Long answer·Hard exam skill (4/5)·No calculator
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Question
Use the kinetic theory model to obtain the pressure relation for an ideal gas in a cube of side . Consider molecules of mass and use the mean square speed in the final result.
Total: 5 marks
(a) Write the change in momentum when a molecule with velocity component elastically hits a wall perpendicular to the x-axis. (1 mark)
(b) Write the time between two successive hits of that molecule on the same wall. (1 mark)
(c) Find the force contribution of that molecule on the wall. (1 mark)
(d) Use isotropy to obtain . (2 marks)
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