# Find the total temperatures at the exit of the air intake and the compressor respectively.

A jet engine is operating at a Mach number of $$0.8$$ at an altitude of $$10 \;km$$.The efficiency of the air intake is $$0.8$$ and that of the compressor is $$0.87$$.What is the total temperature at the exit of the air intake and the compressor respectively ?(ambient pressure = $$26.5\; kPa$$; ambient temperature =$$223.3\; K$$; gas constant $$\gamma =1.4$$ ;$$P_{rc}=8$$)

Asked on 10th October 2019 in
Total temperature at the exit of the intake is given as $T_{01}=T_{amb}\left [ 1+\frac{\gamma-1}{2}M^{2} \right ] \\=223.3\times \left [ 1+0.2\times(0.8)^{2} \right ] \\=251.88\;K$
Total temperature at the exit of the compressor will be given as $T_{02}=T_{01}\times \left [ 1+\frac{1}{\eta _{c}}\left ( p_{rc}^{\frac{\gamma-1}{\gamma}}-1 \right ) \right ] \\\Rightarrow T_{02}=251.88\times\left [ 1+\frac{1}{0.87}\times\left ( 8^{\frac{0.4}{1.4}}-1 \right ) \right ] \\\Rightarrow T_{02}=486.80\;K$