As shown in the figure below, air enters the diffuser of a jet engine at $18$kPa,$T_1=250K$ with a velocity of $V_1=233\frac{m}{s},$ all data corresponding to high$-$altitude flight. The air flows adiabatically through the diffuser, decelerating to a velocity of $50\frac{m}{s}$ at the diffuser exit.

Assume steady$-$state operation, the ideal gas model for air, and negligible potential energy effects.

$($a$)$ Determine the temperature of the air at the exit of the diffuser, in $K.$

$($b$)$ If the air would undergo an isentropic process as it flows through the diffuser, determine the pressure of the air at the diffuser exit, in kPa $.$

$($c$)$ If friction were present, would the pressure of the air at the diffuser exit be greater than, less than, or equal to the value found in part $($b$)?$