Given a turbo engine with a compression ratio of $9\mathrm{.}39$ into which air of mass $23$ kg$/$s$,$ temperature $9$ oC and pressure $91239$ Pa enters. Fuel with a calorific value of $42391$ kJ$/$kg enters the combustion chamber with a mass flow rate of $0\mathrm{.}53$ kg$/$s$.$ All processes are assumed to be tropic with variable specific heats and the work of the compressor equal to the work of the turbine. The effect on the velocity of the inlet diffuser is negligible. Calculate:

$1)$ The enthalpies before and after the combustion chamber

$2)$ the work of the compressor

$3)$ exhaust gas exit velocity