Problem $02\mathrm{.}061-$ Nitrogen flows through a heat exchanger steadily

Nitrogen enters a steady$-$flow heat exchanger at $150$kPa,$10C,$ and $88\frac{m}{s},$ and it receives heat in the amount of $120k\frac{J}{k}g$ as it flows through it$.$ Nitrogen leaves the heat exchanger at $100$kPa with a velocity of $180\frac{m}{s}.$ Determine the Mach number of the nitrogen at the inlet and the exit of the heat exchanger. The gas constant of $N_2$ is $R=0\mathrm{.}2968k\frac{J}{k}g*K.$ Its constant pressure specific heat and specific heat ratio at room temperature are $c_p=1\mathrm{.}040k\frac{J}{k}g*K$ and $k=1\mathrm{.}4.$

The Mach number of the nitrogen at the inlet of the heat exchanger is The Mach number of the nitrogen at the outlet of the heat exchanger is