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A gas at 300 K has an RMS speed of 400 m/s. What will be its RMS speed at 600 K?

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Question: A gas at 300 K has an RMS speed of 400 m/s. What will be its RMS speed at 600 K?

Options:

  1. 400 m/s
  2. 400 sqrt(2) m/s
  3. 800 m/s
  4. 200 m/s

Correct Answer: 400 sqrt(2) m/s

Solution: 

The RMS speed is proportional to the square root of the temperature. Therefore, at 600 K, the RMS speed will be 400 * sqrt(600/300) = 400 * sqrt(2) m/s.

A gas at 300 K has an RMS speed of 400 m/s. What will be its RMS speed at 600 K?

Practice Questions

Q1
A gas at 300 K has an RMS speed of 400 m/s. What will be its RMS speed at 600 K?
  1. 400 m/s
  2. 400 sqrt(2) m/s
  3. 800 m/s
  4. 200 m/s

Questions & Step-by-Step Solutions

A gas at 300 K has an RMS speed of 400 m/s. What will be its RMS speed at 600 K?
Correct Answer: 565.69 m/s
  • Step 1: Understand that RMS speed (Root Mean Square speed) is related to temperature.
  • Step 2: Know that the RMS speed is proportional to the square root of the temperature.
  • Step 3: Identify the initial temperature (T1) which is 300 K and the final temperature (T2) which is 600 K.
  • Step 4: Calculate the ratio of the final temperature to the initial temperature: T2/T1 = 600 K / 300 K = 2.
  • Step 5: Take the square root of the ratio: sqrt(2).
  • Step 6: Multiply the initial RMS speed by the square root of the temperature ratio: 400 m/s * sqrt(2).
  • Step 7: This gives the new RMS speed at 600 K.
  • RMS Speed and Temperature Relationship – The root mean square (RMS) speed of a gas is directly proportional to the square root of its absolute temperature, as described by the equation v_rms = sqrt(3kT/m), where k is the Boltzmann constant, T is the temperature, and m is the mass of the gas particles.
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