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 $1k\frac{g}{s}.$

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$=100,000Pa$

Hint $2$: Treat air as ideal gas

Air's gas constant is $R=287\frac{J}{k}\frac{g}{K}$