The pressure of a gas and mean molecular kinetic energy

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Recall questions on The pressure of a gas and mean molecular kinetic energy.

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Questions from this subtopic

Each one with the model answer underneath.

1. 1

   State the kinetic theory expression for the pressure of an ideal gas, defining every symbol with its unit.

   Model answer

   pV = ⅓Nm⟨c²⟩, where p is pressure in Pa, V volume in m³, N the number of molecules, m the mass of one molecule in kg and ⟨c²⟩ the mean square molecular speed in m² s⁻².

2. 2

   Write the kinetic theory pressure equation in terms of the density of the gas.

   Model answer

   p = ⅓ρ⟨c²⟩, where ρ is the density of the gas in kg m⁻³. The density is the total molecular mass Nm divided by the volume V.

3. 3

   Outline how the motion of molecules gives rise to the pressure a gas exerts on its container.

   Model answer

   Molecules strike the container wall and rebound, and each collision changes the molecule's momentum. The rate of change of momentum of all the molecules striking a wall is the force on that wall, and the force divided by the wall area is the pressure.

4. 4

   Explain the origin of the factor of one third in the kinetic theory pressure equation.

   Model answer

   Molecular motion is random, so on average the mean square speed is shared equally between the three perpendicular directions. The mean square speed along any one axis is therefore one third of ⟨c²⟩.

5. 5

   What is meant by the mean square speed of the molecules of a gas?

   Model answer

   It is the average of the squares of the individual molecular speeds.

6. 6

   Define the root mean square speed.

   Model answer

   The root mean square speed is the square root of the mean square speed, written cᵣₘₛ = √⟨c²⟩ and measured in m s⁻¹.

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