 Solution

ID: past-exam-of-the-theoretical-mechanics-course-of-the-university-of-oxford/2010/b/4/a/iii/solution

Conservation of the parcel's entropy makes

p / ρ^{γ}

constant along its trajectory. Its initial value is

p_{0} / ρ_{0}^{γ}

, so

p = p_{0} (\frac{ρ}{ρ _{0}})^{γ} .

This is a relation following the specified parcel; parcels with different initial entropy can have different constants.

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