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'Ideal Gases' printed from https://nrich.maths.org/
Why do this problem?
This problem will get students thinking about
the kinetic assumptions underlying ideal
gasses. The problem draws together many different types of
calculation, many involving non-standard estimations. Whilst there
are many calculations to perform, the key purpose is to provoke
thinking which will lead to an increased intuition of the natural
ideas underlying ideal gasses.
Possible approach
Some of the estimations are very difficult to perform with a
high degree of certainty, although it is possible to put reasonable
bounds on many of the quantities. The key point is the any
assumptions made in any estimation are clearly made. For example,
'Assuming that the molecule travels with the average velocity ...'
or 'Assuming that the molecule is moving perpendicularly to one of
the faces ...' are good assumptions for starting some
calculation.
Some students might feel uncomfortable with the lack of
precise, exact numerical answers to many of the parts or with the
fact that the problem will need standard data and equations sourced
from elsewhere. This is good, as it will help to develop the
independent thinking needed to succees with science and mathematics
at higher levels.
Key questions
What does your intuition tell you?
What assumptions have you made in each case?
Does your answer make numerical sense?
Possible extension
Extension is naturally built into this problem, as many parts
can be approached in a sophisticated fashion.
Possible support
Try the first few parts