The total temperature rise in any stage depends on the square of the tangential mach number of the rotor.
θ t = 1 + ( γ − 1 ) M T 2 1 + ( γ − 1 ) M 1 2 2 {\displaystyle \theta _{t}=1+{\frac {(\gamma -1)M_{T}^{2}}{1+{\frac {(\gamma -1)M_{1}^{2}}{2}}}}}
general cascade analysis
stage velocity diagram