$4\mathrm{.}31$ Air enters an insulated diffuser operating at steady state with a pressure of $1$ bar $,$ a temperature of $300$ K $,$ and a velocity of $250\frac{m}{s}.$ At the exit, the pressure is $1\mathrm{.}13$ bar and the velocity is $140\frac{m}{s}.$ Potential energy effects can be neglected. Using the ideal gas model, determine

$($a$)$ the ratio of the exit flow area to the inlet flow area.

$($b$)$ the exit temperature, in K $.$