Hot air flows through a duct with constant area maintained at a very low temperature. At the pipe entrance, the pressure, temperature and Mach number are $250$kPa, $350$ C$,$ and $0\mathrm{.}55$ respectively. The heat transfer from the air to the pipe walls is estimated to be $450$kJ$/$kg$.$ Find the pressure, temperature and Mach number at the outlet of the pipe. Assume air to be a perfect gas, the flow to be steady and neglect the effect of friction.