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The average speed of gas molecules is given by which of the following formulas?

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Question: The average speed of gas molecules is given by which of the following formulas? (2023)

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)

Exam Year: 2023

Solution: 

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

The average speed of gas molecules is given by which of the following formulas?

Practice Questions

Q1
The average speed of gas molecules is given by which of the following formulas? (2023)
  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 which of the following formulas? (2023)
  • Step 1: Understand that we are looking for the average speed of gas molecules.
  • Step 2: Identify the formula that represents the average speed of gas molecules.
  • Step 3: The formula is v_avg = sqrt(8kT/πm).
  • Step 4: Recognize the variables in the formula: k is the Boltzmann constant, T is the temperature, and m is the mass of a molecule.
  • Step 5: Remember that this formula helps us calculate how fast gas molecules are moving on average.
  • Kinetic Theory of Gases – This concept explains the behavior of gas molecules in terms of their motion and interactions, leading to the derivation of average speed.
  • Boltzmann Constant – A fundamental physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas.
  • Temperature and Molecular Mass – Understanding how temperature affects the speed of gas molecules and how molecular mass influences their average speed.
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