A $0\mathrm{.}1m^3$ cylinder is evacuated and filled with $21kg$ of a gas containing $10$mole$\%N_{2}O$ and the balance $N_2.$ The gas temperature is $20C.$ Use the compressibility chart to solve the following problems:

$($a$)$ What is the gauge pressure of the cylinder gas after the tank is filled?

$($b$)$ A fire breaks out in the plant where the cylinder is kept, and the cylinder valve ruptures when the gas pressure reaches $4000$ psig. What was the gas temperature at the moment before the rupture occurred?