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If the RMS speed of a gas is 500 m/s, what is the speed of the gas molecules in

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Question: If the RMS speed of a gas is 500 m/s, what is the speed of the gas molecules in terms of average speed?

Options:

  1. 500 m/s
  2. 250 m/s
  3. 400 m/s
  4. 600 m/s

Correct Answer: 400 m/s

Solution: 

The average speed of gas molecules is related to the RMS speed by the relation v_avg = (v_rms * sqrt(8/3)). Therefore, the average speed is approximately 400 m/s.

If the RMS speed of a gas is 500 m/s, what is the speed of the gas molecules in

Practice Questions

Q1
If the RMS speed of a gas is 500 m/s, what is the speed of the gas molecules in terms of average speed?
  1. 500 m/s
  2. 250 m/s
  3. 400 m/s
  4. 600 m/s

Questions & Step-by-Step Solutions

If the RMS speed of a gas is 500 m/s, what is the speed of the gas molecules in terms of average speed?
Correct Answer: 400 m/s
  • Step 1: Understand that RMS speed (v_rms) is given as 500 m/s.
  • Step 2: Know the formula that relates average speed (v_avg) to RMS speed: v_avg = v_rms * sqrt(8/3).
  • Step 3: Calculate the value of sqrt(8/3). This is approximately 1.632.
  • Step 4: Multiply the RMS speed (500 m/s) by the value from Step 3: 500 m/s * 1.632.
  • Step 5: Perform the multiplication: 500 * 1.632 = 816 m/s.
  • Step 6: Therefore, the average speed of the gas molecules is approximately 816 m/s.
  • RMS Speed vs Average Speed – Understanding the relationship between root mean square (RMS) speed and average speed of gas molecules.
  • Gas Kinetic Theory – Application of kinetic theory principles to derive relationships between different types of molecular speeds.
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