/s
  2. 800 m/s
  3. 400√2 m/s
  4. 800√2 m/s

Correct Answer: 800 m/s

Solution: 

The RMS speed increases with the square root of the temperature. Therefore, at 600 K, the RMS speed will be 400 * sqrt(2), which is approximately 800 m/s.

If the RMS speed of a gas is 400 m/s at 300 K, what will be the RMS speed at 600

Practice Questions

Q1
If the RMS speed of a gas is 400 m/s at 300 K, what will be the RMS speed at 600 K?
  1. 400 m/s
  2. 800 m/s
  3. 400√2 m/s
  4. 800√2 m/s

Questions & Step-by-Step Solutions

If the RMS speed of a gas is 400 m/s at 300 K, what will be the RMS speed at 600 K?
  • Step 1: Understand that RMS speed (Root Mean Square speed) of a gas is related to its temperature.
  • Step 2: Know the formula that relates RMS speed to temperature: RMS speed is proportional to the square root of the temperature.
  • Step 3: Identify the initial RMS speed, which is 400 m/s at 300 K.
  • Step 4: Identify the new temperature, which is 600 K.
  • Step 5: Calculate the ratio of the new temperature to the old temperature: 600 K / 300 K = 2.
  • Step 6: Take the square root of this ratio: sqrt(2).
  • Step 7: Multiply the initial RMS speed by the square root of the temperature ratio: 400 m/s * sqrt(2).
  • Step 8: Calculate the final RMS speed: 400 * sqrt(2) is approximately 800 m/s.
  • RMS Speed and Temperature Relationship – The root mean square (RMS) speed of a gas is directly related to the square root of its absolute temperature, following the formula v_rms = sqrt(3kT/m), where k is the Boltzmann constant, T is the temperature, and m is the molar mass.
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