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The average speed of gas molecules is given by the formula:

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Question: The average speed of gas molecules is given by the formula:

Options:

  1. (8kT/πm)^(1/2)
  2. (3kT/m)^(1/2)
  3. (2kT/m)^(1/2)
  4. (kT/m)^(1/2)

Correct Answer: (8kT/πm)^(1/2)

Solution: 

The average speed of gas molecules is given by the formula v_avg = (8kT/πm)^(1/2), where k is the Boltzmann constant, T is the temperature, and m is the mass of a gas molecule.

The average speed of gas molecules is given by the formula:

Practice Questions

Q1
The average speed of gas molecules is given by the formula:
  1. (8kT/πm)^(1/2)
  2. (3kT/m)^(1/2)
  3. (2kT/m)^(1/2)
  4. (kT/m)^(1/2)

Questions & Step-by-Step Solutions

The average speed of gas molecules is given by the formula:
  • Step 1: Understand that the average speed of gas molecules is represented by the symbol v_avg.
  • Step 2: Know that the formula for average speed is v_avg = (8kT/πm)^(1/2).
  • Step 3: Identify the variables in the formula: k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of a single gas molecule.
  • Step 4: Recognize that k, T, and m are needed to calculate the average speed of gas molecules.
  • Step 5: To find v_avg, you will first multiply 8 by the Boltzmann constant (k) and the temperature (T).
  • Step 6: Then, divide that result by π (approximately 3.14) multiplied by the mass (m) of the gas molecule.
  • Step 7: Finally, take the square root of the entire result to find the average speed (v_avg).
  • Average Speed of Gas Molecules – The average speed of gas molecules is derived from kinetic theory and depends on temperature and mass.
  • Boltzmann Constant – The Boltzmann constant relates the average kinetic energy of particles in a gas with the temperature of the gas.
  • Kinetic Theory of Gases – This theory explains the behavior of gases in terms of particles in constant motion and their collisions.
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