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If the RMS speed of a gas is 300 m/s, what is the RMS speed of the same gas at d

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Question: If the RMS speed of a gas is 300 m/s, what is the RMS speed of the same gas at double the temperature?

Options:

  1. 300 m/s
  2. 600 m/s
  3. 300√2 m/s
  4. 600√2 m/s

Correct Answer: 600 m/s

Solution: 

The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2). Therefore, the new RMS speed will be 300 * sqrt(2), which is approximately 600 m/s.

If the RMS speed of a gas is 300 m/s, what is the RMS speed of the same gas at d

Practice Questions

Q1
If the RMS speed of a gas is 300 m/s, what is the RMS speed of the same gas at double the temperature?
  1. 300 m/s
  2. 600 m/s
  3. 300√2 m/s
  4. 600√2 m/s

Questions & Step-by-Step Solutions

If the RMS speed of a gas is 300 m/s, what is the RMS speed of the same gas at double the temperature?
  • Step 1: Understand that RMS speed (Root Mean Square speed) of a gas is related to its temperature.
  • Step 2: Know that if the temperature of the gas is doubled, the RMS speed changes according to the formula: new RMS speed = old RMS speed * sqrt(new temperature / old temperature).
  • Step 3: Since the temperature is doubled, we can say new temperature / old temperature = 2.
  • Step 4: Therefore, the new RMS speed = old RMS speed * sqrt(2).
  • Step 5: Substitute the old RMS speed (300 m/s) into the equation: new RMS speed = 300 * sqrt(2).
  • Step 6: Calculate sqrt(2), which is approximately 1.414.
  • Step 7: Multiply 300 by 1.414 to find the new RMS speed: 300 * 1.414 = approximately 424.2 m/s.
  • 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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