standard air $($ t $=20$ C & p $=1\mathrm{.}01325$ bar $)$ at a velocity of $13\mathrm{.}5$ m $/$ s is accelerated isentropically in a nozzle to a velocity of $223\mathrm{.}8$ m $/$ s $,$ determine the change in temperature $,$ pressure $,$ density and the change in stagnation temperature $.$