Answer
a)
$c = 347 m/s$
$Ma =0.951$
b)
$ c = 537 m/s$
$Ma = 0.582$
Work Step by Step
a)
The gas const $R = 0.287 KJ/(KG.K)$
Specific heat ratio , $K =1.4$
we have
$ c = \sqrt (KRT)$
Substituting the values
$c = \sqrt(1.4 KJ/(KG.K) \times 0.287 KJ/(KG.K) \times 283K \times ((1000m2/s2)/(1KJ/Kg))$
on solving we get
$c = 347 m/s$
We have $Ma = v/c = (330 m/s)/(347 m/s) = 0.951$
b)
at $T = 800K$
we have$ c = \sqrt (KRT)$
Substituting the values
$ c = \sqrt(1.4 KJ/(KG.K) \times 0.287 KJ/(KG.K) \times 800K \times ((1000m2/s2)/(1KJ/Kg))$
on solving we get
$ c = 537 m/s$
We have $ Ma = v/c = (300 m/s)/(537 m/s) = 0.582$
