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Thermal Physics

Maxwell-Boltzmann distribution, Boltzmann constant and internal energy

  • 2 things to know
  • Papers 1, 2 and 3

Overview

Recall questions on the Maxwell-Boltzmann distribution and how temperature changes it, the Boltzmann constant, pV = NkT, deriving mean kinetic energy = 3/2kT, and the internal energy of an ideal gas.

What you need to know

Answer each one before you reveal it.

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Numbers

In deriving (1/2)m⟨c²⟩ = (3/2)kT, what is the first step using the equations pV = NkT and pV = (1/3)Nm⟨c²⟩?

Key term

What does the Maxwell-Boltzmann distribution describe?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Describe the shape of the Maxwell-Boltzmann distribution curve.

    Model answer

    It is asymmetric with a tail extending to high speeds

  2. 2

    In the Maxwell-Boltzmann distribution, how do the most probable speed, mean speed, and rms speed compare?

    Model answer

    The most probable speed is less than the mean speed, which is less than the rms speed

  3. 3

    State the equation relating the mean translational kinetic energy of a gas molecule to temperature.

    Model answer

    (1/2)m⟨c²⟩ = (3/2)kT, where m is the mass of a molecule, ⟨c²⟩ is the mean square speed, k is the Boltzmann constant, and T is absolute temperature

  4. 4

    Starting from kT = (1/3)m⟨c²⟩, what operation yields the final form of the mean kinetic energy equation?

    Model answer

    Multiply both sides by 3/2 to obtain (3/2)kT = (1/2)m⟨c²⟩

  5. 5

    What does the Maxwell-Boltzmann distribution describe?

    Model answer

    The spread (distribution) of molecular speeds in a gas

  6. 6

    How does the Maxwell-Boltzmann distribution change when the temperature of a gas increases?

    Model answer

    The distribution becomes broader and the peak shifts to higher speeds

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