Nitrogen gas enters a diffuser at $200$ kPa and $300\backslash$deg C with a velocity of $350$ m$/$s$,$

and leaves at $150$ kPa and $25$ m$/$s$.$ It is estimated that $20$ kJ$/$kg of heat is lost from

the diffuser to the surroundings at $100$ kPa and $27\backslash$deg C$.$ The exit area of the diffuser

is $0\mathrm{.}06$ m$2.$ Determine $($a$)$ the exit temperature, $($b$)$ the rate of exergy destruction,

and $($c$)$ the second$-$law efficiency of the diffuser.

$[$For Nitrogen, take R$=0\mathrm{.}297$ kJ$/$kg$.$K$,$ Cp $=1\mathrm{.}04$ kJ$/$kg$.$K$]$