Edexcel A-Level Physics 9PH0
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Thermodynamics
The kinetic theory equation and its derivation
- 2 things to know
- Papers 2 and 3
Overview
Recall questions on pV = ⅓Nm⟨c²⟩ and what each symbol means, the four assumptions of the model, and the steps from one molecule in a cube to the pressure on a wall.
What you need to know
Answer each one before you reveal it.
How is pressure defined, and how does a molecule bouncing between the faces of a cube give rise to a force?
Questions from this subtopic
Each one with the model answer underneath.
- 1
State the kinetic theory equation relating the pressure and volume of a gas to the motion of its molecules:
Model answer
The equation is pV = ⅓Nm⟨c²⟩.
- 2
In pV = ⅓Nm⟨c²⟩, what do N, m and ⟨c²⟩ each represent?
Model answer
N is the number of molecules, m is the mass of one molecule and ⟨c²⟩ is the mean square speed of the molecules.
- 3
What four assumptions does the kinetic theory model of an ideal gas make?
Model answer
Molecules are in rapid random motion; their own volume is negligible compared with the volume of the container; all collisions are perfectly elastic; and there are no forces between molecules except during collisions.
- 4
State the equation that defines pressure in terms of force and area:
Model answer
Pressure is given by p = F/A, the force acting normally per unit area.
- 5
In the derivation, how does a single molecule bouncing off a wall give rise to a force?
Model answer
The molecule's momentum changes by 2mc, so by Newton's second law the rate of change of momentum is the force the wall exerts on the molecule; by Newton's third law the molecule exerts an equal and opposite force on the wall.
- 6
For a molecule moving between opposite faces of a cube of side l, what is the time between successive impacts on the same face?
Model answer
The molecule travels a distance 2l between impacts, so the time is 2l/c.
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