Answer
$T_{2} = 490K$
$ c_{1}/c_{2} = 1.16$
Work Step by Step
Given that air temperature $T1= 200^oF = 659K$
Initial air pressure $P_{1} =170psi$
Final air pressure $ P_{2} = 60psi$
Specific heat ratio $k = 1.4$
As per the relation between P and T
$p_{1}/p_{2} = (T_{1}1/T_{2})^(k/(k-1))$
re-arranging
$(T_{1}1/T_{2}) =(p_{1}/p_{2})^((k-1)/k)$
we get
$T_{2} = T_{1}(p_{2}/p_{1})^((k-1)/k)$
Substituting the values we wil obtain
$T_{2} = 490K$
Initail speed $c_{1} = \sqrt(K_{1}RT_{1})$
Final speed $c_{2} = \sqrt(K_{2}RT_{2})$
$K_{1} =K_{2}$, since the air has ideal gas behavior.
So the ratio $c_{1}/c_{2} = \sqrt(KRT_{1})/\sqrt(KRT_{2})$
= $\sqrt(T_{1})/\sqrt(T_{2})$
substituting the values
$ c_{1}/c_{2} = 1.16$
