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 $p/{\rho }^{\gamma }$ constant along its trajectory. Its initial value is $p_0/{\rho }_0^{\gamma }$, soThis is a relation following the specified parcel; parcels with different initial entropy can have different constants.