Problem Compressed air is stored in a $4-$m$^3$ rigid tank. The air's initial pressure and temperature are $10$ bar and $127$ C $.$ We open the tank$\text{'}$s valve to allow air discharge at a constant mass flow rate of $\backslash (1\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$

a$)$ Is this problem a steady state? $[2$ points$]$

b$)$ Compute air's initial density. $[3$ points$]$

c$)$ Compute the air's density inside the tank after $8$ seconds. $[20$ points$]$

$-$ Hint $1$: $1$ bar $=100,000$ Pa

$-$ Hint $2$: Treat air as ideal gas

$-$ Air's gas constant is $\backslash (\backslash$mathrm$\{$R$\}=287\backslash$mathrm$\{$~J$\}/\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$K$\}\backslash )$