Question $5$:

Prove that for an isentropic flow between two states $1$ and $2$ through a duct,

T$2/$T$1=(1+($$-1)/2*$ M$1^2)/(1+($$-1)/2*$ M$2^2)$

where:

$*$ T$1$ and T$2$ are the stagnation temperatures at states $1$ and $2,$ respectively.

$*$ M$1$ and M$2$ are the Mach numbers at states $1$ and $2,$ respectively.

$*$ is the specific heat ratio of the gas.